High School Science Part I

1

Measurement in Science and Technology We all make use of measurements in our daily life. A milkman measures milk, a shopkeeper measures rice or pulses, a farmer measures his field, a tailor measures the cloth before tailoring and so on. Everybody measures something or the other with different types of devices. It is seen that if we know what to measure and how to measure it, we can do many things well in life. Measurement is one of the basic life skills necessary for everyday life. It is also useful and essential in the learning of science and technology. There is a constant need for measurement in our everyday life. Let us find out little more about the process of measurement. What does this process of measurement involve? Which tools are used for accurate and precise measurement? On which factors are measurement techniques based? This lesson will make you aware of several such aspects of measurement. In this lesson you will study about different measurement systems including the ancient system of measurement and the SI units. You will also learn about the methods of measurement of various physical quantities like length, mass, time, area and volume. OBJECTIVES After completing this lesson, you will be able to: • cite examples of the uses of various parts of our body and senses to measure length; • state the limitations of the use of body parts and senses for measurement and justify the need for a standard to measure anything exactly; • describe the Indian and various other measurement systems used in the ancient times; • define a physical quantity with examples; • differentiate between fundamental and derived units; • write S.I. units of different fundamental physical quantities; • use multiples and submultiples of different units; • define the least count of a measuring instrument; • name the various devices and instruments used to measure length, mass and time stating the standard in each case; • measure area of regular and irregular figures; • measure volume of regular and irregular solids.

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1.1 HISTORICAL BACKGROUND OF MEASUREMENT 1.1.1 Body parts and senses used for measurement Since ancient times, people used their senses and body parts to measure various things. They did this because it became necessary for them in their daily life to deal with other people. Let us find out how senses and body parts help us in measurement. (a) Use of our body parts and senses for measurement We have five senses, which help us to find out about the things around us. These senses are seeing, hearing, smelling, tasting and touching. For example, if we see a tall and a short building or a tall and short person we can feel the difference in their heights. Similarly, if we touch a body we can feel the hotness or coldness of the body. Thus, our senses do help us to guess or estimate the height, length and hotness or coldness of a body and other things around us. Here, estimation means a rough measurement made by our senses. (b) Use of body parts for measurement In ancient days, long before measuring instruments were invented, people actually used different parts of their body to measure length. Figure 1.1 shows various parts of our body, which were used and can still be used to carry out various measurements. But since these measurements are dependent on the size of the person, they may vary from person to person. The length of the cubit, for example, depends on the arm length of the measurer. Thus, cubits had different lengths. To have a better understanding, let us perform an activity.

Thumb

Han

d

First finger Hand span

Fig. 1.1 Use of body parts for measurement

ACTIVITY 1.1 Aim : To understand the accuracy in the use of body parts for measurement. What is required? A ruler, a measuring tape. What to do? ! With the help of a ruler, measure the length of various parts of your body like the arm or the palm, which are normally used for measurement. ! Repeat the measurements for your friend or for a younger brother and sister also. You can use a measuring tape also for this activity. ! Compare the measurements. What do you observe? You will find that there is a difference in the measurement of your body parts with those of your friends.

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(c) Limitations of our senses and body parts Though we use our senses and body parts for various measurements, we cannot trust them to measure exactly and accurately. Can you depend on your eyes to judge accurately the height or lengths of different objects? Look at figure 1.2a. Which circle is larger-A or B? Well, both are of the same size. Larger circles around the central one make it appear smaller. Small circles around the central circle make the other appear larger.

(b) Estimating the length of a line segment

A

B

(a) Estimating the size of the circle

Fig. 1.2 Limitations of our senses and body parts in measurement

There are many more such instances where objects can fool our eyes. Now look at figure 1.2b and tell which line segment is larger. Verify your estimation by measuring each line segment with the help of a scale. In the above mentioned cases we tried to guess the length or size by seeing i.e. tried to give an estimate, which may or may not be correct. Thus, the use of senses or body parts for measurement does not provide accuracy of measurement, ! reliability of measurement, ! uniformity of measurement, The limitations of the use of senses and body parts have made us to develop some devices and instruments for accurate measurements. !

1.1.2 Indian measurement system a) Indian measurement system in the ancient period Measurement plays an important role in our lives. We have been using measurement right from the pre-historic time. Let us have a brief look into the historical development of measurement system in India. In ancient periods, the lengths of the shadows of trees or other objects were used to know the approximate time of the day. Long time durations were expressed in terms of the lunar cycles, which even now is the basis of some calendars. In India, excellent examples of measurement practices in different historic periods are available. Our ancient literature reveals that in India different types of measurement practices were followed in different periods. For example, about 5000 years ago in the ‘Mohenjodaro era’, the size of bricks all over the region was same. The length, breadth and width of bricks were taken as a standard and were always in ratios of 4:2:1. Similarly around 2400 years ago during the Chandragupta Maurya period there was a well-defined system of weights and measures. The government at that time ensured that everybody used the same weights and measures. According to this system, the smallest unit of length was 1 Parmanu. Small lengths were measured in anguls. For long distances Yojana was used. One yojana is roughly equal to 10 kilometres.

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The Indian medicine system, Ayurveda, also had well-defined units for the measurement of the mass and volume. The measurement system was strongly followed to ensure the proper quantity of medicine for particular disease. Different units of measurements used in the period of Chandragupta Maurya 8 Parmanus = 1 Rajahkan (dust particle from the wheel of a chariot) 8 Rajahkans = 1 Liksha (egg of lice) 8 Likshas = 1 Yookamadhya 8 Yookamadhyas = 1 Yavamadhya 8 Yavamadhyas = 1 Angul 8 Anguls = 1 Dhanurmushti (Reference: Kautilaya’s Arthashastra)

b) Indian measurement system in the medieval period In the medieval period also the measurement system was in practice. As described in Aini-Akbari by Abul Fazl-i-Allami, during the period of Moghul Emperor Akbar, the gaz was used as the unit of measuring length. Each gaz was divided into 24 equal parts and each part was called Tassuj. This system was extensively used to measure land pieces, for construction of buildings, houses, wells, gardens and roads. You should know that, the gaz was widely used as a unit of length till the metric system was introduced in 1956. Even today in many parts of our country, particularly in the rural areas, gaz is being used as a unit of length. c) Indian measurement system during British period In order to bring about uniformity in the system of measurement and the weights used, a number of efforts were made during the British period. The British rulers wanted to connect Indian weights and measures to those being used in Great Britain at that time. During this period the inch, foot, and yard were used to measure length whereas grain, ounce, pounds, etc. were used to measure mass. These units and weights were used in India till the time of Independence in 1947. The essential units of mass used in India included Ratti, Masha, Tola, Chhatank, Seer and Maund. Raatti is a red seed whose mass is approximately 120 mg. It was widely used by goldsmiths and by practitioners of traditional medicine system in India. Relation between various units of mass used during the British period 8 Ratti 12 Masha 5 Tola 16 Chhatank 40 Seer 1 Maund CHECK YOUR PROGRESS 1.1

= = = = = =

1 Masha 1 Tola 1 Chhatank 1 Seer 1 Maund 100 Pounds troy (exact)

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1. Name the smallest unit of length during the Chandragupta Maurya period. 2. List out our body parts normally used for measurement. 3. In which period was ‘gaz’ used as a unit to measure length? 1.2 THE MODERN MEASUREMENT SYSTEM In order to overcome the limitations of senses and body parts, and to bring about a worldwide uniformity in the measurement system, the need for exact measurement was felt. For this, a standard of measurements had to be developed which everybody everywhere accepts. The problem of measuring lengths exactly was first solved by the Egyptians in 3000B.C. They did this by inventing the standard cubit. They realized that the length of the arm actually did not matter as long as people of Egypt were concerned. Then they made measuring sticks exactly of the same length as that of standard cubit. In this way they made sure that the cubit was the same length all over Egypt. That is really how measurement is carried out today. In fact, for each measurement a standard is chosen. Every measuring instrument has to be compared with that standard. The present measurement system, which is accepted world-over, has its origin in the French Revolution. You will study the details of the modern system of measurement, in the following sections. 1.2.1 Fundamental quantities and units You have read that measurements are concerned with quantities like length, mass, time, density etc. Any quantity which can be measured is called a physical quantity. Out of the different physical quantities, there are seven physical quantities in terms of which other physical quantities can be measured. These fundamental physical quantities are length, mass, time, electric current, temperature, luminous intensity and amount of substance. Such quantities are considered to be the basic or fundamental physical quantities. If you are asked to measure the quantity of a given amount of milk, you will express the volume of milk in some accepted units of volume. Likewise, if an engineer measures the length of a road that connects two cities, he should express the distance in an accepted unit of length. Such a procedure makes life more comfortable. If there were no common units accepted by all, life would be miserable. Such units are much more essential in scientific measurements to facilitate communication of information at international level. Any measurement of a quantity includes a reference standard or unit in which the quantity is measured and the number of times the quantity contains that unit. Thus, when we say that the length of a rod is 4 metres, the rod is four times the metre, which is the unit of length. Metre is the standard length that is adopted as a standard for comparison while measuring length. In the process of measurement the accepted reference standard which is used for comparison of a given quantity is called a unit. 1.2.2 The SI units Scientists have developed and used several systems for expressing the units of physical quantities. However, all measurements in any system are based on the units of the basic or fundamental physical quantities. The units of the fundamental or basic quantities that are independent of each other are called fundamental units.

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Keeping in view the importance of the proper units for measurement, there have been attempts over centuries in several developed civilizations to suggest standard units of measurements at international level. In the year 1967, the XIII General Conference on Weights and Measures rationalised the MKSA (Metre, Kilogram, Second, Ampere) system of units and adopted a system based on six basic units. It was called the Systeme Internationale de unites known as SI units in all languages. In 1971, the General Conference added another basic unit to the SI units i.e., mole for the amount of substance. The fundamental units in different systems are different. The international system of units, known as SI units, are commonly used for all scientific purposes. This system has seven basic units for seven physical quantities, which are given in Table 1.1. Table 1.1: SI units and their symbols Physical quantity

Unit

Length Mass Time Temperature Amount of substance Electric current Luminous intensity

metre kilogram second kelvin mole ampere candela

Symbol m kg s K mol A cd

Perhaps you may be confused by mass and amount of substance and also with luminous intensity as given in Table 1.1. The mass of a body is the amount of matter contained in the body, while a mole is the amount of any substance equal to its molecular mass. 1 mole of HCl = 36.46 g 2 moles of HCl = 36.46 x 2 = 72.92 g Luminous intensity is the amount of light emitted by a point source per second in a particular direction. The yard and mile as units of length are still in use in USA. Units of length still in use in USA 1 mile = 8 furlongs 1 furlong = 220 yards 1 yard = 3 feet 1 foot = 12 inches 1 yard = 0.9144 m (exactly) 1 inch = 2.54 cm (exactly) 1 mile = 1.61 km The guiding principle in choosing a unit of measurement is to relate it to common man’s life as far as possible. As an example, take the unit of mass as kilogram or the unit of

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length as metre. In our day-to-day business we buy food articles in kg or tens of kg. We buy cloth in metres or tens of metres. If gram had been chosen as the unit of mass or millimetre as unit of length, we would be unnecessarily using big numbers in our daily life. It is for this reason that the basic units of measurements are very closely related to our daily life. 1.2.3 Standard units of fundamental quantities Once we have chosen the fundamental units of the SI, we must decide on the set of standards for the fundamental quantities. a) Mass: The SI unit of mass is kilogram. One kilogram is the mass of a particular cylinder made of Platinum–Iridium alloy, kept at the International Bureau of Weights and Measures in France. This standard was established in 1887 and there has been no change because this is an unusually stable alloy. Prototype kilograms have been made out of this alloy and distributed to member states. The national prototype of India is the Kilogram no 57. This is preserved at the National Physical Laboratory, New Delhi. b) Length: The SI unit of length is metre. Earlier the metre (also written as meter) was defined to be 1/107 times the distance from the Equator to the North Pole through Paris. This standard was abandoned for practical reasons. In 1875, the new metre was defined as the distance between two lines on a Platinum-Iridium bar stored under controlled conditions. Such standards had to be kept under severe controlled conditions. Even then their safety against natural disasters is not guaranteed, and their accuracy is also limited for the present requirements of science and technology. In 1983 the metre was redefined as the distance travelled by light in vacuum in a time interval of 1/ 299792458 seconds. This definition establishes that the speed of light in vacuum is 299792458 metres per second. c) Time: The SI unit of time is second. The time interval second was originally defined in terms of the time of rotation of earth about its own axis. This time of rotation is divided in 24 parts, each part is called an hour. An hour is divided into 60 minutes and each minute is subdivided into 60 seconds. Thus, one second is equal to 1/86400th part of the solar day. But it is known that the rotation of the earth varies substantially with time and therefore, the length of a day is a variable quantity, may be very slowly varying. The XIII General Conference on Weights and Measures in 1967 defined one second as the time required for Cesium–133 atom to undergo 9192631770 vibrations. The definition has its roots in a device, which is named as the atomic clock. d) Temperature: The SI unit of temperature is kelvin (K). The thermodynamic scale on which temperature is measured has its zero at absolute zero, and has its lower fixed point corresponding to 273.15 K at the triple point of water (0o C). One unit of thermodynamic temperature (1K) is equal to 1/273.15 of the thermodynamic temperature of the triple point of water. e) Electric current: The SI unit of electric current is the ampere (A). One ampere is defined as the magnitude of current that when flowing through two long parallel wires, each of length equal to 1 m, separated by 1 metre in free space, results in a force of 2 x 10-7 N between the two wires. f) Amount of substance: The SI unit of amount is mole (mol). One mole is defined as

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the amount of any substance, which contains, as may elementary units, as there are atoms in exactly 0.012 kg of C-12. g) Luminous intensity: The SI unit of luminous intensity (I) is candela (Cd). The candela is defined as the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity of 1/683 watt per steradian in that direction. 1.2.4 Derived units The basic units or the fundamental units are independent of each other. The units of all other physical quantities can be expressed in terms of these basic units. Such units are called derived units. Thus, the units, which are obtained by the combination of fundamental units, are known as derived units. For example, area can be expressed in terms of the basic unit of length, as given below: You know the area of a surface is the product of length and breadth. Therefore, the unit of area will be equal to the product of the unit of length and the unit of breadth (remember that breadth is also length). Unit of area = metre x metre = (metre)2 Thus, the unit of area is m2. Similarly, volume is equal to length x breadth x height of the object. Therefore, the unit of volume = unit of length x unit of breadth x unit of height = metre x metre x metre = (metre)3 Thus, the unit of volume is m3. The derived units of other physical quantities are also found in the same way. Some of the commonly used derived units are given in Table 1.2. Table 1.2 : SI units and symbols of some derived units Physical quantity Area Volume Density Velocity Acceleration Force Work

SI Unit

Symbol

square metre cubic metre kilogram per cubic metre metre per second metre per square second kilogram metre per square second (also called Newton) kilogram square metre per square second (also called Joule)

m2 m3 kg/m3 m/s m/s2 kg m/s2 (called N) kg m2/s2 (called J)

There are some other commonly used derived units with special names. They are given in the Table 1.3. Table 1.3: Some commonly used derived units

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Physical quantity Force Pressure Energy Power

Special name Newton Pascal joule watt

Symbol N Pa J W

SI Unit kg m/s2 N/m2 Nm J/s

1.2.5 Multiples and sub-multiples of units Sometimes the measurement of physical quantities can give very large or very small numbers. The smaller and larger units of the basic units are multiples of ten only. They strictly follow the decimal system. These multiples or submultiples are given special names. These are listed in Table 1.4. For example, the mass of the earth and mass of the electron are found to be as follows: Mass of earth (M)

=

5,970,000,000,000,000,000,000,000 kg

Mass of an electron (me)

=

0.000,000,000,000,000,000,000,911 kg

You will notice that it is not a convenient way to express the mass of earth or the mass of an electron. It takes up space and time to read it. Thus, for convenience, large numbers or very small decimals are expressed in an abbreviated form. The abbreviations in common use are based upon the powers of ten as given in the Table 1.4. Table 1.4: Representation of large and small quantities in powers of ten Large quantities

Small quantities

100 = 1 10 = 101 100 = 102 1,000 = 103 10,000 = 104 100,000 = 105 1,000,000 = 106

1 = 100 0.1 = 10–1 0.01 = 10–2 0.001 = 10–3 0.0001 = 10-4 0.00001 = 10–5 0.000001 = 10-6

Thus, 103 = 10 ×10 × 10 = 1000 1 1 = = 0.001 3 10 1000 Example 1.1: Suppose a large ship has a mass of nine hundred thousand kilograms. Express it in powers of ten. Solution: Given, mass of ship = 900,000 kg Thus, in powers of ten, the mass of ship = 9 × 105 kg Example 1.2: Express the number 0.00034 in terms of powers of ten. Solution: 0.00034 = 3.4 × 10 – 4 This concept has been used to express multiples and submultiples of basic units of −3 and, 10 =

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measurement – again for the purpose of convenience. For example, let us take the SI unit of length, i.e. metre. Its multiples and submultiples would be: Multiple 1000 metres = 1 kilometre or 103 m = 1 km

Sub-multiple 1/1000 metres = 1 millimetre or 10–3 m = 1 mm

As the metric system uses the base 10, the change from one unit to the another is very easy and it uses simple prefixes to denote multiples or submultiples of the basic units. For example, prefix kilo always means 1000 whether it is kilometre (1000 m) or kilogram (1000 g), kilowatt (1000 W) or whatever. Similarly, the prefix centi always means 1/100 while the prefix milli always denotes 1/1000. A list of prefixes for multiples and submultiples is given in Table 1.5. Table 1.5: Prefixes for multiples and submultiples Name

Symbol

Equivalent

deca hecta kilo mega giga terra deci centi milli micro nano pico

da h k M G T d c m µ n p

101 102 103 106 109 1012 10–1 10–2 10–3 10–6 10–9 10–12

CHECK YOUR PROGRESS 1.2 1. What are the characteristics of a physical quantity? 2. Differentiate between fundamental and derived units. 3. What is the difference between mass and amount of a substance? 4. Derive the unit of the following quantities: (i) Force = Mass × acceleration (ii) Pressure = Force/Area 5. Represent 237 nm in metres. 1.3 MEASUREMENT OF QUANTITIES We use measurements of different types in our daily life. For example, while buying cloth, we measure its length and while buying milk or kerosene we measure its volume. But for accurate and precise measurement, we have to follow certain methods. Let us study some of them. Let us consider a physical quantity, say length. We know that its standard of measurement is metre. Measuring sticks with the same length as the standard metre have been made which we commonly call as the metre stick. This one metre long stick is divided into 100 equal parts, i.e. into 100 centimetres. Each centimetre is further divided into 10 millimetres. Thus, the smallest division on a metre scale is 1 millimetre. This is the least count of the

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metre scale. Thus, the minimum or the least quantity that can be measured by a given instrument is called its least count. For example, the least count of a metre scale is 1 mm or 0.1 cm. A metre scale cannot measure lengths less than 1mm. The least count of any measuring instrument is, thus, very important. We must always quote the result of a measurement only up to the least count of the measuring instrument used. Besides, the method and the selection of proper measuring device for a particular measurement are also very important. 1.4.1 Length and its measurement As we have studied in the last section, length is the distance between two points and it is measured in terms of metres. Different types of devices are used to measure lengths. For example to measure the length of your table, you will use a ruler or measuring tape. But to measure the diameter (thickness) of a wire, you will require a screw gauge. These devices had been made by comparing them with a standard length called standard metre. The standard metre is a fixed length decided by scientists and accepted by all. a) Using a scale to measure length To measure the length of a given line segment AB (Fig 1.3), the metre scale is kept along the line segment with its graduations parallel to it. The metre scale must be so placed that its divisions are as close as possible to the line segment to be measured. Its zero end is made coincident with one end of the line segment. Note the point where the other end of the line segment lies. Suppose, it lies beyond the 2 cm mark and is coincident with the second small division after it. Since each of these marks is 1 mm, the total length of the line segment is 2 cm + 2 mm = 2 cm + 0.2 cm = 2.2 cm A

B 1

2

3

4

5

6

7

8

9

10

11

12

Fig. 1.3 To measure the length of a line segment using a metre scale

Remember that while looking at the reading on a scale, we must keep our eyes in front of and in line with the reading to be taken. In case of a metre scale, it is not always possible to make the zero mark on the scale coincident with one end of the line to be measured. With repeated use, the ends of measuring scale get somewhat worn-out and ill defined. In such cases, we keep the metre-scale with any of its divisions other than zero coincident with one end of the line. Suppose we place the scale (ruler) in such a way that the two ends of the line segment coincides with 2.0 cm and 4.2 cm marks, respectively (Fig 1.4). Then, the length of the line segment is 4.2 cm – 2.0 cm = 2.2 cm That is, it is the difference between the readings on a scale at its two ends. A 1

2

B 3

4

5

6

7

8

9

10

11

12

Fig. 1.4 The length of a line segment is the difference between the readings on a scale at its two ends.

If we have to measure a larger length, such as length of a playground, we use a measuring

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tape that may be 10 m, 15 m or 50 m long. Sometimes, we are required to measure very small lengths, say (less than 1 mm) like the diameter of a thin wire, the dimensions of fine machine parts, etc. We cannot use a metre scale for such measurements. For such distances, measuring instruments like the vernier callipers and the screw gauge are used. Vernier callipers, as shown in Fig 1.5, is an instrument used to measure the length or thickness of a solid body up to 0.01 cm accurately. A screw gauge as shown is Fig. 1.6, is an instrument used to measure the length or thickness of a solid body up to 0.001 cm. accurately However, each measuring instrument is limited to a certain accuracy of measurement which depends on its graduation. To measure the thickness of a wire or a metallic sheet we require screw gauge. N A A

C

E

D

B 0

B

5

20 15 10 9

G Q

D

Fig.1.5 Vernier callipers

Fig.1.6 Screw gauge

To measure large distances like the distance of your school from your house, or distance between two cities or the distance between the earth and moon, we use indirect methods of measurement. For example, to measure the distance between two cities, we will measure the average speed of certain vehicle, say a car, and the time taken by it to cover that distance. The product of the speed and time will give the required distance. 1.3.2 Mass and its measurement Like length there are many other measurements, which we make in our daily life by using different measuring standards and instruments. For any object, say this book, if some body asks you to answer the question, “How much stuff is there in it”? It means he is trying to find out the mass of the object. As you have studied earlier in this lesson, mass of a body is defined as the amount of matter contained in the body. The standard mass chosen by the scientists is called kilogram. This standard is used to compare the masses of unknown bodies. In order to measure the mass of different bodies different types of balances or scales are used. The most common is the one we see with the shopkeepers and vendors. What standard masses are used by shopkeepers to measure quantities? What do their balance look like? Have you seen a balance like the one in figure 1.7(a) or 1.7(b).

Sugar 1 Kg

(a) ACTIVITY 1.2 Fig. 1.7 (a) The shopkeeper’s balance (b) A modern balance

(b)

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Aim : To make a sensitive balance to compare the masses of light objects. What is required? A tall bottle like a squash bottle or an oil bottle, two square pieces having each side about 15 cm in length cut from a sheet of a chart paper, a few drinking straws, pins, sewing thread, gum, plasticine (or wet atta) What to do? !

Use the square papers to make pans as shown in Fig.1.8.

!

Draw a small square at a distance of 2 cm from the edges.

!

Fold the paper along the outline of the inner square. Fold again along dotted lines and fix the paper to outer side of the scale pan with gum. Pass lengths of sewing thread through the centre of the four sides. Make a knot so that four stands are of the same length. Measure the drinking straw and find its mid-point. Pass a pin through this point. Balance the pin on a piece of small rubber (eraser) which is glued or fixed with cello tape to the bottle cap. Tie the pans near the two ends of the straw in such a way that they are at equal distances from the mid-point, i.e. the pin. Check to see if they are balanced, otherwise use little bits of atta or plasticine on the pans. This balance can be used to compare the weights of small objects like paper clips and buttons. Try and find out the amount of water loss when leaves dry up by weighing them when green and drying them on a hot plate and re-weighing.

!

!

! !

!

!

!

!

Pin Stapil

Straw

PanFig.

Pan 1.8 Method to make a sensitive balance

A shopkeeper’s balance, however, does not provide accurate measurement of masses that is needed. In some cases, for example, to find the mass of a piece of gold or the

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composition of chemicals required to make aspirin, etc. For accurate measurement of masses a physical balance is used. Figure 1.9 shows a physical balance. Known masses from a standard box are used with this balance.

Fig. 1.9 A physical balance

1.3.3 Time and its measurement Time is measured when you answer questions like, how long does it take to reach Delhi from Bombay? How long do the fruits last? When does the school start? All these questions relate to happenings of two events with a gap between them. For example, if someone says, “It took me 17 hours to travel by train from Delhi to Bombay”, she is thinking of a measurement of the time interval between a first event (i.e. leaving Delhi) and a second event (i.e. arriving Bombay). She may have measured this interval which is a time interval by looking at her watch when she departed and when she arrived. Thus, when we measure time we measure the interval of time between two events. Sundial Long long ago, people noticed that shadows were long in the morning and evening, and were the shortest when the sun was directly overhead at noon. From these observations they learnt to tell the hour of the day. Based on it, the world’s first timepiece – the sundial was made. The sundial was a hemispherical opening in a block of stone or wood. It had an upright rod, called gnamon fixed in the center of the opening (Fig. 1.10). The shadow of the gnamon travelled over the day, telling the time of the day. But the sundial had certain limitations. Can you think of them?

Fig. 1.10 A sundial

Time is measured in seconds (s), minutes (m), hours and days with stop watches and clocks. Our early ancestors used the alternation of the day and night as a clock. They did

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this because this phenomenon repeats itself at regular intervals of time. As such, they considered this as a standard with which they used to compare an unknown time interval. Such a system, which repeats itself at regular intervals of time, is called periodic system. The measurement of time is really the comparison of an unknown time interval with the standard time interval of a periodic system. Based on this, instruments like sundials, water and sand clocks were used in early times to measure time intervals. In fact, water clock was the ancestor of our mechanical clocks. Let us perform an activity to understand the working of a water clock. ACTIVITY 1.3 Aim : To use a water clock to measure your pulse or your friend’s pulse What is required? Water, beaker, a paper cup and a pin What to do? ! With the help of a pin make a very small hole in the bottom of the cup. ! Place your finger over the hole and fill the cup with water. ! Hold the cup over a sink or a larger beaker and remove your finger from the hole. The water should drip from the hole and you should be able to count the drops easily. If water runs out instead of dripping, get another cup and try to make a smaller hole. ! After preparing the water clock (Fig. 1.11), use your middle finger and lightly feel your pulse. ! You start counting your pulse, you tell your friend to start counting the drops from the cup at the same time. Both of you have to start and stop at the same time. ! Record the time taken by the heart to beat 15 times in terms of ‘drops’. ! Repeat this with your friend. Is there a difference in the pulse rate between you and your friend?

Fig. 1.11 Working of a water clock

These clocks of early times however, were inconvenient to use because the sundial could not be moved form one place to another place and sand and water clocks had to be attended regularly. The real advancement in the construction of clocks came with the introduction of the pendulum. Let us see how pendulum helped us in measuring time. The pendulum—A tool to measure time

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Tie a small stone to one end of a long can be used as a string and hang it with the help of the other end to a firm support. This may be used as simple pendulum. Pull t h e stone gently to one side and let it go. The stone begins t o C B A move to and fro, i.e. oscillates (Fig. 1.12). Make sure that it Stone does not move in circles. When the pendulum was at rest, it was at A. This Fig. 1.12 A simple pendulum position is called the mean position. When it swings, it moves form A to B, back to A, from A to C and back to A. In this way it completes one full swing. Each swing is called one oscillation. The distance from A to B or from A to C is called amplitude of the oscillation. Amplitude of a pendulum is the maximum distance the pendulum moves away from the mean position while it is oscillating. The time taken for one oscillation is called the time period of the pendulum. Once your pendulum has started swinging steadily you can use your stopwatch or a wristwatch with seconds hand to find out your pendulum’s time period. For this, you may count how long your pendulum takes to make 20 oscillations and then from it, the time for one oscillation can be calculated. Pendulum clock The pendulum was used as a time controller in clocks. 1656, Christian Huygens, a Dutch scientist, made first pendulum clock, which was regulated by a mechanism using a ‘natural’ period of oscillation. Although, Galileo had invented the pendulum and noticed that the time taken by the weights hanging from a chain or rod to swing back and forth is exactly same amount of time. The whole system was enclosed in a case and thus became the grandfather clock. The length of pendulum and the acceleration to gravity at a place determined the time taken inFig. 1.13 A pendulum clock oscillation.

I n the

the

due one

Though with the discovery of pendulum clocks, time keeping became almost accurate, but it had certain limitations like acquiring large space, and difficulty in movement from one place to the other. Therefore, spring watches were discovered. Such watches have a flat steel-bound spring, which is coiled tight by winding the spring. As the time passes the spring uncoils moving the hour and minutes hands attached to it. Thus, it tells us the time. With the advancement of science and technology and to meet the need of more accurate time measurement, quartz clocks and atomic clocks came into existence.

(a) Stop Watch

(b) Electronic Watch

(c) Quartz Clock

Measurement in Science and Technology : 19 : Fig. 1.14 Different types of clocks

Quartz clocks Quartz clocks came into existence in 1929 when quarts crystal rings were used in the mechanical clock. But they became popular in 1970. The rings were connected to an electrode in a circuit. When a current is passed through the circuit, the crystal vibrates at a regular frequency. This helps us to measure time. The quartz clocks lose one second in every 10 years. CHECK YOUR PROGRESS 1.3 1. You are given some words like pans, beam, pointer, weights, objects. Use these words to fill up blanks in the following paragraph, which gives a general description of a balance. “A balance has two_____________supported from a rigid_____________ At the center of the support there is a _____________which is free to move. In one pan the _____________to be measured are placed. In the other pan _____________ are placed one by one to balance both the pans. 2. Estimate the length of this page of your book in the following ways: (i) by just looking at it (i.e., seeing) (ii) with the help of your fingers (iii) by using your ruler (in cm) 3. Why were the clocks of early times inconvenient to use? 1.4 MEASUREMENT OF AREA The concept of area finds considerable use in our day to day life. For example, we have to consider the area of the top of the table while buying glass or mica for it. Similarly, the farmer has to consider the area of his field while estimating about the crop yield and so on. Now, the question arises what ‘area’ is? In fact, the area of a figure can be defined as the surface enclosed by the figure or the extent of the surface of the figure. Like every other physical quantity, we need a unit of area also, for its measurement. The area of a square of side 1m is taken as SI unit of area, which is one square metre, and it is abbreviated as 1 m2. To measure areas, we often use the units cm2, mm2, km2, etc. Also knowing that 100 cm = 1m, we have 104 cm2 = 1m2 and 1 km2 = 106 m2, 1 m2 = 10–6 km2 Now, let us see, how the areas of different types of figures are measured. 1.4.1 Areas of regular figures To measure the areas of regular geometrical figures like a rectangle, a triangle, or a circle, we have well-known formulae. Some of these are given in Table 1.6 Table 1.6: Formulae to calculate the areas of some geometrical figures Figure Area Rectangle

length ×breadth

: 20 : Measurement in Science and Technology

Triangle

½ ×base × height

Circle

π× (radius)2

Parallelogram

base × altitude

Using these formulae, we can calculate the required area. For example, if you are asked to find the area of a rectangular playground whose sides are given as 50 m and 60 m, you can easily calculate the area by finding the product of the two sides of the playground. 1.4.2 Area of irregular figures You can easily find the areas of regular figures by using formulae. But the problem arises in the case of irregular figures. Because, an irregular figure does not have any Fig. 1.15 Method to find the defined length, breadth, etc. We cannot, therefore, use any area of an irregular figure formulae to calculate its area. In such cases, we make use of graph papers having squares of side 1 cm each as shown in Fig. 1.15. First, we draw the outline of the given figure of irregular shape on that graph paper. Then we count the number of complete squares in it and the number of incomplete squares. While counting the incomplete squares, we count only those squares that lie half or more within the figure; the other incomplete squares are neglected. The total number of squares thus counted gives the approximate area of the given irregular surface in cm2. In order to measure the areas of the irregular figures of very big size like field or playground, we split them into regular-shaped figures. Then the area of each figure is calculated and added to find the total area. CHECK YOUR PROGRESS 1.4 1. By what factor will the area of a rectangle increase if all its sides are increased 3 times? 2. A circular tabletop has a radius of 1.4 m. What is the area of mica needed to cover it? 3. How will you measure the area of the leaf of a plant? 4. The area of a figure is 60 m2, what is its value in cm2? 1.6 MEASUREMENT OF VOLUME You would have seen that all the materials occupy certain space. The total space occupied by any piece of matter is referred to as its volume. The SI unit used for volume Table 1.7: Volume of regular solids measurement is the volume of a cube of side 1m each. We call this unit as one Solids Volume cubic metre, abbreviated as 1m3. To Cube (side)3 measure smaller or larger volumes, we use other appropriate units like cm3, Cuboid Length × breadth × height mm3, or km3. Sphere (4π/3)× (radius)3 Now, let us study how to measure the Cylinder π(radius)2× height volume of different types of bodies.

Measurement in Science and Technology : 21 :

1.6.1 Volumes of regular solids To measure the volumes of regular solids like cube, sphere or cylinder etc., we have well known formulae. Some of such formulae these are given in Table 1.7. You would have seen a milkman or a kerosene dealer using volume-measuring vessels as shown in Fig. 1.15 These are generally cylindrical or conical in shape and have their capacity in litres. A litre is one-thousandth part of the SI unit of volume, i.e. m3. 1 litre = 10-3m3 a) Taking a reading of liquid level in a measuring cylinder It is observed that liquids like water form a concave meniscus as shown in Fig. 1.17a, while

100 90 Concave meniscus 80 1,000

500

250

70 60 50 40 30 20 Convex meniscus 10

1 Litre

1/2 Litre

1/4 Litre

Fig. 1.16 Volume measuring vessels

a

b

Fig. 1.17 (a) Liquid with concave meniscus (b) Liquid with convex meniscus

those like mercury form a convex meniscus Fig. 1.17b. Now, question arises how to take correct readings of the liquids in such cases. We must keep our eyes in line with the flat middle part of the liquid while taking a reading. If we just look at the measuring cylinder and water level we will get a wrong reading. 1.6.2 Volume of irregular solids In order to measure the volume of irregular solids, we follow an indirect way of measurement. For this purpose, we use a graduated cylinder or an overflow can. Let us see, how? a) Using graduated cylinder For small solids, we half-fill the given graduated cylinder with water and note the reading. Now, dip the solid in it after tying it with a thread as shown in Fig. 1.17. You will notice that the water level rises in the cylinder. Note this reading also. Thus, the difference in the readings of the water level before and after insertion of the solid gives the

70 60 50 40

70 60 50 40

30 20 10

30 20 10

Fig. 1.18 Measuring the volume of a solid using graduated cylinder

: 22 : Measurement in Science and Technology

volume of the solid. We cannot use water if the given solid is a piece of water soluble material, such as rock salt. In such a case, we must use a liquid in which the given solid neither dissolves nor reacts chemically.

80 70 60 50

40 b) Using an overflow can 30 If the given solid is so large that it cannot be dipped 20 10 in a graduated cylinder, then we use a large overflow can with a spout. We fill the overflow can with water Fig. 1.19 Measuring the volume of a solid till it starts overflowing as shown in Fig 1.19. using an overflow can

We wait till no more drops overflow. We then place a clean graduated cylinder below the nozzle of the overflow can and dip the given solid in it. Some water overflows and collects in the graduated cylinder. The volume of water overflown is carefully noted. This is equal to the volume of the given solid. CHECK YOUR PROGRESS 1.5 1. Why do we need a suitable oil while determining the volume of a piece of rock salt using a graduated cylinder? 2. How many cm3 will be there in one litre? 3. What is the shape of the meniscus of milk in a cylinder? 4. What is the volume of a sphere of radius 7 cm? LET US REVISE !

!

!

! !

!

!

!

!

Measurement is basically a process of comparison and involves two things: a number and a unit. The unit of physical quantity is a standard value of it in terms of which other quantities of that kind are expressed. There are seven fundamental quantities amount of subsances namely length, mass, time, temperature, amoung of substances light intensity and electric current. There are seven SI units and a number of derived units. A metre scale is used to measure large lengths. To measure small lengths, we use vernier callipers or screw gauge. Area is measured in square metre (m2) and graph papers are used for estimating the areas of irregular figures. The total space occupied by any piece of matter is called its volume. It is measured in cubic metres (m3). The unit ‘litre’ is also used to measure the volume of liquids. Standard measuring vessels are used to measure volumes of liquids like milk, kerosene oil, mobile oil at petrol pumps, etc. In the laboratory, we use graduated cylinder and an overflow can to measure the volume of large irregular bodies. TERMINAL EXERCISES

Measurement in Science and Technology : 23 :

A. Multiple choice type questions. 1. Which of the following is not an SI unit? (a) Metre (b) Pound (c) Kilogram (d) Second 2. If the mass of a solution is 10µg, it is the same as (a) 10-6g (b) 10-12g (c) 10-9g (d) 10-3g 3. A line segment was measured using a scale. One end of the line segment coincided with the 1.3cm mark on the scale. The other end coincided with 7.2 cm mark. The length of the line segment is (a) 1.3cm (b) 7.2cm (c) 8.5cm (d) 5.9cm 4. Rajesh travelled from city A to city B by car. The average speed of the car was 70 km/ h. It took 4h 30min to cover the distance. The distance between the two cities is (a) 315km (b) 280km (c) 2100km (d) 17.5km B. Descriptive type questions. 1. What are the limitations of using our senses and body parts for measurement? 2. Define the following key concepts (i) Estimation (ii) Standard of measurement (iii)Standard metre (iv) Time interval (v) Pendulum 3. Name the SI units used to measure length, mass, time and temperature. 4. Give four examples of periodic systems? 5. Define amplitude and time period of a pendulum. 6. Airplane pilot cannot use his senses to guide his plane through thick clouds. He must depend on the plane’s instruments. Why? 7. In a village 100 acres of land was distributed among ten farmers. The farmers were very happy because all of them got equal-sized plot of land. How did the Head of the Panchayat manage to do this? 8. Goldsmith uses a balance to measure gold ornaments. Why does he use an instrument for this purpose? 9. In 100 metre race, you must have seen that for each athlete the judge looks at a stop watch to measure the ‘time’ required by the athlete to complete 100 metres. What does this ‘time’ mean? 10. Describe the method for finding out the area of a leaf. 11. Measure the diameter of a glass marble by using a scale and two wooden blocks. Which other instrument can be used for finding it more accurately? Why? 12. A thin wire is closely wound on a pencil with its successive turns in contact with each

: 24 : Measurement in Science and Technology

other. If turns of the wire occupy a total distance 2 cm, what is the diameter of the wire. Which other instrument can be used for more accurate result? 13. How much volume of petrol is needed to fill a spherical tank of radius 2.1 m? 14. Why a standard reference is taken as a unit? ANSWERS TO CHECK YOUR PROGRESS 1.1 1. Parmanu 2. Arm, angul, cubit, etc. 3. During the period of Moghul emperor Akbar. 1.2 1. It can be measured and is a subject of study through our five senses. 2. a) Fundamental units are only seven in number whereas derived units are very large in number. b) Fundamental units are independent of each other but derived units are obtained from fundamental units. 3. Mass of a body is the amount of matter contained in a body while the amount of substance is equal to its molecular mass. 4. Unit of force = Unit of mass x Unit of acceleration = kg ms-2 5. Unit of pressure = Unit of force/Unit of area = kg ms-2 / m2 = kg m-1s-2 6. 237nm = 237 x 10-9m = 2.37 x 10-7m 1.3 1. pans – beam – pointer – objects – weight 2. Do as in section 1.3.1. 3. They were heavy and bulky and could not be taken from one place to another. 1.4 1. 2. 3. 4.

9 times 6.16 m2 refer section 1.4.2 600000cm2

1.5 1. 2. 3. 4.

We cannot use water because rock salt will dissolve in water but not in oil. 1000 cm3 concave 1437.33 cm3

GLOSSARY Area of a figure: the surface enclosed by a figure or the extent of the surface of a figure. Derived units: Units that are obtained by the combination of fundamental units. Fundamental units: The units of fundamental or basic quantities that are independent of each other. Least count: The minimum or least quantity that can be measured by a given instrument. Physical quantity: Any quantity that can be measured. Periodic system: A system that repeats itself at regular intervals of time. Unit: The accepted reference standard which is used for comparison of a given quantity. Volume: The total space occupied by any piece of matter.

Structure and Properties of Matter : 25 :

2

Structure and Properties of Matter All the objects around us whether living or non-living are matter. Water we drink, food we eat, air we breathe, chair we sit on, are all examples of matter. Matter is anything that has mass and takes up space. Matter appears in a huge variety of forms such as rocks, trees, computer, clouds, people, etc. Matter embraces each and everything around us. Therefore, in order to understand the world, it would be necessary to understand the matter. Each pure kind of matter is called substance. Here, pure we mean the same through out. Thus, aluminium is one substance and water is another. Please remember, the scientific meaning of substance is a little different from its every day meaning and we shall discuss it a little later in this lesson. OBJECTIVES After completing this lesson, you will be able to: z

z z z z z z z

z z

define various states of matter as solid, liquid and gas, and distinguish one from the other based on their properties; classify the matter based on their composition as element, compound and mixture; differentiate between atoms and molecules; state Dalton’s atomic theory and explain various laws of chemical combinations; define isotopes, atomic mass and molecular mass; express chemical reaction in form of a balanced chemical equation; define mole concept and molar quantities such as molar mass and molar volume; apply mole concept to a chemical reaction and show a quantitative relationship between masses of reactants and products; define Gay Lussac’s law of combining volume and Avogadro’s law; solve numerical problems based on various concepts covered above;

2.1 CLASSIFICATION OF MATTER Earlier Indian and Greek philosophers and scientists attempted to classify the matter in the form of five elements - Air, Earth, Fire, Sky and Water. This classification was more of philosophical nature. In modern science, however, there are two main ways of classifying the matter : i)

Based on physical states: All matter, at least in principle, can exist in three states, solid, liquid and gas.

: 26 : Structure and Properties of Matter

ii) Based on composition and properties: The classification of matter includes elements, compounds and mixtures. 2.1.1 PHYSICAL STATE OF MATTER A given kind of matter may exist in different physical forms under different conditions. Water, for example, at one atmospheric pressure, may exist as solid, liquid or gas with change of temperature. Sodium metal is normally solid, but it melts to a silvery liquid when heated to 98 oC. Liquid sodium changes to a bluish gas if the temperature is raised to 883 oC. Similarly, chlorine, which is normally a gas can exist as a yellow liquid or solid under appropriate conditions. These three different forms of matter differ from each other in their properties. Solids are rigid with definite shapes. Liquids are less rigid than solids and are fluid, i.e. they are able to flow and take the shape of their containers. Like liquids, gases are fluids, but unlike liquid, they can expand indefinitely. Can you think of other differences between a gas and liquid? A gas can be compressed easily whereas a liquid cannot. You might be aware, natural gas is compressed and supplied as fuel for vehicles in the name of CNG (compressed natural gas). It is not possible to compress a liquid. It is still more difficult to compress a solid. All these three forms of matter (solid, liquid and gas) are generally referred as states of matter. Taking fluidity/ rigidity and compressibility, we can write characteristic properties of solid, liquid and gas in the Table 2.1. Table 2.1: Characteristics of different states of matter States of matter

Fluidity/rigidity

Compressibility

Solid Liquid Gas

Rigid Fluid Fluid

Negligible Very low High

As mentioned, a substance can exist in three forms depending upon temperature and pressure. Water at room temperature (25 oC) exists in liquid form and at 0 oC and 1 atmospheric pressure as solid. If we go on increasing temperature of water at constant pressure, more and more of it will go into vapour form and at 100 oC will start boiling,. If we continue heating at this temperature (100 oC), entire liquid water will be converted into vapour. This is true with most of the liquids. Definitely melting and boiling points of different substances will be different. Can you think why this variation in their melting point and boiling point occurs? You will study later on that intermolecular forces are different in different liquids, and therefore their boiling points and melting points are different. In gaseous form, intermolecular forces are very weak and unable to keep molecules together in aggregation. However, in case of solids, these forces are very strong and capable of keeping molecules in fixed positions. This is the reason solids are rigid and hard and cannot be compressed. Liquids have properties intermediate to solid and gases as intermolecular forces between molecules in liquid are definitely more than gases and less than solids but strong enough to keep the molecules in aggregation (Fig. 2.1). Due to weak intermolecular forces in gases, molecules in gases can move freely and can occupy any space available to them. This property of gases is responsible for their effusion/diffusion. Molecules in gases are far apart and therefore when pressure is applied they can be brought closer and gases can be compressed.

Structure and Properties of Matter : 27 : Solid

Liquid

Gas

Solid

Liquid

Vibrating particle

Container (b)

Gas (a)

Fig. 2.1. Gases, liquids and solids (a) Bulk appearance and (b) the molecular picture.

ACTIVITY 2.1 Fill gas in a balloon and tightly tie its mouth. Now hold it with both hands and compress. What do you find? Balloon can be compressed easily. 2.2 CLASSIFICATION OF MATTER BASED ON COMPOSITION - ELEMENTS, COMPOUNDS AND MIXTURES Another method of classification of matter is based on its composition. A substance is matter that has a definite or constant composition and has distinct properties. Examples are aluminium sliver, water, carbon dioxide, nitrogen, oxygen etc. Substances differ from one another in composition and can be identified by their properties like colour, smell, taste, appearance, etc. Aluminium has uniform composition. Similarly water has uniform composition. No doubt there are also matter which do not have uniform composition. Such matter are called mixtures. Some examples of mixtures are air, soft drink, milk, and cement. Mixtures are either homogeneous or heterogeneous. Suppose you add 5g of sugar to water kept in a glass tumbler. After stirring, the mixture obtained is uniform through out. This mixture is homogeneous through out and is called solution. Air is solution of several gases (oxygen, nitrogen, water vapour, carbon dioxide etc). Suppose you mix sand with iron filings, sand grains and the iron filings remain visible and separate. This type of mixture in which the composition is not uniform, is called a heterogeneous mixture. If you add oil to water, it creates another heterogeneous mixture because the liquid thus obtained does not have a uniform composition. We can create homogeneous and heterogeneous mixtures and if need arises we can separate them into pure components by physical means without changing the identities of the components. We can recover sugar from its water solution by heating and evaporating the solution to dryness. From a mixture of iron filings and sand, we can separate iron filings using magnet. After separation we can see that the components have the same composition and properties as they did to start with. 2.2.1 Elements Oxygen and magnesium, these two substances which have uniform composition through out are elements. Antoine Laurent Lavoisier (1743-94), a French chemist was first to explain an element. He defined an element as basic form of matter that cannot be broken down into simpler substances even by chemical means. Elements serve as the building blocks for various types of other substances, starting from water up to extremely complex substances like protein. Oxygen, nitrogen, magnesium, iron, gold all are example

:of28element : Structure and Properties of already Matter studied in your lower classes. Today more than 112 which you have elements are known and we know various details about them. An element consists of only one kind of atoms. These elements are represented by suitable symbols, as you must have read in your previous classes. Fig. 2.2 shows the most abundant element in earth crust and in the human body. As can be seen from the figure, only five elements (oxygen, silicon, aluminium, iron and calcium) comprise over 90 per cent of Earth’s crust. Out of these five, oxygen is the most abundant element in our body.

All others Magnesium 2.8% Calcium

(a) 5.3% Oxygen 45.5%

4.7% 6.2% 8.3%

(b) Oxygen 65%

Iron

All others 1.2%

Aluminum Carbon 18%

Silicon 27.2%

Hydrogen 10%

Fig.2.2 (a) Elements in Earth’s crust (b) Elements in human body

Phosphorus 1.2% Calcium 1.6% Nitrogen 3%

2.2.2 Compounds Most elements can interact with one or more other elements to form compounds. A compound is a substance that consists of two or more different elements chemically united in a definite ratio. A pure compound, whatever its source, always contains definite or constant proportions of the elements by mass. As you have read, water is composed of two elements: hydrogen and oxygen. Property of water is completely different from its constituent elements: hydrogen and oxygen which are gases. Similarly when sulphur is ignited in air, sulphur and oxygen (from air) combine to form sulphur dioxide. All sample of pure water contain these two elements combined in the ratio of one is to eight (1: 8) by mass. For example, 1.0 g of hydrogen will combine with 8.0g of oxygen. This regularity of composition by mass will be discussed later on as law of constant composition). This composition does not change whether we take water from river of India or of United States or the ice caps on Mars. Unlike mixtures compounds can be separated only by chemical means into their pure components. In conclusion, the relationship among elements, compounds and other categories of matter are summarised in Fig. 2.3. We have just read that elements are made of one kind of atoms only. Now we shall discuss how concept of an atom emerged and how far this forms the basis of our other studies in science.

Matter

Mixture

Homogeneous mixtures

Separation by Physical methods

Pure substances

Separation by Heterogeneous Fig. 2.3 Classification of matter Compounds mixtures

Chemical methods

Elements

Structure and Properties of Matter : 29 :

CHECK YOUR PROGRESS 2.1 1. Which of the following matter fall(s) in the category of substance? (i) Ice (ii) Milk (iii) Iron (iv) Air (v) Water (vi) Hydrochloric acid 2. Which one of the following is solution? (i) Mercury (ii) Air (iii) Coal (iv) Milk 2.3 DALTON’S ATOMIC THEORY In the fifth century B.C. Indian philosopher Maharshi Kanad postulated that if one goes on dividing matter (Padarth), he would get smaller and smaller particles and a limit will come when he will come across smallest particles beyond which further division will not be possible. He (Kanad) named the particles Parmanu. More or less during the same period Greek philosophers, Leuappus and Democritus suggested similar ideas. This idea was not accepted at that time but it remained alive. Not much experimental work could be done until Lavoisier gave his law: Law of conservation of mass and law of constant proportions sometimes in 1789. English scientist and school teacher, John Dalton (17661844) provided the basic theory about the nature of matter: All matter whether element, compound or mixture is composed of small particles called atoms. Dalton’s theory can be summarized as follows: z z

z

z

Elements are composed of extremely small indivisible particles called atoms. All atoms of a given element are identical, having the same size, mass and chemical properties. The atoms of one element are different from the atoms of all other elements. Compounds are composed of atoms of more than one element. In any compound the ratio of the numbers of atoms of any two of the elements present is either an integer or a simple fraction. A chemical reaction involves only the separation, combination, or rearrangement of atoms; it does not result in their creation or destruction.

In brief, an atom is the smallest particle of an element that maintains its chemical identity throughout all chemical and physical changes. Most of the earlier findings and concepts related to law of conservation of mass and law of constant proportions (Fig. 2.4) could be explained to a great extent. Dalton’s theory also predicted the law of multiple proportions. However, today we know that atoms are not truly indivisible; they are themselves made up of particles (protons, neutrons, electrons, etc), which you will learn later on.

Atoms of element XFig. 2.4Atoms elementproportions Y Compound of element X and Y Law ofofconstant

: 30 : Structure and Properties of Matter

Modern technology has made it possible to take photograph of atoms. The scanning tunnelling microscope (STM) is a very sophisticated instrument. It can produce image of the surfaces of the elements, which show the individual atoms (Fig.2.5).

Fig.2.5 Image from a scanning tunneling microscope

Now let us see how atoms and molecules are related with each other. 2.4 ATOMS AND MOLECULES We have just seen, the first chemist to use the name ‘atom’ was John Dalton. Dalton used the word ‘atom’ to mean the smallest particle of an element. He then went on explaining how atoms could react together to form molecules; which he called ‘compound atoms’. Today we know what a molecule is. A molecule is an aggregate of two or more than two atoms of the same or different elements in a definite arrangement held together by chemical forces or chemical bonds. We can also define a molecule as smallest particle of an element or of a compound which can exist alone or freely under ordinary conditions and shows all properties of that substance (element or compound). A molecule will be diatomic if there are two atoms, for example, chlorine (Cl2), carbon monoxide, CO; will be triatomic if there are three atoms, for example, water (H2O) or carbon dioxide, (CO2), will be tetratomic and pentatomic if there are four and five atoms respectively. In general, a molecule having atoms more than four will be called polyatomic. There are eight atoms in a molecule of sulphur and nine atoms in a molecule of ethyl alcohol and we write formulas as S8 and C2H5OH respectively (Fig. 2.6). Only a few years back, a form of carbon called buckminsterfullerene having molecular formula, C60 was discovered. The details you will study in lesson 20.

H2O water

NH3 Ammonia

CH3CH2OH Ethyl alcohol

S

P Cl

Cl

P

P P

S

S

S

S

S

S

Cl2 P4 Chlorine

Phosphorus

S8 Sulphur

Fig. 2.6 Atomic structure of some molecules

S

Structure and Properties of Matter : 31 :

2.5 CHEMICAL FORMULAE OF SIMPLE COMPOUNDS A molecule is represented by using symbols of elements present in it. This representation is called molecular formula of the compound. Thus, a molecular formula of a substance tells us how many atoms of each kind are present in one molecule. In Fig. 2.6, you will find that atoms in a molecule are not only connected in definite ways but also exhibit definite spatial arrangements. Properties of molecules depends upon the ways atoms are connected and on spatial configuration of the molecules. CO2 and H2O both are triatomic molecules but they have entirely different properties. CO2 is a linear molecule and is a gas but H2O is a bent molecule and a liquid. Sodium chloride (common salt) contains equal number of sodium and chlorine atoms and is represented by the formula, NaCl. Sulphuric acid, H2SO4 contains three elements : hydrogen, oxygen and sulphur. 2.5.1 Valency and formulation Every element has a definite capacity to combine with other elements. This combining capacity of an element is called its valency. In normal course, hydrogen has 1, oxygen has 2, nitrogen has 3 and carbon has 4 valency. Valency of an element depends upon how it combines with other elements. This will depend upon the nature of the element. Sometime an element shows more than on valency. We say element has variable valency. For example, nitrogen forms several oxides: N2O, N2O2, N2O3, N2O4 and N2O5. If we take valency of oxygen 2 then valency of nitrogen in these oxides will be 1,2,3,4 and 5 respectively. Very soon, you will learn in lesson 3 that valency of an element depends on its electronic configuration. Valency of F, Cl, Br and I is normally taken as 1. In NaCl, valency of Na is also 1. All alkali metals such as K, Cs, Rb have 1 valency. Valency of oxygen is 2 and that of phosphorus is 5, we can write the formula of phosphorus pentaoxide as P2O5. Thus, we can write the formula of water (H2O), ammonia (NH3), carbon dioxide (CO2), magnesium oxide (MgO), phosphorus pentaoxide (P2O5), hydrochloric acid gas (HCl), phosphorus tribromide (PBr3) etc. if we know the elements constituting these compounds and their (elements) valencies. Since valencies are not always fixed (as P has different valencies in P2O5 and in PBr3 in the above example), sometimes we face problem. Writing formula of a compound is easy only in binary compounds (i.e. compound made of only two elements). However, when we have to write formula of a compound which involves more than two elements (i.e. of polyatomic molecules), it is somewhat cumbersome task. You will learn later on that basically there are two types of compounds: covalent compounds and ionic compounds. Covalent compounds are of the type H2O, NH3 etc. An electrovalent or ionic compound is made of two charged constituents. One positively charged called ‘cation’ and other negatively charged called ‘anion’. Here again we should know the charge (valency) of both types of ions for writing formula of an ionic compound. Compounds like sodium nitrate (NaNO3), potassium chloride (KCl), potassium sulphate (K2SO4), ammonium choride (NH4Cl), sodium hydroxide (NaOH) etc. are made of two or more than two elements. For writing the formula of the compounds we should know the charge (valency) of positively and negatively charged constituents of the compounds in such cases. Remember in an ionic compound, sum of the charges of cation and anion should be zero. A few examples of cation and anions along with their valency are provided in Table 2.2.

: 32 : Structure and Properties of Matter

Table 2.2 Valency of some common cations and anions which form ionic compounds Anions

Valency

Chloride ion, Cl Nitrate ion, NO-3 Carbonate ion, Sulphate ion, SO42Bicarbonate ion, HCO-3 Hydroxide ion, OH Nitrite ion, NO 2 Phosphate ion, PO34_ Acetate ion CH3COOBromide ion, Br Iodide ion, I Sulphide ion, S2-

-1 -1 -2 -2 -1 -1 -1 -3 -1 -1 -1 -2

Cations

Valency

Potassium ion, K Sodium ion, Na+ Magnesium ion, Mg2+ Calcium ion, Ca2+ Aluminium ion, Al3+ Lead ion, Pb2+ Iron ion, Fe3+(Ferric) Iron ion (Ferrous) Fe2+ Zinc ion, Zn2+ Copper ion, Cu2+ Mercury, Hg2+ (mercuric) Ammonium ion, NH4+ +

+1 +1 +2 +2 +3 +2 +3 +2 +2 +2 +2 +1

Suppose you have to write the formula of potassium sulphate which is an electrovalent compound and made of potassium and sulphate ions. Here, charge on potassium ion is +1 and that on sulphate ion is –2. Therefore, for one sulphate ion two potassium ions will be required. We can write, [K+]2 [SO42-]1 = K2SO4 Similarly for writing formula of sodium nitrate, charge (valency) of sodium ion is +1 and that of nitrate ion is -1, therefore, for one sodium ion, one nitrate ion will be required and we can write. [Na+]1 [NO3–]1 = NaNO3 Now, it is clear that digit showing charge of cation goes to anion and digit showing charge of anion goes to cation. For writing formula of calcium phosphate we take charge of each ion into consideration and write the formula as discussed above as, [Ca2+]3 [PO-34]2 = Ca3(PO4)2 Writing formula of a compound comes by practice therefore write formula of as many ionic compounds as possible based on the guidelines given above. 2.5.2 Empirical and molecular formula Molecular formula of a substance is not always identical with the simplest formula that expresses the relative numbers of atoms of each kind in it. Simplest formula of an element is expressed by using its symbol as O for oxygen, S for sulphur, P for phosphorus and Cl for chlorine. Molecular formula of these substances are O2, S8, P4 and Cl2 respectively. The simplest formula of a compound is called its empirical formula. The empirical formula of a compound is the chemical formula that shows the relative number of atoms of each element in the simplest ratio. In contrast, the molecular formula tells us the actual number of atoms of each element in a molecule. It may be the same as the empirical formula or some other integral multiple of the empirical formula. Empirical and molecular formulae of a few compounds are given in Table 2.3.

Structure and Properties of Matter : 33 :

Table 2.3: Empirical and molecular formulae Substance

Empirical formula

Molecular formula

water

H2O

H2O

ammonia

NH3

NH3

ethane

CH3

C2H6

hydrogen peroxide

HO

H2O2

carbon dioxide

CO2

CO2

hydrazine

NH2

N2H4

Formula of an ionic substance is always an empirical formula. For example, NaCl is empirical formula not a molecular formula of sodium chloride. You will study later on that ionic substances do not exist in molecular form. CHECK YOUR PROGRESS 2.2 1. Give one evidence of modern technology which supports Dalton’s atomic theory. 2. Write formula of the following compounds (i) Ferric phosphate (ii) Barium chloride (v) Magnesium sulphate (iii) Calcium carbonate (vi) Sodium phosphate (iv) Phosphorous tribromide (vii) Sulphur trioxide 3. Write differences between an atom and a molecule. 4. Write empirical formulae of the following molecules: C2H4, HCl, HNO3 2.6 LAWS OF CHEMICAL COMBINATIONS French chemist, Antoine Laurent Lavoisier (1743-1794) experimentally showed that matter can neither be created nor destroyed in a chemical reaction. This experimental finding was known as law of conservation of mass. In fact, this could be possible due to precise measurement of mass by Lavoisier. Law of conservation of mass helped in establishing the law of definite composition or law of constant proportions. This law states that any sample of a pure substance always consists of the same elements combined in the same proportions by mass. For instance, in water, the ratio of the mass of hydrogen to the mass of oxygen is always 1:8 irrespective of the source of water. Thus, if 18.0 g of water are decomposed, 2.0 g of hydrogen and 16.0 g of oxygen are always obtained. Also, if 2 g of hydrogen are mixed with 16.0 g of oxygen and mixture is ignited, 18.0 g of water are obtained after the reaction is over. In the water thus formed or decomposed, hydrogen to oxygen mass ratio is always 1:8. Similarly in ammonia (NH3), nitrogen and hydrogen will always react in the ratio of 14:3 by mass. John Dalton thought about the fact that an element may form more than one compound with another element. He observed that for a given mass of an element, the masses of the other element in two or more compounds are in the ratio of simple whole number or integers. In fact this observation helped him in formulation of his fundamental theory

: 34 : Structure and Properties of Matter

popularly known as Dalton’s ‘Atomic theory’ which is discussed in Section 2.3. Let us take two compounds of nitrogen and hydrogen : (i) ammonia (NH3) and (ii) hydrazine (N2H4). In ammonia, as discussed above, 3.0 g of hydrogen react with 14 g of nitrogen. In hydrazine, 4.0 g of hydrogen react with 28 g of nitrogen or 2.0 g of hydrogen reacts with 14.0 g of nitrogen. It can be seen that for 14 g of nitrogen, we require 3.0 g of hydrogen in NH3 and 2.0 g of hydrogen in hydrazine (N2H4). This leads to the ratio That is, masses of hydrogen which combine with the fixed mass of nitrogen in ammonia and in hydrazine are in the simple ratio of 3:2. This is known as law of multiple proportions. 2.6.1 Gay Lusaac’s law of combining volume and Avogadro’s hypothesis The French chemist Gay Lusaac experimented with several reactions of gases and came to the conclusion that the volume of reactants and products in large number of gaseous chemical reactions are related to each other by small integers provided the volumes are measured at the same temperature and pressure. For example, in reaction of hydrogen gas with oxygen gas which produces water vapour, it was found that two volumes of hydrogen and one volume of oxygen give two volumes of water vapour To be more specific, if 100 mL of H2 gas combines with exactly 50 mL of O2 gas we shall obtain 100 mL of H2O vapour provided all the gases are measured at the same temperature and pressure (say 100 oC and 1 atm pressure). As you know, the law of definite proportions is with respect to mass. Gay Lussac’s findings of integer ratio in volume relationship is actually the law of definite proportions by volume. The Gay Lussac’s law was further explained by the work of Italian physicist and lawyer Amedeo Avogadro in 1811. Avogadro’s hypothesis which was experimentally established and given the status of a law later on, states as follows: The volume of a gas (at fixed pressure and temperature) is proportional to the number of moles (or molecules of gas present). Mathematically we can express the statement as V∝n You will study in section 2.8 that 1 mole of a substance is 6.022 × 1023 particles/ molecule of that substance. Where V is volume and n is the number of moles of the gas. (It is clear from the relationship that more volume will contain more number of molecules). Avogadro’s law can be stated in another simple way “Equal volumes of all gases under the same conditions of temperature and pressure contain the same number of molecules” For example, 2H2(g) 2 volumes 2 mol of H2

+

O2(g) 1 volume 1 mol of O2

→

2H2O(g) 2 volumes (Gay Lussac’s law) 2 mol of H2O (Avogadro’s law)

Multiplying both sides of equation by the same number, equation does not change. Now let us multiply by 6.022 × 1023, we get

Structure and Properties of Matter : 35 :

2 × 6.022 × 1023 molecules of H2

Similarly,

+ Cl 2 (g)

H 2 ( g)

or

1 × 6.022 × 1023 molecules of O2 →

2 × 6.022 × 1023 molecules of H2O 2 HCl (g)

1 volume

1 volume

2 volume

1 mol of H2

1 mol of Cl2

2 mol of HCl

6.022 × 1023 molecules of H2

6.022 × 1023 molecules of Cl2

2 × 6.022 × 1023 molecules of HCl

Experimentally, it has been found that at standard temperature (0 oC) and standard pressure (1 bar) volume of 1 mol of most of the gases is 22.7 litres. Since this volume is of 1 mol of a gas, it is also called molar volume. Volume of liquids and solids does not change much with temperature and pressure and same is true with its molar volume. If we know molar mass and density of a solid or of a liquid, we can easily calculate its molar mass molar volume by the relationship, volume = _________________ density 2.7 ISOTOPES AND ATOMIC MASS As you might have read in your earlier classes that an atom consists of several fundamental particles: electrons, protons and neutrons. An electron is negatively charged and a proton is positively charged particle. Number of electrons and protons in an atom is equal. Since charge on an electron is equal and opposite to charge of a proton, therefore, an atom is electrically neutral. Protons remain in the nucleus in the centre of the atom and nucleus is surrounded by negatively charged electrons. The number of protons in the nucleus is called atomic number, and is denoted by Z. There are also neutral particles in the nucleus and they are called neutrons. Mass of a proton is nearly equal to the mass of neutron. Total mass of nucleus is equal to the sum of masses of protons and neutrons. The total number of protons and neutrons is called mass number or the nucleons number denoted by A. By convention, atomic number is written at the bottom left corner of the symbol of the atom and mass number is written at the top left corner. For example, we write, 42He, 73Li and 126Cfor helium, lithium and carbon 12

respectively. The symbol 6 C indicates that there is a total of 12 particles (nucleons) in the nucleus of carbon atom, 6 of which are protons. Thus, there must be 12 – 6 = 6 neutrons. Similarly,

16

O has 8 protons and 8 electrons and there are 8 neutrons. Also atomic number, Z differentiates the atom of one element from the atoms of another. Also an element may be defined as a substance whose atoms have the same atomic number. Thus, all atoms of an element have nuclei containing the same number of protons and having the same charge. But the nuclei of all the atoms of a given element do not necessarily contain the same number of neutrons. For example, atoms of oxygen, found in nature have the same number 8

: 36 : Structure and Properties of Matter

of protons which makes it different from other elements, but their neutrons are different. This is the reason that the masses of the atoms of the same elements are different. For example, one type of oxygen atom contains 8 protons and 8 neutrons in the nucleus, second type 8 protons and 9 neutrons and third type contains 8 proton and 10 neutrons. We represent them as 168O, 178O and 188O. Atoms of an element that have same atomic number(Z) but different mass number(A) are called isotopes. 2.7.1. Atomic mass The mass of an atom is related to the number of protons, electrons, and neutrons it has. Atom of an element is extremely small and therefore it is not easy to weigh it. No doubt, it is possible to determine the mass of one atom relative to another experimentally. For this, it is necessary to assign a value to the mass of one atom of a given element so that it can be used as a standard. Scientists agreed to chose an atom of carbon isotope (called carbon-12). Carbon-12 has six protons and six neutrons and has been assigned a mass of exactly 12 atomic mass unit (amu now known as u). Thus one atomic mass unit is defined as a mass exactly equal to one twelfth of the mass of one carbon-12 atom. Mass of one carbon-12 atom = 12 amu or 12 u massof one carbon atom or 1 amu = 12 Mass of every other element is determined relative to this mass. Further, it has been found by experiment that hydrogen atom is only 0.0840 times heavier than C-12 atoms. Then on carbon-12 scale, atomic mass of hydrogen = 0.0840×12.00 u = 1.008 u. Similarly, experiment shows that an oxygen atom is, on the average, 1.3333 times heavier than C-12 atom. Therefore, Atomic mass of oxygen = 1.3333×12.00 u = 16.0 u Atomic mass of a few elements on C-12 scale is provided in Table 2.4. If you see Table 2.4, you will find that atomic mass is not a whole number. For example, atomic mass of carbon is not 12 u but 12.01 u. This is because most naturally occurring elements (including carbon) have more than one isotope. Therefore when we determine atomic mass of an element we generally measure or calculate average mass of the naturally occurring mixture of isotopes. Let us take one example. Carbon has two natural isotope C-12 and C-13 and their natural abundance is 98.90 per cent*, 1.10 per cent, respectively . Atomic mass of C-13 has been determined to be 13.00335 u. Therefore, average atomic mass of carbon = (0.9890) (12.000 u) + (0.010) (13.00335 u) = 11.868 + 0.1430 = 12.01 u Thus, ‘atomic mass’ of an element means average atomic mass of that element. These days actual masses of atoms have been determined experimentally using mass spectrometer. You will learn about this in your higher classes.

Structure and Properties of Matter : 37 :

Table 2.4 Atomic masses* of some common elements Element

Symbol

Mass(u)

Element

Symbol

Mass(u)

Aluminium Argon Arsenic Barium Boron Bromine Caesium Calcium Carbon Chlorine Chromium Cobalt Copper Fluorine Gold Helium Hydrogen Iodine Iron Lead Lithium

Al Ar As Ba B Br Cs Ca C Cl Cr Co Cu F Au He H I Fe Pb Li

26.98 39.95 74.92 137.34 10.81 79.91 132.91 40.08 12.01 35.45 52.00 58.93 63.54 19.00 196.97 4.00 1.008 126.90 55.85 207.19 6.94

Magnesium Manganese Mercury Neon Nickel Nitrogen Oxygen Phosphorus Platinum Potassium Radon Silicon Silver Sodium Sulphur Tin Titanium Tungston Uranium Vanadium Xenon Zinc

Mg Mn Hg Ne Ni N O P Pt K Rn Si Ag Na S Sn Ti W U V Xe Zn

24.31 54.94 200.59 20.18 58.71 14.01 16.00 30.97 195.09 39.10 (222)** 28.09 107.87 23.00 32.06 118.69 47.88 183.85 238.03 50.94 131.30 65.37

* During calculation we convert per cent into fraction by dividing by 100. Thus, 98.90 per cent becomes 0.9890. *Atomic masses are average atomic masses. They are given correct up to second decimal places. In practice, we use round figures and for this rounding off is necessary. **Radioactive 2.7.2 Molecular mass You have just read that a molecule can be represented in form of a formula popularly known as molecular formula. Molecular formula may be of an element or of a compound. Molecular formula of a compound is normally used for determing the molecular mass of that substance. If the substance is composed of molecules (for example, CO2, H2O or NH3), it is easy to calculate the molecular mass. Molecular mass is the sum of atomic masses of all the atoms present in that molecule. Thus the molecular mass of CO2 is obtained as C 1 × 12.0 u = 12.0 u 2O 2 × 16.0 u = 32.0 u Total = 44.0 u CO2 We write molecular mass of CO2 = 44.0 u Similarly, we obtain molecular mass of ammonia, NH3 as follows : N 1 × 14.0 u = 3H 3 × 1.08 u = NH3 Total =

14.0 u 3.24 u 17.24 u

: 38 : Structure and Properties of Matter

Molecular mass of ammonia, NH3 = 17.24 u. For substances which are not molecular in nature, we talk of formula mass. For example, sodium chloride, NaCl is an ionic substance. For this, we write formula mass which is calculated similar to molecular mass. In case of NaCl, formula mass = mass of 1 Na atom + mass of 1 Cl atom = 23 u + 35.5 u = 58.5 u. You will learn about such compounds later on in your lesson 5. CHECK YOUR PROGRESS 2.3 1. Silicon has three isotopes with 14, 15 and 16 neutrons respectively. What is the mass number and symbol of these three isotopes? 2. Calculate molecular mass of the following compounds C3H8, PCl5, SO3 2.8 MOLE CONCEPT When we mix two substances, we get one or more new substance(s). For example when we mix hydrogen and oxygen and ignite the mixture, we get a new substance water. This can be represented in the form of an equation, 2H2 (g) + O2(g) → 2H2O (l) In above equation, 2 molecules (4 atoms) of hydrogen react with 1 molecule (2 atoms) of oxygen and give two molecules of water. Similarly, we always like to know how many atoms/molecules of a particular substance would react with atoms/molecules of another substance in a chemical reaction. No matter how small they are. The solution to this problem is to have a convenient unit of matter that contains a known number of particles (atoms /molecules). The chemical counting unit that has come into use is the mole. The word mole was apparently introduced in about 1896 by Wilhelm Ostwald who derived the term from the Latin word ‘moles’ meaning a ‘heap’ or ‘pile’. The mole whose symbol is ‘mole’ is the SI base unit for measuring amount of substance. It is defined as follows: ‘A mole is the amount of pure substance that contains as many particles (atoms, molecules, or other fundamental units) as there are atoms in exactly 0.012 kg of C-12 isotope’. In simple terms, mole is the number of atoms in exactly 0.012 kg (12 grams) of C-12. Although mole is defined in terms of carbon atoms but the unit is applicable to any substance just as 1 dozen means 12 or one gross means 144 of any thing. Mole is scientist’s counting unit like dozen or gross. By using mole, scientists (particularly chemists) count atoms and molecules in a given substance. Now it is experimentally found that the number of atoms contained in exactly 12 grams of C-12 is 602,200 000 000 000 000 000 000 or 6.022×1023. This number (6.022×1023) is called Avogadro constant in honour of Amedeo Avogadro an Italian lawyer and physicist and is denoted by symbol, NA. We have seen that Atomic mass of C = 12 u Atomic mass of He = 4 u We can see that one atom of carbon is three times as heavy as one atom of helium. On the same logic 100 atoms of carbon are three times as heavy as 100 atoms of helium. Similarly 6.02×1023 atoms of carbon are three times as heavy as 6.02 × 023 atoms of helium.

Structure and Properties of Matter : 39 :

But 6.02×1023 atoms of carbon weigh 12 g, therefore 6.02×1023 atoms of helium will weigh 1/3× 12g = 4g. We can take a few more examples of elements and can calculate the mass of one mole atoms of the element. Numerically it is equal to its atomic mass expressed in gram. Mass of one mole of a substance is called its molar mass. Mass of one mole atoms of oxygen will be 16 g. Mass of one mole of fluorine will be 19 g. Now if we take mass of one mole molecule of oxygen it would be 32 g because there are two atoms in a molecule of oxygen (O2). When we do not mention atom or molecule before mole, we always mean one mole of that substance in its natural form. For example, if we simply say one mole of oxygen, it means that we are referring one mole molecule of oxygen as oxygen occurs in nature as molecular oxygen. If we take an example of a molecule of a compound, we find that same logic is applicable. For example, mass of one mole molecule of water will be 18 g as molecular mass of water is 18u. Remember molar mass is always expressed as grams per mole or g /mol or g mol-1. For example, Molar mass of oxygen (O2) = 32 g mol-1 Molar mass of lead (Pb) = 207 g mol-1 We have just seen in Section 1.6 that atoms of two different elements combine with one another in the ratio of small whole number. A modern interpretation of this observation is that atoms or molecules combine with one another in the ratio of 1:1, 1:2 or 1:3 or any other simple ratio i.e. they combine 1 mol for 1 mol or 1 mol for 2 mol or 1 mol for 3 mol, and so on. Thus mole concept is the cornerstone of quantitative science for chemical reactions which you will study in your higher classes. Table 2.5 Molecular and molar mass of some common substances Formula

Molecular mass(u)

Molar mass (g/mol)

O2 H2 Cl2 P4 CH4 CH3OH NH3 CO2 HCl C6H6 SO2 CO C2H5OH

32.0 2.0 71.0 123.9 16.0 32.0 17.0 44.0 36.5 78.0 64.0 28.0 46.0

32.0 2.0 71.0 123.9 16.0 32.0 17.0 44.0 36.5 78.0 64.0 28.0 46.0

Example 2.1: How many grams are there in 3.5 mol of sulphur? Solution: For converting mass into mole and vice visa, we always need the molar mass. Molar mass of sulphur is 32.0 g mol–1. Therefore, number of grams of sulphur in 3.50 mol of sulphur is  32.0 g  3.50 mol sulphur ×   = 112.0 g sulphur  1 mol 

: 40 : Structure and Properties of Matter

Example 2.2: Calculate number of moles present in 48 g of oxygen. Solution: Molar mass of oxygen = 32 g mol-1 Oxygen in natural form will be molecular oxygen, O2  48 g  Therefore, number of moles of oxygen = -1  = 1.5 mol  32 g mol  CHECK YOUR PROGRESS 2.4 1. Sulphur is a non-metallic element. How many atoms are present in 16.3 g of S? 2. Molar mass of silver is 107.9 g. What is the mass of one atom of silver? 2.9 CHEMICAL EQUATIONS A chemical equation is a shorthand description of a reaction carried out in a laboratory or elsewhere. It gives the formulas for all the reactants and products. For example C + O2 → CO2 2H2 + O2 → 2H2O

..... (1) .......(2)

In a chemical reaction reactants are written on the left and products are written on the right side of the arrow. Arrow (→) indicates conversion of reactant(s) into product(s). In a chemical reaction atoms are neither created nor destroyed. This is known as law of conservation of mass. A chemical equation, therefore, should be consistent with this law. Total number of atoms of each element must be the same in the products and in the reactants. As shown in equation (2) above two molecules (four atoms) of hydrogen react with one molecule (two atoms) of oxygen and give two water molecules in which there are four hydrogen atoms and two oxygen atoms. Since number of atoms of the involved elements is equal on both side of the arrow in the equation, we say the equation is balanced. A balanced chemical equation is quite meaningful in science (chemistry) as it gives a lots of information. In order to make an equation more informative, we also indicate the physical states of the reactants and products. We write in parenthesis ‘s’ if the substance is solid, ‘l’ if the substance is liquid and ‘g’ if the substance is a gas. Accordingly, equation (1) and (2) can be written as, C (s) + O2 (g) → CO2 (g) 2H2 (g) + O2 (g) → 2H2O (l) 2.9.1

Balancing of a chemical equation

Balancing of a chemical equation is essential as we can derive meaningful information from this. Before balancing a chemical equation, please ensure that correct formulas of reactants and products are known. Let us consider burning of methane in oxygen to give carbon dioxide and water. First write reactants and products, CH4 + O2

reactants

→

CO2 + H2O (unbalanced equation)

products

In this equation, hydrogen and carbon appear in only two formulas each, while oxygen appears three times. So we begin by balancing the number of carbon and hydrogen atoms. Here if we examine both sides, carbon appears in methane on left and in carbon dioxide on

Structure and Properties of Matter : 41 :

the right side. Therefore, all carbon in methane, CH4 , must be converted to carbon dioxide. One molecule of CH4, however, contains four hydrogen atoms, and since all the hydrogen atoms end up in water molecule, two water molecules must be produced for each methane molecules. Therefore, we must place coefficient 2 in front of the formula for water to give CH4 + O2

→

CO2 + 2H2O (unbalanced)

Now we can balance oxygen, since there are four oxygen atoms on right hand side of equation (two in CO2 and two in two molecules of H2O). Therefore, we must place 2 in front of the formula for oxygen, O2. By doing this we get equal atoms of oxygen on both sides of equation. CH4 + 2O2

→

CO2 + 2H2O

(balanced)

Now number of atoms of each element is equal on both sides of the chemical equation. In order to make the chemical equation more informative, indicate states of each reactant and product. CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O(l) Balancing of equation comes only by practice and therefore let us take one example. Example2.3: Bottled gas sold as cooking gas contains butane, C4H10 as the major component. Butane when burns in sufficient oxygen (present in air) gives carbon dioxide and water. Write a balanced chemical equation to describe the reaction. Solution: Work out the balanced equation in steps Step 1: Write an unbalanced equation showing correct formulas of reactants and products C4H10 + butane

O2

→

oxygen

CO2 +

H2O (unbalanced equation)

Carbon water dioxide

Now balance C and H as they appear only in two places. Step II: Balance the number of C atoms. Since 4 carbon atoms are in the reactant, therefore, 4CO2 must be formed. C4H10 + O2 →

4CO2 + H2O

(unbalanced)

Step III: Balance the number of hydrogen atoms There are 10 hydrogen atoms in butane and each water molecule requires 2 hydrogen atoms, therefore, 5 water molecules will be formed. C4H10 + O2 → 4CO2 + 5H2O

(unbalanced)

Step IV: Balance the number of O atoms There are 8 oxygen atoms in the carbon dioxide and 5 oxygen atoms with H2O molecules. Therefore, 13 atoms or 13/2 molecules of oxygen will be required. C4H10 + 13/2 O2 → 4CO2 + 5H2O

: 42 : Structure and Properties of Matter

Normally we do not write fractional coefficient in equation as one may interpret that molecules can also be available in fraction. Therefore, we multiply both sides by 2 and get the final balanced equation 2C4H10 + 13O2 → 8CO2 + 10H2O

(balanced)

We can also write states of the substances involved. 2C4H10 (g) + 13O2 (g) → 8CO2 (g) + 10H2O(l) Remember : (i) Use the simplest possible set of whole number coefficients to balance the equation. (ii) Do not change subscript in formulas of reactants or products during balancing as that may change the identity of the substance. For example, 2NO2 means two molecules of nitrogen dioxide but if we double the subscript we have N2O4 which is formula of dinitrogen tetroxide, a completely different compound. (iii) Do not try to balance an equation by arbitrarily selecting reactant(s) and product(s). A chemical equation represents a chemical reaction which is real. Thus real reactants and products only can be taken for balancing. 2.9.2 Uses of balanced equations A balanced chemical equation gives a lot of meaningful information. First it gives the number of atoms and molecules taking part in the reaction and corresponding masses in atomic mass units (amu or u). Second it gives the number of moles taking part in the reaction, with the corresponding masses in grams or in other convenient units. Let us consider the reaction between hydrogen and oxygen once again 2H2 (g)

2 molecules of hydrogen 4.0 u

→

+ O2 (g)

2H2O(l)

1 molecule of oxygen 32.0 u

2 molecules of water 36 u

But in normal course we deal with a large number of molecules, therefore, we can consider the above reaction as follows: 2H2

2 molecules of hydrogen

+

O2

→

1 molecule of oxygen

2H2O

2 molecules of water

Suppose we multiply entire chemical equation by 100, we can write 2 × 100 molecules + 1 × 100 molecules of → 2 × 100 of hydrogen oxygen molecules of water If we multiply entire equation by Avogadro constant, 6.022 × 1023 , we get 2 × 6.022 × 1023 molecules + 1 × 6.022 × 1023 molecules of hydrogen

molecules of oxygen

→ 2 × 6.022 × 1023 of water

Structure and Properties of Matter : 43 :

Since 6.022 × 1023 molecules is 1 mole, therefore, we can also write or

2 mol of

+ 1 mol of

hydrogen

→ 2 mol of water

oxygen

Therefore, equation can be written as 2H2

+

2 mol of hydrogen

O2

→

1 mol of oxygen

Or 4.0 g of hydrogen + 32.0 g of oxygen

2H2O 2 mol of water

→

36 g of water

Thus a chemical equation can also be interpreted in terms of masses of reactants consumed and product(s) formed. This relationship in chemical reaction is very important and provides a quantitative basis for taking definite masses of reactants to get a desired mass of a product. Example 2.4: In the reaction CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O(l) How much CO2 will be formed if 80 g of methane gas (CH4) is burnt? Solution: CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O(l) 1 mol 2 mol 1 mol 2 mol or 16 g 64 g 44 g 36 g We can see in the above equation that 16 g of CH4 gives 44 g of CO2. Therefore, for getting 80 g of CH4, the mass of CO2 required will be

=

44 g × 80 g = 44 × 5 g = 220 g of CO 2 16 g

CHECK YOUR PROGRESS 2.5 1. Balance the following equations. (i) H3PO3 → H3PO4 + PH3 (ii) Ca + H2O → Ca(OH)2 + H2 (iii) C3H8 + O2 → CO2 + H2O 2. Name the following compounds. Na2O, Cu2Cl2, BaO, Na2SO4 z

z

LET US REVISE Matter is anything that has mass and occupies space. It can be classified on the basis of its (i) physical state as solid, liquid or gas, and (ii) chemical composition/constitution as element, compound or mixture. An element is basic form of matter that cannot be broken down into simpler substances even by chemical reaction. A compound is a substance composed of two or more different types of elements chemically combined in a definite proportion by mass. A mixture contains more than one substance (element or compound) mixed in any proportion.

: 44 : Structure and Properties of Matter z

z

z

z

z

z

z

z

z

z

z

z

z

A solution is a homogeneous mixture of two or more than two substances. Major component of the solution is called solvent. According to law of constant proportions, a sample of a pure substance always consists of the same elements combined in the same proportions by mass. When an element combines with another element and forms more than one compound, then different masses of one element that combine with a fix mass of another element are in ratio of simple whole number or integer. This is the law of Multiple proportions. John Dalton introduced the idea of an atom as an indivisible particle of matter. An atom is the smallest particle of an element which can exist and retains all the chemical properties of that element. A molecule is the smallest particle of an element or of a compound which can exist freely under ordinary conditions and shows all properties of that substance. A molecule can be expressed in form of a chemical formula using symbols of constituent elements. A molecular formula shows the actual number of atoms of different elements in a molecule of an element or of compound. In other words, composition of any compound can be represented by its formula. For writing formula of a compound valence or valency of the elements is used. Valency is combining capacity of an element and is related to its electronic configuration. An empirical formula shows the simplest whole number ratio of the atoms of different elements present in a compound. Atoms of the isotope 12C are assigned a atomic mass unit of 12 and the relative masses of all other atoms are obtained by comparison with the mass of a carbon-12. The mole is the amount of substance which contains the same number of particles (atoms, ions or molecules) as there are atoms in exactly 0.012 kg of 12C. Avogadros constant is defined as the number of atoms in exactly 12 g of C-12 and is equal to 6.022 × 1023 mol-1. Mass of one mole atoms or one mole molecules of a substance is its molar mass and volume of one mole of the substance is its molar volume. A chemical equation is a shorthand description of a reaction. A balance chemical equation provides quantitative information about reactants consumed and products formed in a chemical reaction. A balance chemical equation obeys law of conservation of mass and law of constant proportions. TERMINAL EXERCISES

1. There are many examples of homogeneous and heterogeneous mixtures in the world around you. How would you classify: sea-water, air (unpolluted), smoke, black coffee, tea, soil, soda water and wood ash?

Structure and Properties of Matter : 45 :

2. Characterize gases, liquids and solids in terms of compressibility, fluidity and density. 3. What is atomic theory proposed by Dalton? Describe how it explains the great variety of different substances. 4. Give normal state (solid, liquid or gas) of each of the following: (i) Nitrogen (ii) Copper (iii) Bromine (iv) Oxygen (v) ethyl alcohol (vi) hydrogen peroxide 5. Label each of the following as a substance, a heterogeneous mixture, or a solution. (i) bromine (iv) soil (in front of your home) (vii) river water (ii) petrol (v) stone (viii) Coal (iii) concrete (vi) beach sand (ix) Soda water 6. Write the number of protons, neutrons and electrons in each of the following: 19 F, 188O, 40 Ca 9 20 7. Give the symbol for each of the following isotopes (i)

Atomic number 19, mass number 40

(ii)

Atomic number 18, mass number 40

(iii)

Atomic number 7, mass number 15

8. Boron has two isotopes with masses of 10.01294 and 11.00931 u and abundance of 19.77% and 80.23%. What is the average atomic mass of boron? (Ans.10.81 u) 9. How does an element differ from a compound? How are elements and compounds different than mixture? 10. How will you define a solution based on its composition? 11. Charge of one electron is 1.6022 × 10-19 coulomb. What is the total charge on 1 mol of electron? If there is same amount of charge on one proton, calculate total charge on 1 mol of protons. 12. How many molecules of O2 are in 8.00 g of O2? If the O2 molecules were completely split into O (oxygen atom), how many moles of atoms of oxygen would be obtained? (Ans. Number of molecules in 8 g of O2 =1.5055 × 1023 molecules Number of atoms in 8 g of O2 = 3.0110 × 1023 atoms) 13. Assume that a human body is 80% water. Calculate the number of the molecules of water that are present in the body of a person who has mass of 65 kg. (Ans. 1.7 × 1027 molecules of water) 14. Using atomic masses given in the table of this lesson calculate the molar masses of each of the following compounds: CO,CH4, NaCl, NH3 and HCl

: 46 : Structure and Properties of Matter

15. Average atomic mass of carbon is 12.01 u. Find the number of moles of carbon in (i) 2.00 g of carbon and (b) 3.00 × 1021 atoms of carbon. 16. Balance the following equations (i) H2O2 → H2O + O2 (ii) S + O2 → SO3 (iii) C2H2 + O2 → CO + H2O (iv) MnO2 + HCl → MnCl2 + Cl2 + H2O 17. Classify the following molecules as mono, di, tri, tetra, penta and hexatomic molecules. H2, P4, SF4, SO2, PCl3, C2H2, CH3OH, PCl5, H2O2, HCl, Cl2O 18. What is meant by molecular formula? Hydrogen peroxide has the molecular formula H2O2. What mass of oxygen can be formed from 17 g of H2O2 if decomposition of H2O2 takes place. 19. Write ‘true’ or ‘false’. A balanced chemical equation shows (i) the formulas of the products (ii) the molar proportions in which the products are formed (iii) that a reaction can occur (iv) the relative number of atoms and molecules which react (v)

that a reaction is exothermic

20. What is the mass of (i) 6.02 × 1023 atoms of O (ii) 6.02 × 1023 atoms of P (iii) 6.02 × 1023 molecules of P4 (iv) 6.02 × 1023 molecules of O2 [Ans. (a) 16.0 g (b) 31.0 g

(c) 124.0 g

(d) 32 g]

21. How many atoms are there in (i)

two moles of iron

(ii)

0.1 mol of sulphur

(iii) 18 g of water, H2O (iv) 0.44 g of carbon dioxide, CO2 [Ans. (a) 1.204 × 1024 (b) 6.02 × 1022 (c) 1.8 × 1024 and (d) 1.8 × 1022] 22. Define the following (i)

Law of constant proportions

(ii)

Law of multiple proportions

Structure and Properties of Matter : 47 :

(iii)

Avogadro’s Law

(iv)

Gay Lussacis Law

(v)

Dalton’s atomic theory

23. Convert into mole (i) 12 g of oxygen gas (O2) (ii) 20 g of water (H2O) (iii)

22 g pf carbon dioxide (CO2) (Ans. (a) 0.375 mol (b) 1.11 mol (c) 0.50 mol) ANSWERS TO CHECK YOUR PROGRESS

2.1

1. (i), (iii), (v) and (vi) 2. (ii)

2.2

1. refer text 2. (i) FePO4 (ii) BaCl2 (iii) CaCO3 (iv) PBr3 (v) MgSO4 (vi) Na3PO4 (v) SO3 3. refer text 4. CH2, HCl, HNO3

2.3

1. 2814Si,

Si,

29 14

S

30 14

2. C3H8 = 44 u PCl5 = 207.5 u SO3 = 80 u 2.4

1. 3.08 × 1023 S atom 2. 1.77 × 10–22 g of Ag

2.5

1. (i) 4H3PO3 → 3H3PO4 + PH3 (ii) Ca + 2H2O → Ca(OH)2 + H2 (iii) C3H8 + 5O2 → 3CO2 + 4H2O 2. Sodium oxide, Cuperous chloride, Barium oxide, Sodium sulphate

GLOSSARY Atomic mass: The average mass of an atom in a representative sample of atoms of an element. Compound: Matter that is composed of two or more different kinds of elements chemically combined in definite proportions. Chemical reaction: A process in which substances are changed into other substances through rearrangement/combination of atoms. Diffusion: The gradual mixing of the molecules of two or more substances owing to random molecular motion.

: 48 : Structure and Properties of Matter

Element: Matter that is composed of one kind of atoms, each atom of a given kind having the same properties (Mass is one such property). Heterogeneous mixture: A mixture which has no uniformity in composition. Homogeneous mixture: A mixture with the same composition throughout Isotopes: Isotopes are atoms having the same atomic number, Z but different mass number, A. Mass number: Number of protons plus number of neutrons in the nucleus of an atom of an element. Matter: Anything that has mass and occupies space. Mole: Mole is amount of substance that contains as many elementary particles as there are atoms in 0.012 kg of C-12 isotope. Molar mass: The mass (in gram) of one mole of a substance. Molar volume: The volume of one mole of a substance. Molecular mass: The sum of atomic masses (in u) of all the atoms of a molecule.

3

Atomic Structure In the previous lesson, you have studied that the atoms are the smallest constituents of matter. But what is the structure of an atom? Why are atoms of different elements different? Let us try to find out the answers to some of these questions in this lesson. We will start the study of this lesson by recapitulating the postulates of Dalton’s atomic theory .At that time, many Greek philosophers believed that the atoms cannot be further subdivided, i.e. they were structure less entities. But as you will study in this lesson, various developments such as the discoveries of sub-atomic particles such as electron, proton etc. led to the failure of this idea. Based on these discoveries, various atomic models were proposed by the scientists. In this lesson, we would discuss how various models for the structure of atom were developed and what were their main features. We would explain the success as well as the shortcomings of these models. These models tell us about the distribution of various sub-atomic particles in the atom. From the knowledge of structure of atom the arrangement of electrons around the nucleus can be obtained. This arrangement is known as electronic configuration. The electronic configurations of some simple elements are discussed in this lesson These electronic configurations would be useful in explaining various properties of the elements. The electronic configuration of an element governs the nature of chemical bonds formed by it. This aspect is dealt in lesson 5 on chemical bonding. OBJECTIVES After completing this lesson, you should be able to: ! state the reasons of failure of Dalton’s atomic theory; ! name and list the fundamental particles present in the atom; ! recall the developments of various atomic models; ! list the shortcomings of Bohr’s atomic model; ! compute the electronic configuration of first 18 elements. 3.1 FAILURE OF DALTON’S ATOMIC THEORY You have read about Dalton’s atomic theory in lesson 2. Dalton’s theory explained various laws of chemical combination about which you have read earlier in lesson 2. At that time, the atom was considered to be indivisible. Later, certain experiments showed that an atom is made up of even smaller particles which are called subatomic particles. You will now study about the discovery of these subatomic particles namely electrons, protons and neutrons.

: 52 : Atomic Structure

3.1.1 Discovery of electron During 1890s’ many scientists performed experiments using cathode ray tubes. A cathode ray tube is made of glass from which most of the air has been removed. Such a cathode ray tube has been shown in Fig. 3.1. You can see in the figure that there are two metal electrodes; the negatively charged electrode is called cathode whereas the positively charged electrode is called anode.

High

Volta g

e

(–)

Metal electrode (Cathode)

(+)

Evaluated glass vessel

Fig. 3.1 Cathode ray

Metal electrode (anode) tube

An English physicist J.J. Thomson studied electric discharge through a cathode ray tube. When high voltage was applied across the electrodes, the cathode emitted a stream of negatively charged particles, called electrons. mass =

=

charge of the electron charge per unit mass of the electron

1.60 ×10−19 C e = = 9.10 ×10-28 g e / m 1.76 ×108 C g −1

Since the electrons were released from the cathode irrespective of the metal used for it or irrespective of the gas filled in the cathode ray tube, Thomson concluded that all atoms must contain electrons. Robert Millikan (1868-1953) received the Nobel prize in Physics in 1923 for determining the charge of the electron. The discovery of the electron led to the conclusion that the atom was no more indivisible as was believed by Dalton and others. Hence, the idea of indivisibility of atom as suggested by Dalton was proved incorrect. In other words, the atom was found to be divisible. If the atom was divisible, what were are its constituents? You have read above that one such particle is an electron. Now, what are the other particles present in an atom? Let us study the next section and find out the answer. 3.1.2 Discovery of proton In 1886, Eugen Goldstein observed that rays flowing in a direction opposite to that of the cathode rays were positively charged. Such rays were named as canal rays because they passed through the holes or the canals present in the perforated cathode. In 1898, Wilhelm

Atomic Structure : 53 :

Wien, a German physicist, measured e/m for canal rays. It was found that the particles constituting the canal rays are much heavier than electrons. Also unlike cathode rays, the nature and the type of these particles varied depending upon the gas present in the cathode ray tube. The canal rays had positive charges which were whole number multiples of the amount of charge present on the electron. The positive nature of the canal rays was explained as follows: In a cathode ray tube, the electrons emitted from the cathode collide with the atoms of the gas present in the tube and knock out one or more electrons present in them. This leaves behind positive ions which travel towards the cathode. If the cathode has holes in it ,then these positive ions can pass through these holes or canals. Hence, they are called the canal rays. The canal rays are shown in Fig. 3.2. Anode

Cathode +

+ +

+

+

+ +

+

Fig. 3.2 Canal rays

When the cathode ray tube contained hydrogen gas, the particles of the canal rays obtained were the lightest and their e/m ratio was the highest. Rutherford showed that these particles were identical to the hydrogen ion (hydrogen atom from which one electron has been removed). These particles were named as protons and were shown to be present in all matter. Now it is the time to check your understanding. For this, take a pause and solve the following questions: CHECK YOUR PROGRESS 3.1 1. Name the extremely small particles which constitute matter. 2. What do we call the negatively charged particles emitted from the cathode? 3. What is a cathode ray tube? 4. What is an anode? 5. Why the canal rays obtained by using different gases have different e/m values? 3.2 EARLIER MODELS OF ATOM Based on the experimental observations, different models were proposed for the structure of the atom. In this section, we will discuss two such models namely Thomson model and Rutherford model. 3.2.1 Thomson model All matter is made of atoms and all the atoms are electrically neutral. We have just seen that all atoms contain the electrons. Based on these facts, Thomson concluded that there must be an equal amount of positive charge present in the atom. He proposed that an atom could be considered as a sphere of uniform positive charge in which electrons are embedded. This is shown below in Fig.3.3.

: 54 : Atomic Structure Special cloud of positive charge

This model is similar to a water-melon according to which an atom can be thought of as a sphere of positive charge in which the electrons are embedded like seeds. This model is also called plum pudding model or raisin pudding model because the electrons resembled the raisins dispersed in a pudding (an English dessert).

Electrons

During this period only, the phenomenon of Fig. 3.3 Thomson model of atom radioactivity was also being studied by the scientists. This phenomenon of spontaneous emission of rays from atoms of certain elements also proved that the atom was divisible and it contained sub –atomic particles. Ernest Rutherford and his coworkers were also carrying out experiments which revealed that the radiation could be of three types: α(alpha), β(beta) and γ(gamma). You will study more about them in lesson 14. In 1910, Rutherford and his co-workers performed an experiment which led to the downfall of the Thomson model. Let us now study about the contribution of Rutherford. 3.2.2 Rutherford’s model Rutherford who was a student of J.J Thomson was studying the effect of alpha (a) particles on matter. The alpha particles are helium nuclei. They are obtained by the removal of two electrons from the helium atom. Hans Geiger (Rutherford’s technician) and Ernest Marsden (Rutherford’s student) directed α particles from α radioactive source on a thin piece of gold foil (about 0.00004 cm thick). This is shown below in Fig. 3.4. Ernest Rutherford, (1871-1937) who received the Nobel Prize in Chemistry in 1908 for proposing the nuclear model of the atom. Beam of a particles

Scattered of a particles

–

– –

–

– –

+ –

–

– –

–

Circular fluorescent screen

–

Thin gold foil (a)

Most particles are undeflected

–

(b)

Fig.3.4 (a) The experimental set-up for the α particle bombardment on thin gold foil, (b)Scattering of α particles

If Thomson model was correct,then most of the a particles should pass through the gold foil and their path should only be deflected by a small amount. They were surprised to find out that although the majority of the a particles passed through the gold foil undeflected (or were deflected with minor angles), some of them were deflected by a large angles and a few even bounced back. This is shown in Fig. 3.4(b). In 1911, Rutherford explained the above observation by proposing another model of the atom. He suggested that :

Atomic Structure : 55 :

(i) Most of the mass of atom and all of its positive charge reside in a very small region of space at the centre of the atom, called the nucleus. (ii) The electrons revolve around the nucleus in circular paths. This model is also known as Rutherford’s nuclear model of the atom and is shown in Fig. 3.5.

– Electron

+ Nucleus

This model resembeled the solar system in which the Fig. 3.5 Rutherford’s nuclear nucleus was similar to the Sun and the electrons were similar model of atom to the planets. Ruthurford was able to predict the size of the nucleus by carefully measuring the fraction of α particles deflected. He estimated that the radius of the nucleus was atleast 1/10000 times smaller than that of the radius of the atom. We can imagine the size of the nucleus with the following similarity. If the size of the atom is that of a cricket stadium then the nucleus would have the size of a fly at the centre of the stadium. Thus, most of the space in the atom is empty through which the majority of the αparticles could pass. When the α- particles come close to the nucleus, they are repelled by its positive charge and hence they show a large deflection. Wherefrom this positive charge comes in the nucleus? The nucleus was supposed to contain positively charged particles, called protons. The positive charge on a proton was equal but opposite in nature to that on an electron. This quantity of charge, i.e. 1.602 x 10 –19 C is called the electronic charge and is expressed as a unit charge, i.e., the charge of an electron is –1 whereas that of a proton is +1. CHECK YOUR PROGRESS 3.2 1. Who proposed the nuclear model for the structure of atom? 2. Define nucleus. 3. What is a proton? 3.3 DISCOVERY OF NEUTRON Although Rutherford’s model of the atom could explain the electrical neutrality and the results of scattering experiment but a major problem regarding the atomic masses remained unsolved. The mass of helium atom (which contains 2 protons) should be double than that of a hydrogen atom (which contains only one proton). [The electron being very light weight particle as compared to that of a proton, its contribution to the atomic mass can be ignored]. Actual ratio of helium and hydrogen masses is 4:1. Rutherford and others, thus, suggested that there must be one more type of subatomic particle present in the nucleus which may be neutral but must have mass. Later in 1932, James Chadwick showed the existence of this third type of subatomic particle. This was named as neutron. The neutron was found to have a mass slightly higher than that of a proton electrically neutral. Thus, if the helium atom contained 2 protons and 2 neutrons in the nucleus, its mass ratio to hydrogen as 4:1 could be explained. The characteristics of these three particles, called as fundamental particles are given in Table 3.1.

: 56 : Atomic Structure

James Chadwick (1891-1972) was a British physicist. He received the Nobel prize in 1935 for showing the existence of neutron in the nucleus of an atom. Table 3:1 Characteristics of the subatomic particles. Particle

Symbol

Mass(kg)

Charge

Coulomb (C) in multiple units

Electron Proton Neutron

e p n

9.10939 x 10-31 1.67262 x 10-27 1.67493 x 10-27

–1.6022x10-19 +1.6022 x 10-19 0

-1 +1 0

CHECK YOUR PROGRESS 3.3 1. What is a neutron? 2. How many neutrons are present in the α-particle? 3. How will you distinguish between an electron and a proton? 3.4 ATOMIC NUMBER, MASS NUMBER AND ISOTOPES Why do the atoms of different elements differ from each other? The numbers of protons present in the atom of an element are different from those present in the atom of another element. Thus, the number of protons present in the atom of each element is fixed and is a characteristic property of that element as you have already learnt in lesson 2. This number is called the atomic number and is denoted by Z .Hydrogen has one proton in its nucleus and therefore, its atomic number is 1. Similarly, two protons are present in the nucleus of helium atom and hence its atomic number is 2. What about the number of electrons present in hydrogen and helium? Since the atom is electrically neutral, the number of electrons present in these atoms is 1 and 2 respectively.In addition to the protons, the helium atom also has neutrons present in its nucleus. The total number of protons and neutrons present in the nucleus of an atom of an element is called its mass number. It is denoted by A. Helium nucleus contains 2 protons and 2 neutrons; hence, its mass number is 4.The atomic number and the mass number of an element (X) can be denoted as follows: A Z

X

Thus, helium can be represented as 42H Similarly, 126C means that the carbon atom has 6 protons and hence 12–6 = 6 neutrons. But some carbon atoms can have 7 or 8 neutrons also. The mass number of these carbon atoms would be 6+7=13 or 6+8=14.Such atoms which have the same atomic number but have different mass number are called isotopes. Thus, carbon has three isotopes. These isotopes can be represented as shown below: 12 6

C,

13 6

C,

14 6

C

CHECK YOUR PROGRESS 3.4 1. How is atomic number related to the number of protons present in the atom? 2. What is the mass number of an atom which has 7 protons and 8 neutrons? 3. Calculate the number of neutrons present in the following isotopes of hydrogen. 1 H, 12H, 13H 1

Atomic Structure : 57 :

3.5 DRAWBACKS OF RUTHERFORD’S MODEL As you have studied in section 3.3, Rutherford’s model could not solve the problem of atomic mass. The existence of the neutron thus accounted for the mass of the atom. Another drawback which Rutherford’s model suffered was that it could not explain the stability of the atom. According to the electromagnetic theory of radiation, a moving charged particle, such as the electron which is constantly accelerating because of change in directions of motion, should emit radiation. The energy of the radiation would come from the motion of the electron. Thus, the electron would emit radiation and follow a spiral path as shown in Fig.3.6.

Fig. 3.6 Spiral path of an electron

The energy of the electron would keep on decreasing (as the electron would keep on emitting radiation) till the electron finally falls into the nucleus. But actually it does not happen. The electron does not collapse into the nucleus. Thus, Rutherford’s model needed the improvements which were later on suggested by Bohr. Bohr’s model now will be discussed in the next section. CHECK YOUR PROGRESS 3.5 1. What were the two drawbacks of Rutherford’s model? 3.6 BOHR’S MODEL OF ATOM In 1913, Niels Bohr proposed a model which was an improvement over Rutherford’s nuclear model. Bohr proposed that an electron moves around the nucleus in a well defined circular path. He set down following two main postulates to explain the stability of atom particularly hydrogen atom (i) An electron can have only a definite circular path around the nucleus with specific energy values. This circular path he called orbit or energy level (ii) Electron may go to next higher energy level (orbit) when given a definite amount of energy. In other words, an electron absorbs energy when it goes to higher energy level from a lower energy level. Contrary to this, electron will emits out a definite amount of energy when it comes from a higher energy level to lower energy level. If E2 is energy of an electron in higher energy level and E1 is energy of electron in lower energy level, then energy released ∆E will be expressed as, ∆E = E2 – E1 If the electron remians in the same orbit, the energy would neither be released nor absorbed. These orbits will, therefore, were called stationary orbits or stationary states. Niels Bohr (1885-1962). He was a Danish physicist He was awarded the Nobel Prize in Physics in 1922. Although Bohr model could explain a number of aspects related to hydrogen atom but it could not explain stability of atoms having more than one electron. After the nature of electron was studied in detail, it was found that an electron cannot remain in a fixed circular orbit as envisaged by Bohr. Bohr model was rejected on this ground.

: 58 : Atomic Structure

Based on the nature of electron, concept of circular orbit was modified and a three dimensional shell with definite energy came into existence. These shells are similar to circular path/energy levels given by Bohr. These shells are represented by letters K, L, M, N etc. Each shell is associated with a definite energy. The energies of these shells go on increasing as we move away from the nucleus. The maximum number of electrons which can be accommodated in each shell is given by 2n2 where n can take values 1, 2, 3….etc. Thus, the first shell can have two electrons whereas the second shell can have 8 electrons. Similarly the maximum number of electrons present in third and fourth shells would be 18 and 32, respectively. Each shell could be further sub-divided into various sublevels of energy called subshells. These subshells are denoted by letters s, p, d, f, etc about which you would study in your higher classes. CHECK YOUR PROGRESS 3.6 1. What are stationary states? 2. What will happen to the energy of electron when it goes from an orbit of higher energy to that of a lower energy? 3. What is a shell? 4. How many electrons can be present in a L-shell? 3.7 ELECTRONIC CONFIGURATION OF ELEMENTS From the above discussions, you are aware that shells of different energies exist in an atom. The electrons occupy these shells according to the increasing order of their energy. You also know that the first shell can have two electrons whereas the second shell can accommodate eight electrons. Keeping these points in mind, let us now study the filling of electrons in various shells of atoms of different elements. Hydrogen atom has only one electron. Thus electronic configuration of hydrogen can be represented as 1. The next element helium (He) has two electrons in its atom. Since the first shell can accommodate two electrons; hence, this second electron can also be placed in first shell. The electronic configuration of helium can be represented as 2. The third element, Lithium (Li) has three electrons. Now the two electrons occupy the first shell whereas the third electron goes to the next shell of higher energy level, i.e. second shell. Thus, the electronic configuration of Li is 2, 1. Similarly, the electronic configurations of beryllium (Be) and boron (B) having four and five electrons respectively can be written as follows: Be 4 electrons Electronic configuration - 2, 2. B 5 electrons Electronic configuration - 2, 3. The next element carbon (C) has 6 electrons. Now the sixth electron also goes to the second shell which can accommodate eight electrons. Hence, the electronic configuration of carbon can be represented as 2, 4. Similarly, the next element nitrogen having 7 electrons has the electronic configuration 2, 5. The electronic configuration of other elements can be given on the same lines. The electronic configuration of first twenty elements is given in Table 3.2 and depicted in Fig. 3.7.

Atomic Structure : 59 :

Fig. 3.7 Electronic configuration of some elements

Table 3.2: Electronic distribution in shells of first twenty elements Element/symbol

No. of electrons

Hydrogen, H Helium, He Lithium, Li Beryllium, Be Boron, B Carbon, C Nitrogen, N Oxygen, O Fluorine, F Neon, Ne Sodium, Na

1 2 3 4 5 6 7 8 9 10 11

Magnesium, Mg

12

Aluminium, Al

13

Silicon, Si

14

Phosphorus, P

15

Sulphur, S

16

Chlorine, Cl

17

Argon, Ar

18

Potassium, K

19

Calcium, Ca

20

Arrangement of electrons in shells Electrons Common distribution valency in shells 1 in first shell 2 in first shell 2 in first shell + 1 in second shell 2 in first shell + 2 in second shell 2 in first shell + 3 in second shell 2 in first shell + 4 in second shell 2 in first shell + 5 in second shell 2 in first shell + 6 in second shell 2 in first shell + 7 in second shell 2 in first shell + 8 in second shell 2 in first shell + 8 in second shell + 1 in third shell 2 in first shell + 8 in second shell + 2 in third shell 2 in first shell + 8 in second shell + 3 in third shell 2 in first shell + 8 in second shell + 4 in third shell 2 in first shell + 8 in second shell + 5 in third shell 2 in first shell + 8 in second shell + 6 in third shell 2 in first shell + 8 in second shell + 7 in third shell 2 in first shell + 8 in second shell + 8 in third shell 2 in first shell + 8 in second shell + 8 in third shell + 1 in fourth shell 2 in first shell + 8 in second shell + 8 in third shell + 2 in fourth shell

1 2 2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8 2,8,1

1 0 1 2 3 4 3 2 1 0 1

2,8,2

2

2,8,3

3

2,8,4

4

2,8,5

3,5

2,8,6

2

2,8,7

1

2,8,8

0

2,8,8,1

1

2,8,8,2

2

: 60 : Atomic Structure

3.7.1 Valence electron and valency We have just discussed the electronic configuration of first 20 elements. We can see from the table 3.2 that electrons are located in different shells around the nucleus. The electrons in the last shell (popularly known as valence shell) govern the chemical properties of the atoms. These electrons are known as valence electrons. Valency or combining capacity of an atom of an element depends on the number of these electrons as mentioned in lesson 2. Valency of 20 elements along with their electronic configuration is also provided in Table 3.2. In next lesson, you would study how these electronic configurations are useful in understanding the periodic arrangement of elements. These electronic configurations are also helpful in studying the nature of bonding between various elements which will be dealt in lesson 5. CHECK YOUR PROGRESS 3.7 1. How many shells are present in the nitrogen atom? 2. Name the element which has the completely filled first shell. 3. The electronic configuration of an element having atomic number11 is_____________ ! ! !

! ! ! ! ! !

LET US REVISE Electrons are present in all the atoms. Thomson proposed the plum-pudding model of the structure of atom. Rutherford’s model of the structure of atom suggested that most of the mass and all of positive charge of an atom is concentrated in its nucleus and the electrons revolve around it in. The neutrons are neutral particles present in the nucleus. Atomic number is the number of protons present in the nucleus of an atom. Mass number gives the number of protons and neutrons present in an atom Isotopes have same atomic number but different mass numbers. Bohr’s model gave the idea of definite orbits or stationary states. The electrons occupy various shells in an atom in the increasing order of their energy. The maximum number of electrons which can be accommodated in a shell is 2n2. TERMINAL EXERCISES

A. Fill in the blanks. 1. The nucleus consists of ———————and ———————— 2. The model which resembled the solar system was proposed by—— 3. Anode rays travel towards—————————— 4. An electron has ——————— charge. B. Classify the following statements as true or false. 1. The plum pudding model was proposed by Rutherford. 2. Cathode is the negatively charged electrode. 3. Neutrons are constituents of atoms of all elements. 4. The number of electrons present in a neutral atom is always equal to the number of protons.

Atomic Structure : 61 :

C. Multiple choice type questions. 1. An α-particle has (a) 2 protons only. (b) 2 neutrons only (c) 2 protons and 2 neutrons (d) 2 neutrons 2. Isotopes have (a) same mass number (b) same atomic number (c) different atomic number (d) same mass as well as atomic number 3. The mass of a neutron (a) is less than that of a proton. (b) is greater than that of a proton. (c) is equal to that of a proton. (d) zero 4. The filling of second shell starts with (a) He (b) Li (c) C (d) N 5. The electronic configuration of Cl is (a) 2, 8 (b) 2, 8, 4 (c) 2, 8, 6 (d) 2, 8, 7 6. Which of the following elements has completely filled shells? (a) H (b) O (c) Ne (d) Mg D. Descriptive type questions. 1. How can you say that electrons are present in all types of matter? 2. Define an orbit. 3. Calculate the number of neutrons present in 168O and 199F 4. The mass number of iron is 56. If 30 neutrons present in its atom, what is its atomic number? 5. Which of the following are isotopes? 126C, 146C, 147N ANSWERS TO CHECK YOUR PROGRESS 3.1 1. 2. 3. 4. 5. 3.2 1. 2.

atoms electrons A glass tube from which most of the air has been removed. It has two electrodes. It is a positively charged electrode. because the positive ions resulting from the different gases have different masses.

J.J. Thompson The small region of space at the centre of the atom where most of the mass and all of the positive charge is located. 3. An alpha particle is the helium nucleus which is obtained by the removal of two electrons from the helium atom. 3.3 1. A neutron is a neutral subatomic particle having mass slightly higher than proton. 2. 2 3. (i) An electron has negative charge whereas a proton has a positive charge.

: 62 : Atomic Structure

(ii) An electron is present outside the nucleus whereas a proton is present in the nucleus. (iii) The electron has very less mass as compared to a proton. 3.4 1. 2. 3. 3.5 1. 3.6 1.

Atomic number is equal to the number of protons present in the nucleus of the atom. 15 0, 1, 2. It could not explain the correct atomic masses and the stability of atoms.

Stationary states are energy levels of definite energy. When an electron is present in a stationary state, its energy does not change. 2. Its energy would decrease. 3. A shell is a group of energy levels having similar energy. 4. 8 electrons. 3.7 1. 2 2. He 3. 2, 8, 1 GLOSSARY Alpha particles: Positively charged particles ejected at high speeds from certain radioactive substances; Atom: The smallest particle of an element that retains the chemical properties of that elemen. Atomic nucleus: The tiny central core of an atom that contains neutrons and protons. Atomic number: The number of protons in the nucleus of an atom of an element. Electron: A negatively charged subatomic particle found in the space about the nucleus. Electron shell: The collectio of orbitals with same principal quantum number. Electronic configuration: The complete description of the orbitals occupied by all the electrons in an atom on ion. Isotopes: Forms of an element composed of atoms with same atomic number but different mass number owing to a difference in a number of neutrons. Mass number: The number of proton plus neutrons in the nucleus of an atom of an element. Neutrons: An electrically neutral subatomic particle found in the nucleus. Orbital: Regions occupied by electrons in S, P, d, f, subshells, represened by three dimensional boundary surface diagram.. Proton: A positively charged subatomic particle found in the nucleus.

4

Periodic Classification of Elements You must have visited a library. There are thousands of books in a large library. In spite of this if you ask for a particular book, the library staff can locate it easily. How is it possible? In library the books are classified into various categories and sub-categories. They are arranged on shelves accordingly. Therefore location of books becomes easy. In the last two lessons you have studied about the structure of atoms and their electronic configurations. You have also studied that elements with similar electronic configurations show similar chemical properties. Electrons are filled in various shells and subshells in a fairly regular fashion. Therefore, properties of elements are repeated periodically. Such trends in their physical and chemical properties were noticed by chemists in the nineteenth century and attempts were made to classify elements on their basis long before structure of atom was known. In this lesson we shall study about the earlier attempts for classification, the first successful classification which included all the known elements at that time namely Mendeleev’s periodic table, and about the long form of modern periodic table which is an improvement over Mendeleev’s work. Finally we shall learn about some properties of elements and their variations in the periodic table. OBJECTIVES After completing this lesson, you will be able to: ! state different historical classifications of elements in brief; ! state main features of Mendeleev’s periodic table; ! explain the defects of Mendeleev’s periodic table; ! state modern periodic law; ! describe the features of the long form of periodic table; ! define various periodic properties; ! discuss the trends in various periodic properties in the periodic table. 4.1 EARLIER ATTEMPTS OF CLASSIFICATION OF ELEMENTS The first classification of elements was as metals and non-metals. This served only limited purpose mainly because of two reasons: 1. All the elements were grouped in to these two classes only. Moreover the group containing metals was very big.

: 64 : Periodic Classification of Elements

2. Some elements showed properties of both-metals and non-metals and they could not be placed in any of the two classes. After this, scientists made attempts to recognize some pattern or regularity in variation of properties of elements and to classify them accordingly. Now we shall learn about some of them. 4.1.1 Dobereiner’s triads In 1829, Dobereiner, a German scientist made Element Atomic mass some groups of three elements each and called Lithium, Li 7 them triads. All three elements of a triad were Sodium, Na 23 similar in their properties. He observed that the Potassium, K 39 atomic mass* of the middle element of a triad was nearly equal to the arithmetic mean of atomic masses of other two elements. Also, same was the case with their other properties. Let us take the example of three elements lithium, sodium and potassium. They form a Dobereiner’s triad. Mean of the atomic masses of the first (Li) and the third (K) elements: 7 + 39 = 23 u 2

The atomic mass of the middle element, sodium, Na is equal to 23 u. Two more examples of Dobereneir’s triads are given below. Element

Atomic mass

Element

Calcium, Ca Strontium, Sr Barium, Ba

40 88 137

Chlorine, Cl Bromine, Br Iodine, I

Atomic mass 35.5 80 127

40 + 137 = 88.5 u 2 35.5 + 127 Mean of the first atomic masses of the and third elements = = 81.5 u 2 Actual atomic mass of the second element = 88 u

Mean of the atomic masses of the first and third elements =

Actual atomic mass of the second element = 80 u Dobereneir’s idea of classification of elements into triads did not receive wide acceptance as he could arrange only a few elements in this manner. 4.1.2 Newland’s law of Octaves In 1864 John Alexander Newland, an English chemist noticed that “when elements are arranged in the increasing order of their atomic masses* every eighth element had properties similar to the first element.” Newland called it the Law of Octaves. It was due to its similarity with musical notes where, in every octave, after seven different notes the eighth note is repetition of the first one as shown below. 1 lk

2 js

3 xk

*Then known as atomic weight

4 e

5 i

6 /k

7 uh

8 lk

Periodic Classification of Elements : 65 :

Look carefully at the Newland’s arrangement of elements shown below: Li

Be

B

C

N

O

F

(6.9)

(9.0)

(10.8)

(12.0)

(14.0)

(16.0)

(19.0)

Na

Mg

Al

Si

P

S

Cl

(23.0)

(24.3)

(27.0)

(28.1)

(31.0)

(32.1)

(35.5)

K (39.1)

Ca (40.1)

With the help of the arrangement given above, can you tell starting from lithium which is the eighth element? Sodium. And starting from sodium? It is potassium. Properties of all three are similar. Similarly, aluminnium is the eighth element from boron it shows properties similar to it. However, Newland could arrange elements in this manner only up to calcium out of a total of over sixty elements known at his time. Because of this shortcoming his work was not received well by the scientific community. The next break through in classification of elements came in the form of Mendeleev’s work. 4.1.3 MENDELEEV’S PERIODIC LAW AND PERIODIC TABLE 4.3.1a Mendeleev’s periodic law Dmitry Mendeleev** a Russian chemist while trying to classify elements discovered that on arranging in the increasing order of atomic mass*, elements with similar chemical properties occurred periodically. In1869, he stated this observation in the following form which is known as Mendeleev’s Periodic Law. A periodic function is the one which repeats itself after a certain interval. Thus, according to the periodic law the chemical and physical properties of elements repeat themselves after certain intervals when they are arranged in the increasing order of their atomic mass. Now we shall learn about the arrangement of elements on the basis of the periodic law. The chemical and physical properties of elements are a periodic function of their atomic masses*. A tabular arrangement of the elements based on the periodic law is called periodic table. Mendeleev believed that atomic mass of elements was the most fundamental property and arranged them in its increasing order in horizontal rows till he encountered an element which had properties similar to the first element. He placed this element below the first element and thus started the second row of elements. Proceeding in this manner he could arrange all the known elements according to their properties and thus created the first periodic table. ∗ Then known as atomic weight ** Also spelled as Mendeleef or Mendeleyev

: 66 : Periodic Classification of Elements PERIODIC TABLE (Modified form of Mendleeff’s Table) P E R I O D I C S

Group :

I

II

Oxide: Hydride:

R2O RH

RO RH2

A 1 2 3 4

5

First series second series First series second series First series

6

B

B

Be 4 9.012 Mg 12 24.312 Ca 20 40.08 Zn 30 65.37

Rb 37 85.47

Sr 38 87.62 Ag 47 107.87

Cs 55 132.90

second series

* Lanthaandie

IV

V

VI

VII

R2O5 RH4

R2O5 RH3

RO3 RH2

R2O7 RH

A

B

B5 10.811 Al 13 26.981

A

B

C6 12.011 Si 14 28.086 Sc 21 44.96

Ga 31 69.72

Cd 48 112.40

Ge 32 72.59

In 49 114.82

Hg 80 200.59 Ra 88 (226)

Tl 81 204.37 Actinide Elements 89-103

B

N7 14.007 P 15 30.974

Zr 40 91.22

B

O8 15.999 S 16 32.06 Cr 24 51.99 Se 34 78.96

Nb 41 92.906 Sb 51 121.75

Hf 72 178.49 Pb 82 207.19 Ku 104

A

V 23 50.94 As 33 74.92

Sn 50 118.69 *Rare Earths 57-71

A

Ti 22 47.90

Y 39 88.905

Ba 56 137.34 Au 79 196.97

Fr 87 (223)

7

A

H 1 (At. No.) 1.008(At.Wt.) Li 3 6.939 Na 11 22.99 K 19 39.102 Cu 29 63.54

III R2O3 RH3

Po 84 (210)

Zero Noble gases

B

Tc 43 (99)

He 2 4.0026 Ne 10 20.183 Ar 18 39.948 Fe 26 Co 27 Ni 28 55.85 58.93 58.71 Kr 36 83.80 Ru 44 Rh 45 Pd 46 101.07 102.91 106.4

I 53 124.9014

W 74 183.85

Ta 73 180.948

Ro4 Transition Traids

F9 18.998 Cl 17 35.453 Mn 25 54.939 Br 35 79.909

Mo 42 95. 94 Te 52 127.60

Bi 83 208.98

A

VII

Xe 54 131.30 Re 75 186.2

O s 76 Ir 77 Pt 78 190.2 192.2 195.09

At 85 (210)

Rn 86 (222)

Ha 105

( La 57 Ce 58 Pr 59 Nd 60 Pm 61 Sm 62 Eu 63 Gd 64 Tb 65 Dy 66 Ho 67 Er 68 Tm 69 Yb 70 Lu 71 ( 138.91 140.12 140.91 144.24 (147) 150.35 151.96 157.25 158.92 162.50 164.93 167.26 168.93 173.04 174.97

Elements (Rare Earth Series) Actinide Series ( Ac 89 Th 90 Pa 91 U 92 Np 93 Pu 94 Am 95 Cm 96 Bk 97 Cf 98 Es 99 Fm 100 Md 101 No 102 Lr 103 ( (227) 232.04 (231) 238.3 (237) (244) (243) (245) (247) (249) (254) (253) (256) (253) (257)

Fig. 4.1 Mendeleev’s periodic table

4.1.3b Main features of Mendeleev’s periodic table Look at the Mendeleev’s periodic table shown in fig.4.2 carefully. What do you observe? Here, elements are arranged in tabular form in rows and columns. Now let us learn more about these rows and columns and the elements present in them. 1. The horizontal rows present in the periodic table are called periods. You can see that there are seven periods in the periodic table. These are numbered from 1 to 7 (Arabic numerals). 2. Properties of elements in a particular period show regular gradation (i.e. increase or decrease) from left to right. 3. The vertical columns present in it are called groups. You must have noticed that these are nine in number and are numbered from I to VIII and Zero (Roman numerals). 4. Groups I to VII are subdivided into A and B subgroups. Groups Zero and VIII don’t have any subgroups. 5. All the elements in a particular group are chemically similar in nature. They show regular gradation in their physical properties and chemical reactivities. After learning about the main features we shall now learn about the main merits of Mendeleev’s periodic table. 4.1.3c Merits of Mendeleev’s periodic classification 1. Classification of all elements Mendeleev’s was the first classification which successfully included all the elements. 2. Prediction of new elements Mendeleev’s periodic table had some blank spaces in it. These vacant spaces were for elements that were yet to be discovered. For example, he proposed the existence of an

Periodic Classification of Elements : 67 :

unknown element that he called eka-aluminium. The element gallium was discovered four years later and its properties matched very closely with the predicted properties of ekaaluminium. In this section we have learnt about the success of Mendeleev’s periodic classification and also about its merits. Does it mean that this periodic table was perfect? No. Although it was a very successful attempt but it also had some defects in it. Now we shall discuss the defects in this classification. 4.3.1d Defects in Mendeleev’s periodic classification In spite of being a historic achievement Mendeleev’s periodic table had some defects in it. The following were the main defects in it: 1. Position of hydrogen Hydrogen resembles alkali metals (forms H+ ion just like Na+ ions) as well as halogens ( forms H- ion similar to Cl- ion).Therefore, it could neither be placed with alkali metals (group I ) nor with halogens (group VII ). 2. Position of isotopes Different isotopes of same elements have different atomic masses, therefore, each one of them should be given a different position in the periodic table. On the other hand, because they are chemically similar, they had to be given same position. 3. Anomalous pairs of elements At certain places, an element of higher atomic mass has been placed before an element of lower atomic mass. For example, Argon (39.91) is placed before potassium (39.1) CHECK YOUR PROGRESS 4.1 1. Elements A, B and C constitute a Dobereiner’s triad. What is the relationship in their atomic masses? 2. How many elements were included in the arrangement given by Newland? 3. Which property of atoms was used by Mendeleev to classify the elements? 4. How many groups were originally proposed by Mendeleev in his periodic table? 5. Where in the periodic table are chemically similar elements placed, in a group or in a period? 6. Mendeleev’s periodic table had some blank spaces in it. What do they signify? 7. What name was given to the element whose properties were similar to the element eka-aluminium predicted by Mendeleev? 4.2 MODERN CLASSIFICATION Henry Moseley, an English physicist discovered in the year 1913 that atomic number, is the most fundamental property of an element and not its atomic mass. Atomic number, (Z), of an element is the number of protons in the nucleus of its atom. The number of electrons in the neutral atom is also equal to its atomic number. This discovery changed the whole perspective about elements and their properties to such an extent that a need was felt to change the periodic law also. Now we shall learn about the changes made in the periodic law. 4.2.1 Modern periodic law After discovery of atomic number the periodic law was modified and the new law was based upon atomic numbers in place of atomic masses of elements.

: 68 : Periodic Classification of Elements

The Modern Periodic Law states “The chemical and physical properties of elements are a periodic function of their atomic numbers” After the change in the periodic law many changes were suggested in the periodic table. Now we shall learn about the modern periodic table which finally emerged. 4.2.2 Modern periodic table The periodic table based on the modern periodic law is called the Modern Periodic Table. Many versions of this periodic table are in use but the one which is most commonly used is the Long Form of Modern Periodic Table. It is shown in figure 4.3. 1

2

H

He

3

4

5

6

7

8

9

10

Li

Be

B

C

N

O

F

Ne

11

12

13

15

16

17

18

Al Si

P

S

Cl

Ar

31

33

34

35

Na Mg 19

20

21

22

23

24

K

Ca Sc

Ti

V

Cr Mn Fe Co Ni Cu

37

38

39

40

41

42

Rb Sr Y

Zr

55

56

57

58

Cs Ba La 87

88

89

90

Fr Ra Ac

59

Ce Pr 91

61

60

62

63

64

65

66

67

68

69

70

71

72

25 43

26 44

27 45

76

74

75

77

106

Th Pa U

96

97

98

99

100

101

102

103

104

47

73

Ru Re Os Ir

95

29

Ru Rh Pd Ag

92

94

46

Nb Mo Tc

Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta 93

28

105

78

79

Pt Au

30

14 32

Zn Ga Ge As Se Br 48

49

50

51

52

53

Cd In Sn Sb Te I 80

81

82

83

Hg Tl Pb Bi

84

85

Po At

36

Kr 54

Xe 86

Rn

Np Pu Am Cm Bk Cf Es Fm Md No Lr Unq Unp Unh

Fig. 4.3 Modern periodic table

If you look at the modern periodic table shown in the fig.4.3 you will observe that it is not much different from Mendeleev’s periodic table. Now let us learn the main features of this periodic table. 4.2.2a Groups There are 18 vertical columns in the periodic table. Each column is called a group. The groups have been numbered from 1 to 18 (in Arabic numerals) from left to right. Group 1 on extreme left position contains alkali metals (Li, Na, K, Rb, Cs and Fr) and group 18 on extreme right side position contains noble gases (He, Ne, Ar, Kr, Xe and Rn). All elements present in a group have similar electronic configurations and have same number of valence electrons. You can see in case of group 1 (alkali metals) and group 17 elements (halogens) that as one moves down a group, more and more shells are added. Group 1

Group 17

Element

Electronic configuration

Element

Electronic configuration

Li Na K Rb

2,1 2,8,1 2,8,8,1 2,8,8,8,1

F Cl Br I

2,7 2,8,7 2,8,8,7 2,8,18,8,7

All elements of group 1 have only one valence electron. Li has electrons in two shells, Na in three, K in four while Rb has electrons in five shells. Similarly all the elements of group 17 have seven valence electrons however the number of shells is increasing from two in F to five in I. ●

Elements present in groups 1 and 2 on left side and groups 13 to 17 on the right side of the periodic table are called normal elements or representative elements. Their outermost shells are incomplete. They are also called typical or main group elements

Periodic Classification of Elements : 69 : ●

Elements present in groups 3 to 12 in the middle of the periodic table are called transition elements. (Although groups 11 and 12 elements are, strictly speaking, not transition elements). Their two outermost shells are incomplete. However, it should be noted here that more and more electrons are added to valence shell only in case of normal elements. In transitions elements, the electrons are added to incomplete inner shells. Elements 113, 115 and 117 are not known but included at their expected positions.

Group 18 on extreme right side of the periodic table contains noble gases. Their outermost shells contain 8 electrons. ● Inner transition elements:14 elements with atomic numbers 58 to 71 (Ce to Lu) are called lanthanides# and they are placed along with the element lanthanum (La), atomic number 57 in the same position (group 3 in period 6) because of very close resemblance between them. However, for convenience sake they are shown separately below the main periodic table ● 14 elements with atomic numbers 90 to103 (Th to Lr) are called actinides* and they are placed along with the element actinium (Ac), atomic number 89 in the same position (group 3 in period 7) because of very close resemblance between them. They are shown also separately below the main periodic table along with lanthanides. 4.2.2b Periods There are seven rows in the periodic table. Each row is called a period. The periods have been numbered from 1 to 7 (Arabic numerals). ●

In each period a new shell starts filling up. The period number is also the number of shell which starts filling up in it. For example, in elements of 3rd period, the third shell (M shell) starts filling up as we move from left to right@ . The first element of this period sodium Na (2,8,1) has only one electron in its valence shell (third shell) while the last element of this period, argon Ar (2,8,8) has eight electrons in its valence shell. The gradual filing of the third shell can be seen below.

! ! ! ! @

Element

Na

Mg

Al

Si

P

S

Cl

Ar

Electronic configuration

2,8,1

2,8,2

2,8,3

2,8,4

2,8,5

2,8,6

2,8,7

2,8,8

The first period is the shortest period of all and contains only 2 elements, H and He. The second and third periods are called short periods and contain 8 elements each. Fourth and fifth periods are long periods and contain 18 elements each. Sixth and seventh periods are very long periods containing 32 elements* * each.

However, it should be noted here that more and more electrons are added to valence shell only in case of normal elements. In transitions elements, the electrons are added to incomplete inner shells. # These elements have been named after the 1st elements lanthanum present in their position in the periodic table. * These elements have been named after the 1st elements actinium present in their position in the periodic table. ** Including elements up to atomic number 118. Elements 114, 116 and 118 have been reported only recently.

: 70 : Periodic Classification of Elements

4.2.2c Merits of modern periodic table over Mendeleev’s periodic table The modern periodic table is based on atomic number which is more fundamental property of an atom than atomic mass. The long form of modern periodic table is therefore free of main defects of Mendeleev’s periodic table. 1. Position of isotopes All isotopes of the same elements have different atomic masses but same atomic number. Therefore, they occupy the same position in the modern periodic table which they should have because all of them are chemically similar. 2. Anomalous pairs of elements When elements are arranged in the periodic table according to their atomic numbers the anomaly regarding certain pairs of elements in Mendeleev’s periodic table disappears. For example, atomic numbers of argon and potassium are 18 and 19 respectively. Therefore, argon with smaller atomic number comes before potassium although its atomic mass is greater and properties of both the elements match with other elements of their respective groups. CHECK YOUR PROGRESS 4.2 1. According to the modern periodic law the properties of elements are periodic function of which property of theirs? 2. List any two defects of Mendeleev’s periodic table which have been corrected in the modern periodic table? 3. How many group and periods are present in the long form of periodic table? 4. What is the name of the family of elements present in group 2 of the modern periodic table? 5. The elements that are present in the right hand portion of the periodic table are metals or non-metals? 6. How many elements are present in 6th period of the periodic table? 4.3 PERIODIC PROPERTIES In the previous section we have learnt about the main features of the Modern Periodic Table. We have also learnt that in a period the number of valence electrons and the nuclear charge increases from left to right. It increases the force of attraction between them. In a group the number of filled shells increases and valence electrons are present in higher shells. This decreases the force of attraction between them and the nucleus of the atom. These changes affect various properties of elements and they show gradual variation in a group and in a period and they repeat themselves after a certain interval of atomic number. Such properties are called periodic properties. In this section we shall learn about some periodic properties and their variation in the periodic table. 4.3.1 VALENCY (a) Valency in a period : You have already learnt in the previous section that the number of valence electrons increases in a period. In normal elements it increases from 1 to 8

Periodic Classification of Elements : 71 :

in a period from left to right. It reaches 8 in group 18 elements (noble gases) which show practically no chemical activity under ordinary conditions and their valency is taken as zero. Carefully look at the table given below. What do you observe? Valency of normal elements with respect oxygen increases from 1 to 7 as shown below for elements of third period. This valency is equal to the number of valence electrons or group number for groups 1 and 2, or (group number-10) for groups 13 to 17. Group Element No. of valence electrons Valency with respect to oxygen

1 Na 1 1

2 Mg 2 2

13 Al 3 3

14 Si 4 4

15 P 5 5

16 S 6 6

17 Cl 7 7

Formula of oxide

Na2O

MgO

Al2O3

SiO2

P4O10

SO3

Cl2O7

In the following table for elements of second period you will observe that valency of elements of with respect to hydrogen and chlorine increases from 1 to 4 and then decreases to 1 again. Group Element No. of valence electrons Valency with respect to hydrogen and chlorine Formula of hydride Formula of chloride

1 Li 1 1

2 Be 2 2

13 B 3 3

14 C 4 4

15 N 5 3

16 O 6 2

17 F 7 1

LiH LiCl

BeH2 BeCl2

BH3 BCl3

CH4 CCl4

NH3 NCl3

H2O Cl2O

HF ClF

(b) Valency in a group : All the elements of a group have the same number of valence electrons. Therefore, they all have the same valency. Thus valency of all group 1 elements, alkali metals, is 1. Similarly valency of all group 17 elements, halogens, is 1 with respect to hydrogen and 7 with respect to oxygen. 4.3.2 Atomic radii A number of physical properties like density and melting and boiling points are related to the sizes of atoms. Atomic size is difficult to define. Atomic radius determines the size of an atom. For an isolated atom it may be taken as the distance between the centre of atom and the outermost shell. Practically, measurement of size of an isolated atom is difficult; therefore, it is measured when an atom is in company of another atom of same element. It is defined as one-half the distance between the nuclei of two atoms when they are linked to each other by a single covalent bond. 4.3.2a Variation of atomic radii in a period Atomic radii (in picometer) of 2nd and 3rd period elements are given in the table given below. What do you observe? In a period, atomic radius generally decreases from left to right. 2nd Period

Li 155

Be 112

B 98

C 91

N 92

O 73

F 72

3rd Period

Na 190

Mg 160

Al 143

Si 132

P 128

S 127

Cl 99

: 72 : Periodic Classification of Elements

Can you explain this trend? You have learnt in the beginning of this section that in a period there is a gradual increase in the nuclear charge. Since valence electrons are added in the same shell, they are more and more strongly attracted towards nucleus. This gradually decreases atomic radii. 4.3.2b Variation of atomic radii in a group What happens to atomic radii in a group? Atomic radii increase in a group from top to bottom. This can be seen from the data of atomic radii in picometers given for groups 1 and 17 elements below. Element Li

Atomic radius 155

Element F

Atomic radius 72

Na K

190 235

Cl Br

99 114

Rb

248

I

133

As we go down a group the number of shells increases and valence electrons are present in higher shell and the distance of valence electrons from nucleus increases. For example, in lithium the valence electron is present in 2nd shell while in sodium it is present in 3rd shell. Also, the number of filled shells between valence electrons and nucleus increases. Thus in group 1 Li (2,1) has one filled shell between its nucleus and valence electron while Na (2,8,1) has two filled shells between them. Both the factors decrease the force of attraction between nucleus and valence electron. Therefore, atomic size increases on moving down a group. 4.3.3 Ionic radii Ionic radius is the radius of an ion. On converting into an ion the size of a neutral atom changes. Anion is bigger than the neutral atom. This is because addition of one or more electrons increases repulsions among electrons and they move away from each other. On the other hand a cation is smaller than the neutral atom. When one or more electrons are removed, the repulsive force between the remaining electrons decreases and they come a little closer. 4.3.3a Variation of ionic radii in periods and groups Ionic radii show variations similar to those of atomic radii. Thus, ionic radii increase in a group. You can see such increases in groups 1 and 16 elements from the data given below. Group 1 Element Electron radius Li+ 60

Group 16 Element Ionic radius O2140

Na+ K+

95 133

S2Se2-

184 198

Rb+

148

Te2-

221

Ionic radii decrease in a period . It can be seen from the data of ionic radii in picometer for 2nd period elements given below. Element radii

Li+ 60

Be2+ 31

B -

C -

N3171

O2140

F136

Ionic

Periodic Classification of Elements : 73 :

In the data given above, the positions of boron and carbon have been left vacant as they do not form ions. Also, the trend in radii of cations is seen in Li+ and Be2+and in radii of anions is seen in N3–, O2– and F–. 4.3.4 Ionization energy Negatively charged electrons in an atom are attracted by the positively charged nucleus. For removing an electron this attractive force must be overcome by spending some energy. The minimum amount of energy required to remove an electron from a gaseous atom in its ground state to form a gaseous ion is called ionization energy. It is measured in unit of kJ mol-1. It is a measure of the force of attraction between the nucleus and the outermost electron. Stronger the force of attraction, greater is the value of ionization energy. It corresponds to the following process: If only one electron is removed, the ionization energy is known as the first ionization energy. If second electron is removed the ionization energy is called the second ionization energy. Now we shall study the variation of ionization energy in the periodic table. 4.3.3a Variation of ionization energy in a group We have already seen earlier, that the force of attraction between valence electrons and nucleus decreases in a group from top to bottom. What should happen to their ionization energy values? Ionization energy decreases in a group from top to bottom. This can be seen from ionization energy values (in kJ mol-1) of groups 1 and 17 elements given below. Group 1 Element Ionization Energy Li 520

Group 17 Element Ionization Energy F 1680

Na K

496 419

Cl Br

1251 1143

Rb

403

I-

1009

4.3.4b Variation of ionization energy in a period We know that the force of attraction between valence electron and nucleus increases in a period from left to right. As a consequence of this, the ionization energy increases in a period from left to right. This trend is can be seen in ionization energies (in kJ mol-1) of elements belonging to 2nd and 3rd periods. 2nd Period Elements Element Li

Be

B

C

N

O

F

Ne

Ionization Energy

899

801

1086

1400

1314

1680

2080

3rd Period Elements Element Na

Mg

Al

Si

P

S

Cl

Ar

Ionization Energy

738

578

786

1021

1000

1251

1521

520

496

4.3.5 Electron affinity Another important property that determines the chemical properties of an element is the tendency to gain an additional electron. This ability is measured by electron affinity. It is

: 74 : Periodic Classification of Elements

the energy change when an electron is accepted by an atom in the gaseous state. It corresponds to the process X(g) + e– → X–(g) + E Here, X is an atom of an element. The energy change is measured in the unit kJ mol-1. By convention, electron affinity is assigned a positive value when energy is released during the process. Greater the value of electron affinity, more energy is released during the process and greater is the tendency of the atom to gain electron. Let us now learn about its variation in the periodic table. 4.3.5a Variation of electron affinity in a group In a group, the electron affinity decreases on moving from top to bottom, that is, less and less amount of energy is released. Such trends in its values (in kJ mol-1) for group 1 and group 17 elements are given below. Group 1 Element Electron affinity Li 58

Group 17 Element Electron affinity F 333

Na K

53 48

Cl Br

348 324

Rb

45

I-

295

4.3.5b Variation of electron affinity in a period In a period, the electron affinity increases from left to right, that is, more and more amount of energy is released. You can see this increase in electron affinity values (in kJ mol-1) below for elements of 2nd and 3rd periods. 2nd Period elements Element Electron affinity

Li 58

Be -

B 23

C 123

N 0

O 142

F 333

3rd Period elements Element Electron affinity

Na 53

Mg -

Al 44

Si 120

P 74

S 200

Cl 348

4.3.6 Electronegativity You have learnt in the previous section that electron affinity of an element is a measure of an isolated atom to attract electrons towards it self. We normally do not deal with isolated atoms. Mostly we come across atoms which are bonded to other atoms. There is another property which deals with the power of bonded atoms to attract electrons. This property is known as electronegativity. Electronegativity is relative tendency of a bonded atom to attract the bond-electrons towards itself. Electronegativity is a dimensionless quantity and does not have any units. It just compares the tendency of various elements to attract the bond-electrons towards themselves. The most widely used scale of electronegativity was devised by Linus Pauling. Electronegativity is a useful property. You will learn in the next chapter how it helps to understand the nature of chemical bond formed between two atoms. Now let us learn about its variation in groups 1 and 17.

Periodic Classification of Elements : 75 : Group 1 Element Electronegativity Li 1.0

Element F

Group 17 Electronegativity 4.0

Na K

0.9 0.8

Cl Br

3.0 2.8

Rb

0.8

I-

2.5

What do you observe? Electronegativity decreases in a group from top to bottom. Now let us see its variation in 2nd and 3rd period elements. 2nd Period Elements Element Electronegativity

Li 1.0

Be 1.5

B 2.0

C 2.5

N 3.0

O 3.5

F 4.0

3rd Period Elements Element Electronegativity

Na 0.9

Mg 1.2

Al 1.5

Si 1.8

P 2.1

S 2.5

Cl 3.0

Now what do you observe? Electronegativity increases in a period from left to right. 4.3.7 Metallic and non-metallic character You know what are characteristic properties of a metal? They are its electropositive character (the tendency to lose electrons), metallic luster, ductility, malleability and electrical conductance. Metallic character of an element largely depends upon its ionization energy. Smaller the value of ionization energy, more electropositive and hence more metallic the element would be. 4.3.7a Variation of metallic character in a group You know the variation of ionization energy in a group. Can you predict the variation of metallic character on its basis? Metallic character of elements increases from top to bottom. This can best be seen in elements of group 14. Its first element, carbon is a typical nonmetal, next two elements Si and Ge are metalloids and the remaining elements Sn and Pb, are typical metals as shown below. Group 14 Element

Nature

C

Non-metal

Si

Metalloid

Ge

Metalloid

Sn

Metal

Pb

Metal

4.3.7b Variation of metallic character in a period How does metallic character change in a period? Metallic character of elements decreases in a period from left to right as shown below for 3rd period elements Element

Na

Mg

Al

Si

P

S

Cl

Character

Metal

Metal

Metal

Metalloid

Non-metal

Non-metal

Non-metal

: 76 : Periodic Classification of Elements

CHECK YOUR PROGRESS 4.3 Fill in the blanks with appropriate words. 1. The force of attraction between nucleus and valence electrons _______________ in a period. 2. Atomic radii of elements _______________ in a period from left to right. 3. Radius of cation is _______________ than that of the neutral atom of the same element 4. Electronegativity _______________ in a period from left to right and _______________ in a group from top to bottom. 5. Metallic character of elements _______________ from top to bottom in a group. 6. Ionization energy of the 1st element in a period is _______________ in the entire period. !

!

!

!

• •

• • •

•

LET US REVISE The first classification of elements was s metals and non-metals. It served only limited purpose. After atomic masses (old term, atomic weight) of elements had been determined, it was thought to be their most fundamental property and attempts were made to correlate it to their other properties. Dobereiner grouped elements into triads. The atomic mass and properties of the middle element were mean of the other two. He could group only a few elements into triads. For example (i) Li, Na and K (ii) Ca, Sr and Ba (iii) Cl, Br and I. Newland tried to see the periodicity of properties and stated his law of octaves that, “When elements are arranged in the increasing order of their atomic weights every eighth element has properties similar to the first”. He could arrange elements up to calcium only out of more than sixty elements known then. Mendeleev observed correlation between atomic masses and other properties and stated his periodic law as, “The chemical and physical properties of elements are a periodic function of their atomic weights”. Mendeleev gave the first periodic table which is named after him which included all the known elements. It consists of seven horizontal rows called periods and numbered from 1 to 7. It has nine vertical columns called groups and numbered from zero to VIII. Main achievements of Mendeleev’s periodic table were (i) inclusion of all the known elements and (ii) prediction of new elements. Main defects of Mendeleev’s periodic table were (i) position of isotopes, (ii) anomalous pairs of elements like Ar and K and (iii) grouping of dissimilar elements and separation of similar elements. Moseley discovered that atomic number and not atomic mass is the most fundamental property of elements. In the light of this the periodic law was modified to “ The chemical and physical properties of elements are a periodic function of their atomic numbers”. This is the modern periodic table. Modern periodic table is based upon atomic number. Its long form has been accepted by IUPAC. It has seven periods (1 to 7) and 18 groups (1 to 18). It is free of main

Periodic Classification of Elements : 77 :

• •

A. 1

2.

3.

4.

5.

B. 1. 2. 3.

defects of Mendeleev’s periodic table. Elements belonging to same group have same number of valence electrons and thus show same valency and similar chemical properties. Arrangement of elements in the periodic table shows periodicity. Atomic and ionic radii and metallic character increase while ionization energy , electron affinity and electronegativity decrease in a group from top to bottom. Number of valence electrons, ionization energy, electron affinity and electronegativity increase while metallic character and atomic and ionic radii decrease in a period from left to right. TERMINAL EXERCISES Multiple choice type questions. The first attempt to classify elements was made by (a) Mendeleev (b) Moseley (c) Newland (d) Dobereiner Which group has maximum number of elements in the periodic table? (a) 1 (b) 2 (c) 3 (d) 4 The law of octaves applies to (a) B,C,N (b) As, K, Ca (c) Be, Mg, Ca (d) Se, Te, As Representative elements belong to groups (a) 1, 2, 3,4, 5, 6, 7 and 8 (b) 1 and 2 (c) 1, 2, 13, 14, 15, 16, 17 and 18 (d) 1, 2, 13, 14, 15, 16 and 17 Which of the following ions is the largest in size? (a) Al3+ (b) Ba2+ (c) Mg2+ (d) Na+ Mark the following statements as true or false. Ionization energy of an element increases with an increase in atomic number. Electron Affinity of fluorine is greater than that of chlorine. Out of P3+, S2- and Cl- ions Cl- ion is the smallest one.

: 78 : Periodic Classification of Elements

4. The first member of lanthanide series of elements is lanthanum. C. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Descriptive type questions. Name the group and period of element having the atomic number 21. Give an example of Dobereiner triad. State Newland’s law of Octaves. State the Modern Periodic Law. How many groups were present in Mendeleev’s Periodic Table and give their numbers. What are periods and groups in periodic table. List two main achievements of Mendeleev’s periodic table. What are main defects of Mendeleev’s periodic table? How is modern periodic law different from the Mendeleev’s periodic law? Why argon (atomic mass 40) was placed before potassium (atomic mass 39)? In each of the following pairs of ions, which one is bigger in size and why? (i) Li and Ne (ii) O and S (iii) K and K+ (iv) Br and Br12. Define atomic radius. How does it vary in a period and in a group? 13. What is ionization energy? How does it vary in a group? Give two reasons for it. 14. Which element of the following has the highest ionization energy? Na, Ba and Cl 15. Explain why does ionization energy increase from left to right in a period but decrease from top to bottom in a group? 16. What do you understand by ‘periodicity’ of properties? Explain taking metallic character of elements as an example. 17. Potassium is more reactive than sodium. Explain with the help of ionization energy. 18. An element has atomic mass 32 and its nucleus has 16 neutrons. To which group of periodic table does it belong? Explain. 19. The following is a portion of periodic table. Look at it and answer the following questions. 1 2 3-15 16 17 18 H He C D A E B (i) Out of A and B which one has lower ionization energy ? (ii) Which is bigger atom C or D? (iii)

Which is the most electropositive element of all?

(iv)

Which is more metallic in nature D or E?

Periodic Classification of Elements : 79 :

(v) Which is more non-metallic in nature C or D? (vi) Which is the least electronegative element of all? ANSWERS TO CHECK YOUR PROGRESS 4.1 1. Atomic mass of the middle element B must be nearly equal to the average of the other two elements A and C. Or

Atomic mass of B = Atomic mass of A + Atomic mass of B 2

2. 3. 4. 5. 6. 7.

16 Atomic weight 8 Group These were the positions of elements which were yet to be discovered. Gallium

4.2 1. Atomic number 2. Any two of the following: i. Position of isotopes ii. Anomalous pairs of elements iii. Grouping of dissimilar elements iv. Separation of similar element. 3. Seven periods and eighteen groups 4. Alkaline earths 5. Non-metals 6. 32 4.3 1. 2. 3. 4. 5. 6.

increases decreases smaller increases, decreases increases minimum

GLOSSARY Actinides: A group of 14 elements with atomic numbers 90-103 (Th–Lr) which are placed along with the element actinium (Ac), atomic number 89 in the some position in group 3 in the periodic table. Atomic number: It is the number of protons in the nucleus of the atom of an element.

: 80 : Periodic Classification of Elements

Atomic radius: It is defined as one-half the distance between the nuclei of two atoms when they are linked to each other by a single covalent bond. Dobereiner’s triad: A group of three chemically similar elements in which the atomic mass and properties of the middle element are mean of the other two. Electron affinity: It is the energy change when an electron is accepted by an atom in an isolated gaseous state. By convention, it is assigned a positive value when energy is released during the process. Electronegativity: It is a measure of the tendency of a bonded atom to attract the bond-electrons towards itself. Groups: The vertical columns present in periodic table. Ionic radius: It is the radius of an ion i.e. the distance between the centre of ion and its outermost shell. Ionization energy: It is the minimum amount of energy required to remove an electron from an isolated gaseous atom in its ground state to form a gaseous ion. Lanthanides: A group of 14 elements with atomic numbers 58 to 71 (Ce to Lu) which are placed along with the element lanthanum (La), atomic number 57 in the some position in group 3 in the periodic table Mendeleev’s periodic law: The chemical and physical properties of elements are a periodic function of their atomic masses. Modern periodic law : The chemical and physical properties of elements are a periodic function of their atomic numbers. Newland’s law of octaves: When elements are arranged in the increasing order of their atomic weights every eighth element has properties similar to the first. Noble gases: The elements present in group 18 on extreme right side of the periodic table. Their outermost shells contain 8 electrons. Normal elements: These are the elements present in groups 1 and 2 on left side and groups 13 to 17 on the right side of the periodic table whose only outermost shells are incomplete. Periodic properties: These are the properties which repeat themselves after a certain interval of atomic number. Periodic table: A tabular arrangement of the elements based on the periodic law. Periods: The horizontal rows present in the periodic table. Transition elements: These are the elements present in groups 3 to 12 in the middle of the periodic table whose two outermost shells are incomplete.

Chemical Bonding INTRODUCTION: In lessons 3 and 4, you have read about the electronic configurations of atoms of various elements and variation in the periodic properties of elements. But every thing present around us is not just the elements. We see substances which can be either elements or compounds You know that the atoms of same or different kinds may combine. When atoms of same elements combine, we get elements. But we get compounds when atoms of different elements combine. Have you ever thought why do atoms combine at all? In this lesson, we will find an answer to this question. We will first explain what a chemical bond is and then discuss various types of chemical bonds which join the atoms together to give various types of substances. The discussion would also highlight how are these bonds form. The properties of substances depend on the nature of bonds present between their atoms. For example, in the lesson you will learn sodium chloride, the common salt and glucose dissolve in water whereas methane gas or naphthalene does not .This is because the type of bonds present between them are different. In addition to the difference in solubility, these two types of compounds differ in other properties about you will study in this lesson. We will also briefly cover the nature of bonding in metals and correlate it to various characteristic properties of metals. Finally, hydrogen bonding which is an important interaction present between molecules would be explained.

OBJECTIVES After completing this lesson, you should be able to : - give reason for the formation of chemical bonds; - list various types of chemical bonds present in different substances; - describe the formation of an ionic bond with suitable examples; - explain the characteristic properties of ionic compounds; - describe the formation of a covalent bond with suitable examples; - explain the characteristic properties of covalent compounds; - explain bond parameters such as bond length, bond energy and bond polarity; - distinguish between polar and non–polar molecules; - state the differences between ionic and covalent compounds; - explain the nature of bonding present in metals; - explain hydrogen bonding.

WHY DO ATOMS COMBINE ? The answer to this question is hidden in the electronic configurations of the noble gases. It was found that noble gases namely helium, neon, argon, krypton, xenon and radon did not react with other elements to form compounds, i.e. they were nonreactive. Earlier they were also called as inert gases. It was, thus, thought that these noble gases lacked reactivity because they had electronic arrangements which were quite stable. When we write the electronic configurations of the noble gases (see table 5.1 below), we find that except helium all of them have 8 electrons in their outermost shell. Electronic Configuration of Noble gases Name

Symbol

Helium Neon Argon Krypton Xenon Radon

He Ne Ar Kr Xe Ra

Atomic number 2 10 18 36 54 86

Electronic configuration 2 2,8 2,8,8 2,8,18,8 2,8,18,18,8 2,8,18,32,18,8

No. of electrons in the outermost shell 2 8 8 8 8 8

Thus, it was concluded that atoms having 8 electrons in their outermost shell are very stable and they did not form compounds. It was also observed that other atoms such as hydrogen, sodium, chlorine etc. which do not have 8 electrons in their outermost shell undergo chemical reactions. They can stabilize by combining with each other and attaining the above configurations of noble gasses, i.e. 8 electrons (or 2 electrons in case of helium) in their outermost shells. Thus, atoms tend to attain a configuration in which they have 8 electrons in their outermost shells. This is called the octet rule. The octet rule explains the chemical bonding in many compounds. Atoms are held together in compounds by the forces of attraction which are called chemical bonds. The formation of chemical bonds results in the lowering of energy, i.e. as compared to the individual atoms the resulting compound is lower in energy and hence is more stable. Thus stability of the compound formed is an important factor in the formation of chemical bonds. In rest of the lesson; you will study about the nature of bonds present in various substances. We would explain ionic bonding and covalent bonding in detail while briefly touch upon the bonding in metals and hydrogen bonding. Before you start learning about ionic bonding in the next section, you can answer the following questions to check your understanding.

Ionic Bonding When sodium metal and chlorine gas are brought into contact, they react violently and we obtain sodium chloride. This reaction is shown below. 2 Na (s) + Cl2 (g) ->2 NaCl (s)

The bonding in sodium chloride can be understood as follows: Sodium (Na) has the atomic number 11 and we can write its electronic configuration as 2,8,1 i.e. it has one electron in its outermost (M) shell. If it loses this electron, it is left with 10 electrons. The resulting species is positively charged ion. Such a positively charged ion is called a cation. The cation in this case is called sodium cation Na+. This is shown below in Fig. 5.1.

Formation of Sodium Cation Note that the sodium cation has 11 protons but 10 electrons only. It has 8 electrons in the outermost (L) shell. Thus, sodium atom has attained the noble gas configuration (that of Neon as shown in Table 5.1) by losing an electron present in its outermost shell. Thus, according to octet rule, sodium atom can acquire stability by changing to sodium cation. The ionization of sodium atom to give sodium ion requires an energy of 496 kJ mol1. A chlorine atom having the atomic number 17, has the electronic configuration 2,8,7. It can complete its octet by gaining one electron. This is shown below in Fig.5.2.

Formation of chloride ion Note that in the above process, the chlorine atom has gained an additional electron and hence it has become negatively charged ion. Such a negatively charged ion is

called an anion. This anion is called chloride ion (Cl-). The chloride ion has 8 electrons in its outermost shell and it is a stable electronic configuration according to the octet rule. The formation of chloride ion from the chlorine atom releases 349 kJ mol-1 of energy. Thus, an ion is a species having positive or negative electrical charge. Both the cation and the anion are known by the general name ion. A cation is formed by the loss of an electron from the sodium atom whereas an anion is formed by the gain of an electron by chlorine atom. Since the cation (Na+) and the anion (Cl-) formed above are electrically charged species, they are held together by electrostatic force of attraction. This electrostatic force of attraction which holds the cation and anion together is known as electrovalent bond or ionic bond. This is represented as follows:

. Na

. +

: Cl : -> ..

Na+

+

Cl-

Note that only outermost electrons are shown above. Such structures are also called Lewis structures. If we compare the energy required for the formation of sodium ion and that released in the formation of chloride ion, we note that there is a net difference of 147 kJ mol-1 of energy. If only these two steps are involved, then the formation of sodium chloride is not favorable energetically. But sodium chloride exists as a crystalline solid. This is because the energy is released when the sodium ions and the chloride ions come together to form the crystalline structure. The energy so released compensates the above deficiency of energy. The crystal structure of sodium chloride thus obtained is shown below in Fig 5.3.

The crystal structure of sodium chloride You can see that each sodium ion is surrounded by six chloride ions and each chloride ion is surrounded by six sodium ions. The force of attraction between the sodium and chloride ions is uniformly felt in all directions. Thus, no particular sodium ion is bonded to a particular chloride ion. Hence, there is no species such as NaCl in the crystal structure shown above.

Similarly, we can explain the formation of cations resulting from lithium and potassium atoms and the formation of anions resulting from fluorine, oxygen and sulphur atoms. Let us now study the formation of another ionic compound namely magnesium chloride. We will proceed in the same way as we had done for sodium chloride. We will first consider magnesium (Mg) atom. Its atomic number is 12. Thus, it has 12 protons. The number of electrons present in it is also 12. Hence, the electronic configuration of Mg atom is 2, 8, 2. Let us consider the formation of magnesium ion from magnesium atom. We see that it has 2 electrons in its outermost shell. If it loses these two electrons, then it can achieve the stable configuration of 2, 8 (that of noble gas neon). This can be represented in Fig. 5.4 as follows:

Formation of magnesium ion You can see that the resulting magnesium ion has only 10 electrons and hence it has 2+ charge. It is a dipositive ion and can be represented as Mg2+ion. The two electrons lost by the magnesium are gained one each by two chlorine atoms to give two chloride ions. The formation of chloride ion has already been explained above. Thus, one magnesium ion and two chloride ion joins together to give magnesium chloride, MgCl2. Hence, we can write Mg (2,8,2)

+

2Cl 2(2,8,7) or MgCl2

->

Mg2+

2(Cl)

(2,8)

2(2,8,8)

Let us now see what would happen if instead of chloride ion, the magnesium ion combines with another anion say oxide anion. The oxygen atom having atomic number 8 has 8 electrons. Its electronic configuration is 2,6. It can attain a stable electronic arrangement (2,8) of the noble gas neon if it gains two more electrons. The two electrons, which are lost by the magnesium atom, are gained by the oxygen atom. On gaining these two electrons, the oxygen atom gets converted to the oxide anion. This is shown below in Fig 5.5.

Formation of oxide ion The oxide has 2 more electrons as compared to the oxygen atom. Hence, it has 2 negative charges on it. Therefore, it can be represented as O2- ion. The magnesium ion (Mg2+) and the oxide ion (O2-) are held together by electrostatic force of attraction. This leads to the formation of magnesium oxide.

Mg2+ (2,8)

+

O2(2,8)

->

Mg2+ (2,8)

+

O2(2,8)

Thus, magnesium oxide is an ionic compound in which a dipositive cation (Mg2+) and a dinegative anion (O2-) are held together by electrostatic force. Similar to the case of sodium chloride the formation of magnesium oxide is also accompanied with a lowering of energy which leads to the stability of magnesium oxide as compared to individual magnesium and oxygen atoms. Similarly, the ionic bonding present in many other ionic compounds can be explained. The ionic compounds show many characteristic properties which are discussed below: Let us consider the formation of magnesium ion from magnesium atom. We see that it has 2 electrons in its outermost shell. If it loses these two electrons, then it can achieve the stable configuration of 2, 8 (that of noble gas neon). This can be represented in Fig. 5.4 as follows:

COVALENT BONDING In this section, we will study about another kind of bonding called covalent bonding. Covalent bonding is helpful in understanding the formation of molecules. In lesson 2, you studied that molecules having similar atoms such as H2, Cl2, O2, N2 etc. are constituents of elements whereas those containing different atoms like HCl, CO2 etc. are constituents of compounds. Let us now see how are these molecules formed? We will begin with the formation of hydrogen molecule (H2). The hydrogen atom has one electron. It can attain the electronic configuration of the noble gas helium by sharing one electron of another hydrogen atom. When the two hydrogen atoms come closer, there is an attraction between the electrons of one atom and the proton of another and there are repulsions between the electrons as well as the protons of the two hydrogen atoms. In the beginning, when the two hydrogen atoms approach each other, the potential energy of the system decreases due to the force of attraction. The value of potential energy reaches a minimum at some particular distance between the two atoms. If the distance between the two atoms further decreases, the potential energy increases because of the forces of repulsion. The covalent bond forms when the forces of attraction and repulsion balance each other and the potential energy is minimum. It is this lowering of energy which leads to the formation of the covalent bond.

Potential energy diagram We will next consider the formation of chlorine molecule (Cl2). A molecule of chlorine contains two atoms of chlorine. Now how are these two chlorine atoms held together in a chlorine molecule? You know that the electronic configuration of Cl atom is 2,8,7. Each chlorine atom needs one more electron to complete its octet. If the two chlorine atoms share one of their electrons as shown below, then both of them can attain the stable noble gas configuration of argon as shown below. Note that the shared pair of electrons is shown to be present between the two chlorine atoms. Each chlorine atom thus acquires 8 electrons. The shared pair of electrons keeps the two chlorine atoms bonded together. Such a bond, which is formed by sharing of electrons between the atoms is called a covalent bond. Thus,

we can say that a covalent bond is present between two chlorine atoms. This bond is represented by drawing a line between the two chlorine atoms as follows: .. : Cl

.. Cl :

-

..

..

Sometimes the electrons shown above on the chlorine atoms are omitted and the chlorine-chlorine bond is shown as follows: Cl - Cl Similarly, we can understand the formation of oxygen molecule (O2) from the oxygen atoms. The oxygen atom has atomic number 8. It has 8 protons and also 8 electrons. The electronic configuration of oxygen atom is 2,6. Now each oxygen atom needs two electrons to complete its octet. The two oxygen atoms share two electrons and complete their octet as is shown below: The 4 electrons (or 2 pairs of electrons) which are shared between two atoms of oxygen are present between them. Hence, these two pairs of shared electrons can be represented by two bonds between the oxygen atoms. Thus, an oxygen molecule can be represented as follows: The two oxygen atoms are said to be bonded together by two covalent bonds. Such a bond consisting of two covalent bonds is also known as a double bond.

:

.. O

:

=

.. O :

Let us next take the example of nitrogen molecule (N2) and understand how the two nitrogen atoms are bonded together. The atomic number of nitrogen is 7. Thus, it has 7 protons and 7 electrons present in its atom. The electronic configuration can be written as 2,5. To have 8 electrons in the outermost shell, each nitrogen atom requires 3 more electrons. Thus, a sharing of 3 electrons each between the two nitrogen atoms is required. This is shown below: Each nitrogen atom provides 3 electrons for sharing. Thus, 6 electrons or 3 pairs of electrons are shared between two nitrogen atoms. Hence, each nitrogen atom is able to complete its octet. Since 6 electrons (or 3 pairs of electrons) are shared between the nitrogen atoms, we say that three covalent bonds are formed between them. These three bonds are represented by drawing three lines between the two nitrogen atoms as shown below: Such a bond which consists three covalent bonds is known as a triple bond. So far, we were discussing covalent bond formation between atoms of the same elements. But covalent bond can be formed by sharing of electrons between atoms of different elements also. Let us take the example of HCl to understand it.

Hydrogen atom has one electron in its outermost shell and chlorine atom has seven electrons in its outermost shell. Each of these atoms has one electron less than the electronic configuration of the nearest noble gas. If they share one electron pair, then hydrogen can acquire two electrons in its outer most shell whereas chlorine will have eight electrons in its outermost shell. The formation of HCl molecule by sharing of one electron pair is shown below: Similarly, we can explain bond formation in other covalent compounds. After knowing the nature of bonding present in covalent compounds, let us know study what type of properties these covalent compounds have. Properties of covalent compounds The covalent compounds consist of molecules which are electrically neutral in nature. The forces of attraction present between the molecules are less strong as compared to the forces present in ionic compounds. Therefore, the properties of the covalent compounds are different from those of the ionic compounds. The characteristic properties of covalent compounds are given below: a) Physical state Because of the weak forces of attraction present between discrete molecules, called inter-molecular forces, the covalent compounds exist as a gas or a liquid or a solid. For example, O2, N2, CO2 are gases; water and CCl4 are liquids and iodine is a solid. b) Melting and boiling points As the forces of attraction between the molecules are weak in nature, a small amount of energy is sufficient to overcome them. Hence, the melting points and boiling points of covalent compounds are lower than those of ionic compounds. For example, melting point of naphthalene which is a covalent compound is 353K (80o C). Similarly, the boiling point of carbon tetrachloride which is another covalent compound is 350 K (77o C). c) Electrical conductivity The covalent compounds contain neutral molecules and do not have charged species such as ions or electrons which can carry charge. Therefore, these compounds do not conduct electricity and are called poor conductors of electricity. d) Solubility Covalent compounds are generally not soluble in water but are soluble in organic solvents such as alcohol, chloroform, benzene, ether etc.

After understanding the nature of covalent bond and properties of covalent compounds, let us now study about certain characteristic features associated with a covalent bond. Bond parameters A covalent bond has characteristic values associated with it. These are called bond parameters. Some of these parameters are bond length, bond angle, bond energy, bond polarity and bond angle. We will now discuss them one by one. a) Bond length: It is the distance between the nuclei when they combine to form covalent bond. The bond lengths for some common bonds are shown below in Table 5.2. You can note that as the number of bonds between the two atoms increases, the bond length between them decreases. Bond lengths for some common bonds Bond

Bond length (pm)

Bond

Bond length (pm)

C-C C=C CC C-O C=O C=O

154 134 120 143 123 113

N-N N=N N=N O-O O=O

147 124 110 148 121

b) Bond angle: It is the angle between two bonds of a covalent molecule. For example, in water molecule the bond angle is 104.5o. c) Bond energy: The stability of a molecule can be related to the strength of the covalent bonds present in it. The stronger the covalent bonds present in a molecule, the more would be its stability. The strength of the covalent bond can be expressed in terms of the energy required to break the bond. For example, 242 kJ of energy is required to break the Cl-Cl bond of Cl2 molecule present in one mole of chlorine gas. .. : Cl ..

-

.. Cl :(g) -> 2: ..

Cl :(g)

The energy required to break one mole of a bond in isolated molecules of a substance is known as bond energy. The bond energy values for a particular bond can vary slightly from one compound to another. The bond energy values are therefore reported as average bond energies. The average bond energies of some of the bonds are listed in Table 5.3.

You can see from Table 5.3 that the bond energy increases as the number of bonds between two atoms increases. Hence, it indicates that the bonds become stronger and stronger as the number of bonds increases. d) Bond polarity: When a bond is formed between the atoms of the same element, the resulting molecule is called a homonuclear molecule. In such molecules, the electrons forming the bond are equally shared between the atoms. For example, in H2, Cl2, O2 molecules, the bonded electrons are equally shared between the atoms of these molecules. But when two atoms of different elements form a bond, the resulting molecule is known as a heteronuclear molecule. In these molecules, the shared pair of electrons is pulled more by the more electronegative atom towards itself. For example, in HCl molecule the shared pair of electrons is pulled more by the more electronegative chlorine atom. This leads to partial separation of charges which are represented by d+ and d– as shown below: Thus, two poles – one negative (Cl atom) and the other positive (H atom), are formed in the HCl molecule. The dipole in HCl molecule can also be represented by H – Cl where the foot of the arrow represents the positive end of the dipole and the arrow head represents the negative end of the dipole. The bonds such as those present between the HCl molecules are called polar bonds. Hence, such molecules are called polar molecules. Shapes of molecules The bond lengths and bond angles of various molecules can be determined experimentally. The values so obtained give us an idea about the shapes of molecules. The covalent molecules have definite shapes because the covalent bonds are formed along a particular direction. Thus, we can say that the covalent bond is directional in nature. Note that this is in contrast to the ionic compounds in which the electrostatic forces of attraction are felt equally strongly in all the directions. Some examples of common covalent molecules and their shapes are given below in Table 5.4. Name Oxygen(O2) Nitrogen(N2)

Structure .. .. :O=O: :N=N:

Shape linear linear

Bonding in metals You know that some of the characteristic properties of metals are malleability, ductility, conduction of heat and electricity, high melting point etc. The high melting point indicates that bonding in metals is strong in nature. These properties of metals can be explained with the help of electron sea model. According to this model, the cations of metal are present in a sea of electrons as shown below in Fig.5.7.

Electron sea model The electrostatic forces of attraction hold the electrons and the cations together. Since these forces are strong in nature, the melting point of metals is high. The electrons are distributed throughout the metal and they are not confined to any particular metal cation. These electrons are mobile and hence can conduct electricity when the metal is connected to a battery or two electrodes. Similarly, the metal ions can also move and no specific bonds are to be broken in this movement. Since both the electrons and the metal ions can freely move and their environment does not change by this movement, the metals exhibit the malleability and ductility. So far we have discussed chemical bonds resulting from strong forces of attraction, but weaker forces of attraction also play an important role towards the properties of many substances. One such type of interaction present between the molecules is hydrogen bonding. Let us now study about it in detail.

Hydrogen Bonding When hydrogen is bonded to an electronegative atom such as oxygen, nitrogen or fluorine, a special or unique type of attraction is present among the molecules of such compounds. The hydrogen of one molecule is attracted by the electronegative atom of the adjacent molecule. Such type of bonding is shown by dotted lines for hydrogen fluoride and water in Fig.5.8. The strength of hydrogen bonding varies from about 4 kJ mol-1 to 25 kJ mol-1 in various substances. This energy is much less than that required breaking one mole of an ionic or a covalent substance as you can see from Table 5.3. H_____F-----H_____F-----H_____F

The existence of water in liquid state is because of hydrogen bonding. Hydrogen bonding is also responsible for the low density of ice as compared to water. In ice, hydrogen bonding gives an ordered arrangement of water molecules which has a lot of free space in between them. Since ice is lighter than water, it floats on water and provides an insulating layer over water which is very important for the survival of aquatic life.

Hydrogen bonding also explains the miscibility of alcohol in water in all proportions. Glucose which contains six-OH groups makes hydrogen bonds with water molecules and hence is very soluble in water. More than 80 g of glucose dissolves in 100 mL of water. In proteins, hydrogen bonding is responsible for their helical structure

In Text Questions 1. State octet rule 2. Why are noble gases non-reactive? 3. Define the term ion. Name the two types of ions? 4. How many shells are present in Na+ ion? 5. What is the number of electrons present in Cl- ion? 6. Name the type of force of attraction present in ionic compounds. 7. In sodium chloride lattice, how many Cl- ions surround each Na+ ion? 8. How many electron pairs are shared between (i) Cl2 (ii) O2 and (iii) HCl molecules? 9. Which of the following statements are true for covalent molecules? i ) They are poor conductors of electricity. ii ) Their boiling points are high. iii ) They have definite shape 1. Define the terms: cation and anion.

2. Classify the following as cations or anions: Na+, O2-, Cl-, Ca2+, N3-, K+, Mg2+, -OH 3. Explain the formation of Li+ ion from Li atom. 4. How would you explain the bonding in MgCl2? 5. Which of the following statements are correct for ionic compounds: i) They are insoluble in water. ii) They are neutral in nature. iii) They have high melting points. 6. State three characteristic properties of ionic compounds.

7. How does a covalent bond form? 8. What is the number of bonds present in the following molecules? i) Cl 2 ii) N2 iii) O2 9. Classify the following statements as true or false: i) Ionic compounds contain ions which are held together by weak electrostatic forces. ii) Ionic compounds have high melting and boiling points. iii) Covalent compounds are good conductors of electricity. iv) Sodium chloride is a good conductor of electricity. 10. Classify the following compounds as ionic or covalent: i) sodium chloride ii) calcium chloride iii) oxygen iv) hydrogen chloride v) magnesium oxide vi) nitrogen 11. Classify the following molecules as polar or non-polar: i) H2 (ii) HCl (iii) O2 (iv) H2O 12. Why is hydrogen bonding important? Give two examples. 13. Name the type of bonds present in H2O molecule. 14. Explain electron sea model of bonding in metals

What you have learnt

-

Atoms combine to attain a stable arrangement of eight electrons in their outer most shell.

-

Ions are held together by strong electrostatic forces. Hence, ionic compounds have high melting and boiling points.

-

Ionic compounds are good conductors of electricity . They are soluble in water but insoluble in inorganic solvents.

-

Covalent bonds are formed by sharing of electrons between atoms.

-

Covalent compounds have low melting and boiling points. They are poor conductors of electricity.

-

The covalent compounds are generally insoluble in water but are soluble in organic solvents.

-

Covalent bonds are directional in nature and hence covalent compounds have definite shapes.

-

Bond length decreases with the number of bonds whereas the bond energy increases with the number of bonds.

-

Electrons are mobile in metals and hence the metals and hence the metals are good conductors of electricity.

-

Hydrogen bonding is an important interaction and is responsible for variety of properties in various molecules. In water, it is responsible for its liquid nature whereas, it is responsible for its liquid nature whereas in proteins it is responsible for their shape and in glucose it is responsible for its solubility in water.

6

Chemical Arithmetic and Reactions Total number of reactions we study in chemistry is very large. They are of numerous types. In lesson 2, you have learnt how to write and balance chemical equations. In this lesson you will learn, how chemical equations can be classified into various categories on the basis of some of their features. You will also learn about the information that can be obtained from a balanced chemical equation and how we can use this information for making calculations. You have learnt about acids, bases and salts in earlier classes. In this lesson you will learn more about them. OBJECTIVES After completing this lesson, you will be able to: • list various types of reactions; • distinguish between various types of reactions; • classify the reactions according to their rates and energy changes; • work out simple problems based on stoichiometry; • define acids, bases and salts and give their examples; • explain the acid-base equilibrium in aqueous systems; • define pH and solve simple problems based on pH. 6.1 TYPES OF CHEMICAL REACTIONS Chemical reactions can be classified on the basis of some of their features. One classification is based on the nature of chemical change that occurs in the reaction. On this basis reactions can be classified into five types. These are: (i) Combination reactions (ii) Decomposition reactions (iii) Displacement reactions (iv) Double-displacement reactions (v) Oxidation-reduction reactions Let us now learn about these reactions. 6.1.1 Combination reactions A reaction in which two or more substances react to form a new substance is called a combination reaction.

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A special category of combination reactions is the one in which a compound is formed by combination of its constituent elements. Such a reaction is known as synthesis reaction. Following are some examples of combination reactions: 1. Carbon (charcoal, coke) burns in presence of oxygen (or air) to form carbon dioxide (synthesis reaction). CO2(g) C(s) + O2(g) carbon

oxygen

carbon dioxide

2. Hydrogen burns in presence of oxygen (or air) to form water (synthesis reaction). 2H2(g) + O2(g) 2H2O(l) hydrogen

oxygen

water

3. Phosphorus combines with chlorine to form phosphorus pentachloride (synthesis reaction). P4(s) + 10Cl2(g) 4PCl5 (s) phosphorus

chlorine

phosphorus pentachloride

4. Ammonia combines with hydrogen chloride to form ammonium chloride. NH3 (g) + HCl(g) NH4Cl(s) ammonia

hydrogen chloride

ammonium chloride

6.1.2 Decomposition reactions A reaction in which one substance breaks down into two or more simpler substances is known as decomposition reaction. A decomposition reaction always involves breaking of one or more chemical bonds and therefore occurs only when the required amount of energy is supplied. The energy may be supplied in any of the following forms: (i)

Heat: Such decomposition reactions are called thermal decomposition reactions. (ii) Electricity: Such decomposition reactions are called electro-decomposition reactions and the process is known as electrolysis. (iii) Light: Such decomposition reactions are called photo-decomposition reactions and the process is known as photolysis. Following are some examples of decomposition reactions: 1. Potassium chlorate decomposes on heating into potassium chloride and oxygen. 2KClO3 (s) 2KCl(s) + 3O2(g) potassium chlorate

potassium chloride

oxygen

2. When calcium carbonate (limestone) is heated strongly it decomposes into calcium oxide (quicklime) and carbon dioxide. CaCO3(s) CaO(s) + CO2(g) calcium carbonate

calcium oxide

carbon dioxide

3. Hydrogen peroxide decomposes into water and oxygen on heating. 2H2O2(l) 2H2O(l) + O2(g) hydrogen peroxide

water

oxygen

4. Water decomposes into hydrogen and oxygen on passing electricity through it (electrolysis).

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2H 2O(l)

2H2(g)

water

hydrogen

+

O2(g) oxygen

5. Lead nitrate decomposes on heating into lead monoxide, nitrogen dioxide and oxygen. 2Pb(NO3)2(s) 2PbO(s) + 4NO2(g) + O2(g) lead nitrate

lead monoxide

nitrogen dioxide

oxygen

6.1.3 Displacement reactions A reaction in which one element present in a compound is displaced by another element is known as displacement reaction. Following are examples of displacement reactions: 1. Displacement of a metal by a more reactive metal. a. Zinc displaces copper from a solution of copper sulphate. Zn (s) + CuSO4(aq) ZnSO4(aq) + zinc

copper sulphate

zinc sulphate

Cu(s) copper

b. Magnesium displaces copper from a solution of copper sulphate. Mg(s) magnesium

+

CuSO4(aq)

MgSO4(aq)

copper sulphate

magnesium sulphate

+

Cu (s) copper

2. Displacement of hydrogen from solutions of acids by more reactive metals. a. Zinc displaces hydrogen from dilute sulphuric acid. Zn(s) + H2SO4(aq) ZnSO4(aq) + H2(g) zinc

dil. sulphuric acid

zinc sulphate

hydrogen

b. Magnesium displaces hydrogen from dilute hydrochloric acid Mg(s) + 2HCl(aq) MgCl 2(aq) + H2(g) magnesium

dil hydrochloric acid magnesium chloride

hydrogen

2. Displacement of a halogen by a more reactive halogen. Chlorine displaces bromine from a solution of potassium bromide. Cl 2(g) + 2KBr(aq) 2KCl(aq) + Br2(aq) chlorine

potassium bromide

potassium chloride

bromine

6.1.4 Double-displacement reactions A reaction in which two ionic compounds exchange their ions is known as double displacement reaction. The following are the examples of double displacement reactions: a. Reaction between sodium chloride and silver nitrate. NaCl(aq) + AgNO3(aq) AgCl(s) sodium chloride

silver nitrate

+

silver chloride

b. Neutralization of hydrochloric acid by sodium hydroxide. HCl(aq) + NaOH(aq) NaCl(aq) + hydrochloric acid

sodium hydroxide

sodium chloride

NaNO3(aq) sodium nitrate

H 2O(l) water

6.1.5 Oxidation–reduction or redox reactions These are the reaction in which oxidation and reduction processes occur. Let us first learn what these processes are. a) Oxidation: It is a process which involves loss of electrons. Earlier it was defined as a process involving addition of oxygen or loss of hydrogen.

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b) Reduction: Reduction is a process which involves gain of electrons. Earlier it was defined as a process involving removal of oxygen or addition of hydrogen. c) Redox reactions: From the above definitions, you must have noticed above that oxidation and reduction processes are just opposite to each other. None of these processes can occur alone. During a reaction if one substance gets oxidized the other gets reduced. Thus, both the processes occur simultaneously. That is why the reactions in which oxidation and reduction processes occur are called redox reactions or oxidation-reduction reactions. Now let us understand these processes with the help of some examples. (i) Consider burning of coke (carbon) in presence of oxygen: C(s) + O2(g) CO2(g) carbon

oxygen

carbon dioxide

In this reaction carbon is getting oxidized as oxygen is added to it and oxygen is reduced. (ii) When hydrogen sulphide reacts with sulphur dioxide the products are sulphur and water. 2H2S(g) + SO2(g) 3S(s) + 2H 2O(l) hydrogen sulphide

sulphur dioxide

sulphur

water

Here, hydrogen sulphide is oxidized to sulphur due to loss of hydrogen while sulphur dioxide is reduced to sulphur due to loss of oxygen. (iii)When copper (II) oxide is treated with hydrogen, copper and water are produced. CuO(s) + H2(g) Cu(s) + H 2O(l) cupric oxide

hydrogen

copper

water

Here cupric oxide is reduced to copper due to loss of oxygen while hydrogen is oxidized to water due to addition of oxygen. (iv)When sodium metal reacts with chlorine it forms sodium chloride. 2Na(s) + Cl2(g) 2NaCl(s) sodium

chlorine

sodium chloride

Sodium chloride is an ionic compound. Sodium is present in it as sodium ion (Na+) and chlorine as chloride ion (Cl-). This reaction can be considered to occur in the following steps: •

•

Each sodium atom loses one electron and forms sodium ion. Since two sodium atoms are involved in the reaction, the process is: 2Na 2Na+ + 2e– sodium sodium ion Thus, sodium is oxidized due to loss of electron. Each chlorine atom gains one electron and forms chloride ion. Since one chlorine molecule has two atoms of chlorine the process is: Cl2 + 2e– 2Cl– chlorine

chloride ion

Thus, chlorine is reduced due to gain of electrons. (v) When zinc is added to an aqueous solution of copper sulphate, it displaces copper. Zn(s) + CuSO4(aq) ZnSO4(aq) + Cu(s) zinc copper sulphate zinc sulphate copper

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Here zinc is oxidized to zinc ions and copper ions are reduced to copper. This reaction is displacement reaction as well as a redox reaction. (d) Oxidizing and reducing agents : Consider the reaction between zinc and copper sulphate: Zn(s) + CuSO4(aq) ZnSO4(aq) + Cu(s) In this reaction zinc reduces cupric ions to copper. Such a substance which reduces another substance is called a reducing agent. Here, zinc is the reducing agent. Also, in this reaction cupric ions oxidize zinc to zinc ions. Such a substance which oxidizes another substance is called an oxidizing agent. Here, cupric ions are the oxidizing agent. CHECK YOUR PROGRESS 6.1 Match the type of reaction given in column I with the reactions given in column II. I II 1. Displacement A. 2H2S(g) + SO2(g) 3S(g) + 2H2O(1) reaction 2. Double B. NH3 + HCl NH4Cl displacement reaction 3. Combination C. 3CaCl2 + 2K3PO4 Ca3(PO4)2 + 6KCl reaction 4. Redox reaction D. Mg(s) + CuSO4(aq) MgSO4(aq) + Cu(s) 5. Decomposition E. 2H2O2 2H2O + O2 reaction 6.2 NATURE OF CHEMICAL REACTIONS In the last section, we have learnt how chemical reactions have been classified into various types on the basis of the nature of chemical change that occurs in them. In this section we shall learn about some other features of chemical reactions. These features have been discussed below. 6.2.1 Homogeneous–heterogeneous reactions Chemical reactions can be classified on the basis of physical states of reactants and products as homogeneous and heterogeneous reactions. a) Homogeneous reactions The reactions in which all the reactants and products are present in the same phase are called homogeneous reactions. Such reactions can occur in gas phase or solution phase only. A. Gas phase homogeneous reactions These are the reactions in which all reactants and products are gases. (i) H2(g) + Cl2(g) 2HCl(g) hydrogen

(ii)

2SO2(g) sulphur dioxide

chlorine

+

O2(g) oxygen

H+

hydrogen chloride

2SO3(g) sulphur trioxide

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(iii)

N2(g)

+

nitrogen

3H2(g)

2NH3(g)

hydrogen

ammonia

B. Solution phase homogeneous reactions These are the reactions in which all reactants and products are present in a solution. (i)

HCl(aq)

+

hydrochloric acid

(ii) CH3COOC2H5(l) +

NaOH(aq)

NaCl(aq)

sodium hydroxide

sodium chloride

H2O(l)

+

H2O(l) water

CH3COOH(l) + C2H5OH(l)

b) Heterogeneous reactions The reactions in which reactants and products are present in more than one phase are called heterogeneous reactions. Such reactions involve at least one solid substance along with one or more substances in solid, solution or gaseous phase. The following are the examples of heterogeneous reactions. (i) (ii)

CaCO3(s)

CaO(s)

calcium carbonate

calcium oxide

2Mg(s)

+

magnesium

(iii)

BaCl2(aq) barium chloride

+

+

CO2(g) carbon dioxide

O2(g)

2MgO(s)

oxygen

magnesium oxide

Na2SO4(aq)

BaSO4(s)

sodium sulphate

barium sulphate

+

2NaCl(aq) sodium chloride

6.2.2 Slow and fast reactions Different reactions occur at different rates. Rusting of iron is a slow process and requires few days time. On the other hand burning of cooking gas is a fast reaction. On the basis of their rates chemical reactions can be classified as slow and fast reactions. Rusting of iron, curdling of milk, hydrolysis of esters at room temperature (e.g. reaction between ethyl acetate and water), fading of colours of clothes, burning of coal, etc. are some examples of slow reactions. On the other hand, neutralization reaction (e.g. reaction between hydrochloric acid and sodium hydroxide), explosion reactions (e.g. in a fire cracker bomb), action of acids or bases on litmus, and burning of cooking gas are some examples of fast reactions. A large number of reactions are neither slow nor fast. They may be termed as moderate reactions. Burning of candle, thermal decomposition of potassium chlorate, and reaction of zinc with dilute sulphuric acid are some examples of moderate reactions. 6.2.3 Exothermic and endothermic reactions All chemical reactions are accompanied by some energy changes. Energy is either evolved or absorbed during the reaction usually in the form of heat. Depending upon this, the reactions are classified as exothermic and endothermic reactions. a) Exothermic reactions The reactions in which heat is liberated or evolved are called exothermic reactions. In such reactions heat is shown as one of the products. If exact amount of heat evolved is known then this amount is written otherwise simply the word heat is written. Following are the examples of exothermic reactions. (i) 2H2(g) + O2(g) 2H2O(l) + heat or 2H2(g) + O2(g) 2H2O(l) + 571.5 kJ

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(ii) (iii)

C(s) + O2(g) HCl(aq) + NaOH(aq)

CO2(g) + 393.5 kJ NaCl(aq) + H2O(l) +

57.3 kJ

b) Endothermic reactions The reactions in which heat is absorbed are called endothermic reactions. In such reactions heat is shown as one of the reactants. If exact amount of heat absorbed is known then this amount is written otherwise simply the word heat is written. Following are the examples of endothermic reactions (i)

N2(g)

+

2O2(g)

+

heat

2NO(g) nitric oxide

or (ii)

N2(g) 2KClO3(s)

+ +

O2(g) heat

+

potassium chlorate

(iii) 2Pb(NO3)2(s) +

180.7 kJ 2KCl(s)

+

2NO(g) 3O2(g)

potassium chloride

heat

2PbO(s)

lead nitrate

+

4NO2(g)

+

O2(g)

nitrogen dioxide

6.2.4 Reversible and irreversible reactions Chemical reactions can also be classified on the basis whether they can occur only in the forward direction or in forward as well as backward directions. a) Irreversible reactions Most of the reactions would occur till the reactants (or atleast one reactant) have been completely converted into products. For example, if a small piece of zinc metal is put in a test tube containing excess of dilute hydrochloric acid, it completely reacts with it. Zn(s) + 2HCl(aq) H2(g) + ZnCl2(aq) Such reactions occur in forward direction only. The reactions which occur in forward direction only are called irreversible reactions. The following are some more examples of irreversible reactions: (i) 2Mg(s) + O2(g) 2MgO(s) magnesium

(ii)

magnesium oxide

2HgO(s)

2Hg(l)

mercuric oxide

mercury

+

O2(g)

(iii) NaCl(aq) + AgNO3(aq) AgCl(s) + NaNO3(aq) b) Reversible reactions On the other hand consider the reaction: H2(g) + I2(g) 2HI(g) In this reaction hydrogen and iodine are not completely converted into hydrogen iodide. The reason for this is that the moment some HI is formed it starts decomposing back into H2 and I2. 2HI(g) H2(g) + I2(g) The reactions that can occur in forward and reverse directions, simultaneously under same set of conditions are called reversible reactions. Reversible nature of a reaction is indicated by writing two arrows (or two-half arrows) in opposite directions between reactants and products as shown below;

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H2(g) + I2(g) 2HI(g) or H2(g) + I2(g) 2HI(g) Some more examples of reversible reactions are : (i) Synthesis of ammonia N2(g) + 3H2(g) 2NH3(g) (ii) Oxidation of sulphur dioxide to sulphur trioxide O2(g) 2SO3(g) 2SO2(g) + 6.2.5 Equilibrium in reversible reactions In the last section we have learned that a reversible reaction can occur in forward as well as reverse directions simultaneously. Consider the following reaction: 2SO2(g)

+

O2(g)

2SO3(g)

When the reaction is started by taking a mixture of sulphur dioxide (SO2) and oxygen (O2) it would initially occur only in the forward direction and formation of sulphur trioxide (SO3) would begin. Initially the rate of this reaction is fast. As it progresses its rate decreases. This happens because as reactants are consumed their concentrations decrease. Concentration Concentration is a measure of the amount of a substance contained per unit volume. In chemistry it is commonly measured in terms of molarity. Molarity is the number of moles of a substance present in one litre volume. It has the unit of mol L-1. In case of gases it is their number of moles present in one litre volume. And in case of solutions it is the number of moles of solute present in one litre volume of solution. The molar concentration of a substance X is denoted by writing its formula/symbol within a square bracket [X]. As soon as SO3 is formed, it starts decomposing and the backward reaction also starts. Initially its rate is very slow but as the reaction progresses the concentration of SO3 (which is reactant for the reverse reaction) increases and the rate of reverse reaction also increases. Thus, with the progress of reaction, the rate of forward reaction decreases and that of the reverse reaction increases with Fig. 6.1 Changes in rates of forward and backward time. These changes are depicted in the (reverse) reactions in a reversible reaction. When the two figure 6.1. become equal, the reaction attains equilibrium.

After some time, the rate of the forward reaction becomes equal to the rate of the reverse reaction and the reaction reaches equilibrium state (Fig. 6.1). Under these conditions, there is no change in concentration of any reactant or product. A system is said to be in a state of equilibrium if none of its properties change with time. In other words, when a system is in a state of equilibrium, all its properties remain constant.

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At equilibrium the concentrations of reactants [SO2] and [O2] and product [SO3] are related by the following expression known as the law of equilibrium: Kc

=

2 3 _______________

[SO ]

[SO2][O2]

How to write the expression of the law of equilibrium ? To understand how to write the expression of law of equilibrium for any reaction let us take a general reaction: aA + bB cC + dD For this reaction, the law of equilibrium is given by the following expression : [C]c[D]d Kc = _______________ [A]a[B]b In this expression, Kc is the equilibrium constant for the reaction. The numerator is obtained by multiplying the concentration terms for all products after each term has been raised to the power which is equal to the stoichiometric coefficient of that product. Here C and D are the two products and c and d are their respective stoichiometric coefficients. Therefore, numerator would be the obtained by multiplying [C]c and [D]d terms. Also, conventionally if any pure solid or liquid is taking part in the equilibrium, its concentration is taken as 1. Similarly, the denominator is obtained by multiplying the concentration terms of all reactants after each term has been raised to the power which is equal to the stoichiometric coefficient of that reactant. Static and dynamic equilibrium The type of equilibrium attained by reversible reactions is called dynamic equilibrium. Such an equilibrium state is attained as a result of two equal but opposite changes occurring simultaneously so that no net change occurs in the system. Therefore, all the properties of the system acquire constant values. You can encounter a similar situation when a person is walking on a treadmill. His speed of walking is exactly matched by the speed of the treadmill which moves in the backward direction. The net result is that position of the person does not change and he stays there only. Another similar situation in encountered when a person using an escalator for climbing starts moving down on it and matches his speed with that of the escalator. Another type of equilibrium is attained when a system is acted upon by a set of forces that cancel out each other. Such an equilibrium state is attained when no change occurs in it. This type of equilibrium is called static equilibrium. A book lying on a table is in state of static equilibrium because the downward acting gravitational force is balanced and cancelled by the upward acting force of reaction from the table (Newton’s third law of motion). Another similar situation is encountered in the game tug of war when the efforts of the two opponent teams (forces by which they pull the rope) exactly match and they remain where they are.

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Kc of a reaction is its characteristic property at a given temperature and it characterizes the equilibrium state. Its value changes only when temperature is changed. The same equilibrium state (characterized by the value of Kc) is reached finally whether the reaction is started from the reactant side or from the product side or all reactants and products are mixed in arbitrary amounts. CHECK YOUR PROGRESS 6.2 Select the correct choice about the nature of each reaction out of the two options mentioned against it. 1. Burning of petrol in a car (homogeneous / heterogeneous). 2. CaCO3(s) 3. 2HgO(s)

CaO(s) + CO2(g) (exothermic / endothermic) 2Hg(l) + O2(g) (reversible / irreversible)

4. Bursting of crackers (slow / fast) 5. A reversible reaction at a stage when concentration of reactants and products is changing (equilibrium state /non-equilibrium state) 6.3 CHEMICAL CALCULATIONS AND STOICHIOMETRY In lesson 2 you have learnt how to write and balance chemical equations. Stoichiometry deals with the proportions in which elements or compounds react with one another. In this section we shall learn how to use the stoichiometric information in a balanced chemical equation for making some calculations. 6.3.1 Significance of balanced chemical equation Balanced chemical equation carries the following information: a) Qualitative information carried by a balanced chemical equation • Reactants taking part in the reaction • Products formed in the reaction • Physical states of different reactants and products (if given) b) Quantitative information carried by a balanced chemical equation •

Number of molecules of different reactants and products taking part in the reaction

•

Number of moles of different reactants and products taking part in the reaction

•

Masses of different reactants and products taking part in the reaction

•

Relationship between moles of different reactants and products taking part in the reaction

•

Relationship between masses of different reactants and products taking part in the reaction

•

Relationship between volumes of different gaseous reactants and products taking part in the reaction

: 107 : Chemical Arithmetic and Reactions

Let us understand how to get this information from a chemical equation with the help of an example. Information carried by a chemical equation Names Physical states Moles (Molar masses)

Masses

2Na(s) sodium solid 2 moles ( Na= 23 )

+

2H2O(l) water liquid 2 moles (H2O = 2 +16 = 18)

2 x 23 = 46g 1 x 2 = 2g

2NaOH(aq) + sodium hydroxide aqueous solution 2 moles (NaOH = 23 + 16 + 1 = 40)

2 x 18 = 36g

Volume* of L=22.7L gaseous substance

H2(g) hydrogen gas 1mole (H2 = 2)

2 x 40 = 80g 1 x 22.7

From the information listed above we can conclude that: (i) Sodium metal (solid) reacts with water (liquid) and produces sodium hydroxide (aqueous solution) and hydrogen (gas). (ii) 2 moles of sodium react with 2 moles of water and produce 2 moles of sodium hydroxide and 1 mole of hydrogen. Thus the ratio of number of moles of these substances is 2:2:2:1. (iii) 46 g sodium reacts with 36 g water and produces 80 g of NaOH and 2 g of hydrogen. (iv) 2 moles or 46 g sodium produces 22.7 L of hydrogen gas when it reacts with water. (v) 2 moles or 36 g water produces 22.7 L of hydrogen gas when it reacts with sodium. c) Limitations or information not carried by a chemical equation • Conditions under which the reaction takes place • Rate of the reaction whether it is fast, slow or moderate • The extent up to which the reaction takes place before equilibrium state is reached in case of a reversible reaction 6.3.2 Calculations based on chemical equations The information that can be obtained from a chemical equation can be used to make several types of calculations. Let us carry out few such calculations. a) Mole-mole relationship Example 6.1: In the reaction 2KClO3(s)

2KCl(s)

+

3O2(g)

calculate the following: (i) How many moles of oxygen will be produced if 10 moles of KClO3 are decomposed? (ii) How many moles of KCl would be produced with 0.6 moles of O2? Solution: The given reaction is 2KClO3(s) 2KCl(s) + 3O2(g) 2 moles

2 moles

3 moles

*Volume of a gaseous substance can be calculated by making use of the fact that one mole of a gas occupies a volume of 22.7 L at STP (standard temperature and pressure) i.e. at 273 K temperature and 1 bar pressure.

: 108 : Chemical Arithmetic and Reactions

(i) 2 moles of KClO3 produce 3 moles of oxygen. Therefore, 10 moles of KClO3 would produce 3 × 10 = _________ = 15 moles of oxygen. 2 (ii) With 3 moles of oxygen the number of moles of KCl produced = 2 moles With 0.6 moles of oxygen the number of moles of KCl produced 2 × 0.6 = ___________ = 0.4 moles 3 b) Mass-mass relationship Example 6.2: For the reaction N2(g)

+

3H2(g)

2NH3(g)

Calculate the masses of nitrogen and hydrogen required to produce 680 g of ammonia? Solution: The given reaction is: N2(g)

+

3H2(g)

2NH3(g)

1mole 3 moles 2 moles 1 x 28 3x2 2 x (14+3) 28 g 6g 34 g Thus to produce 34 g ammonia the mass of nitrogen required = 28 g Therefore to produce 680 g ammonia the mass of nitrogen required 28 x 680 = _____________ = 560 g 34 Similarly, to produce 34 g ammonia the mass of hydrogen required = 6 g Therefore to produce 680 g ammonia the mass of hydrogen required 6 x 680 = _____________ = 120 g 34 c) Volume-volume relationship Example 6.3 : The following reaction is used industrially for manufacture of sulphuric acid. 2SO2(g) + O2(g) 2SO3(g) How much volume of oxygen at STP (Standard Temperature and Pressure) would be required for producing 100 L of SO3 (at STP)? Solution: In the reaction 2SO2(g) + O2(g) 2SO3(g) 2 mole 1 mole 2 mole 2 x 22.7 L 22.7 L 2 x 22.7 L 2 volumes 1 volume 2 volumes To produce 2 volumes or 2 L of SO3 the oxygen required is 1 volume or 1 L.

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To produce 1L of SO3 the oxygen required is 0.5 L Therefore to produce 100 L of SO3 the volume of oxygen required is 0.5 x 100 = 50 L d) Mixed calculations Example 6.4: Calculate the mass of hydrochloric acid required for neutralizing 1 kg of NaOH Solution: The neutralization reaction involved between hydrochloric acid and sodium hydroxide is as follows : HCl(aq) + NaOH(aq) NaCl(aq) + H2O (l) 1mole 1 mole 1 + 35.5 23 + 16 + 1 = 36.5 g = 40 g Thus, for neutralizing 40 g of NaOH the mass of HCl required is 36.5 g. For neutralizing 1 kg or 1000 g of NaOH the mass of HCl required is 36.5 x 1000 _________________ = 912.5 g 40 Example 6.5: In the reaction 2Na(s)

+

2H2O(l)

2NaOH(aq)

+

H2(g)

calculate the following: (i) The maximum number of moles of sodium that can react with 4 moles of water. (ii) The mass of sodium hydroxide that would be produced when 4.6 g of sodium reacts with excess of water. (iii) The mass and volume at STP of hydrogen gas that would be produced when 1.8 g of water reacts completely with sodium metal. Solution: 2Na(s) + 2 moles 2 x 23 = 46 g

2H2O(l) 2NaOH(aq) + H2(g) 2 moles 2 moles 1 mole 2 x 18 = 36 g 2 x 40 = 80 g

1 x 2

=2g 22.7 L at STP

(i) From the equation it can be seen that 2 moles of water react with 2 moles of sodium 4 moles of water can react with a maximum of 4 moles of sodium. (ii) 46 g sodium reacts to produce 80 g sodium hydroxide 80 x 4.6 4.6 g sodium would produce _______________ = 8.0 g sodium hydroxide. 46 (iii) 6 g of water produces 2 g or 22.7 L of hydrogen at STP 2 x 1.8 22.7 x 1.8 1.8 g of water would produce ___________ = 0.1 g of hydrogen and ______________ = 1.135 L 36 36 of hydrogen at STP.

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CHECK YOUR PROGRESS 6.3 Consider the equation for combustion of benzene (C6H6): 2C6H6(l) + 15O2(g) 12CO2(g) + 6H2O(g) + heat Some statements about this reaction are given below. Read them carefully and indicate against each statement whether it is true (T) or false (F). 1. 2. 3. 4. 5.

It is an exothermic reaction. 0.1 mole of benzene would require 7.5 moles of oxygen for its combustion. 1 mole of benzene would produce 134.4 L of CO2 at STP. 10.8 g water would be produced by combustion of 15.6 g benzene. 200 g of O2 is sufficient to convert 1 mole of benzene completely into CO2 and H2O.

6.4 ACIDS, BASES AND SALTS You have learnt in your earlier classes about three types of substances–acids, bases and salts. They are vital to many life processes and are valuable to industry. Let us do a quick revision about them. 6.4.1 Acids An acid is defined as a substance that furnishes hydrogen ions (H+) in its solution. Actually, the hydrogen ion, H+ does not exist in the aqueous solution as such. Instead, it attaches itself to a water molecule to form the hydronium ion (H3O+). It is customary, however, to simplify equations by using the symbol for the hydrogen ion (H+). The strongest acids are the mineral or inorganic acids. These include sulphuric acid, nitric acid, and hydrochloric acid. More important to life are hundreds of weaker organic acids. These include acetic acid (in vinegar), citric acid (in lemons), lactic acid (in sour milk), and the amino acids (in proteins). Acids have sour taste and turn blue litmus red. They react with metals (which are more reactive than hydrogen) to liberate hydrogen. Zn(s) + H2SO4(aq) ZnSO4(aq) + H 2(g) 6.4.2 Bases Bases are the substances which furnish hydroxyl ions OH– in their solutions. The hydroxides of metals are the compounds that have the hydroxyl group. They are called bases. Hydroxides of alkali metals–lithium, sodium, potassium, rubidium, and caesium have the special name of alkalies. A basic solution is also called an alkaline solution. Bases have bitter taste and turn red litmus blue. Taste of acids and bases Although you will find mention of taste of acids being sour and that of bases being bitter in books, never attempt to taste them yourself. Many of them can cause serious damage if swallowed or even on their contact with tongue. 6.4.3 Salts A salt is a substance produced by the reaction of an acid with a base. It consists of the cation (positive ion) of a base and the anion (negative ion) of an acid. The reaction between an acid and a base is called a neutralization reaction. In solution or in the molten state,

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most salts are completely dissociated into cation and anion and are good conductors of electricity. 2NaOH(s) sodium hydroxide

+ H2SO4(l) sulphuric acid

Na2SO4(aq)

+

2H2O(l)

sodium sulphate

Another typical acid-base reaction is between calcium hydroxide and phosphoric acid to produce calcium phosphate and water: 3Ca(OH)2(s) calcium hydroxide

+ 2H3PO4(l) phosphoric acid

Ca3(PO4)2(aq) +

6H2O(l)

calcium phosphate

CHECK YOUR PROGRESS 6.4 A substance AB is formed by reaction between an acid X and a base Y along with water. The cation and anion of the compound AB are monovalent. 1. What type of substance is AB? 2. Which one out of AB, X and Y would turn red litmus blue? 3. Which one out of AB, X and Y would have sour taste? 6.5 ACID-BASE EQUILIBRIA IN AQUEOUS SYSTEMS In the last section we discussed the nature of three important types of substances–acids, bases and salts. They show their typical properties in aqueous solutions. In this section we shall learn about their behaviour in such solutions. 6.5.1 Electrolytes and non-electrolytes An electrolyte is a substance that conducts electric current through it in the molten state or through its solution. The most familiar electrolytes are acids, bases, and salts, which dissociate in their molten state when dissolved in such solvents as water or alcohol. When common salt (sodium chloride, NaCl) is dissolved in water, it forms an electrolytic solution, dissociating into positive sodium ions (Na+) and negative chloride ions (Cl–). A non-electrolyte is a substance that does not conduct electric current through it in the molten state or through its solution. Non-electrolytes consist of molecules that bear no net electric charge and they do not dissociate in their molten state or in their solutions. Sugar dissolved in water maintains its molecular integrity and does not dissociate and it is a non-electrolyte. 6.5.2 Strong and weak electrolytes In the last section we learned that electrolytes dissociate into ions in their solutions. Some electrolytes are completely dissociated into ions. They are called strong electrolytes. Sodium chloride, potassium hydroxide and hydrochloric acid are strong electrolytes. On the other hand some other electrolytes are dissociated only partially into ions. They are called weak electrolytes. Acetic acid and ammonium hydroxide are weak electrolytes. 6.5.3 Dissociation of acids and bases in water In the last section we learned that some electrolytes are strong while others are weak. In this section we shall study more about dissociation processes that occur in aqueous solutions of acids and bases.

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6.5.3a Dissociation of acids (i) Dissociation of strong acids Strong acids are completely dissociated into ions in their aqueous solutions. Consider dissociation of hydrochloric acid: HCl(aq) H+(aq) + Cl–(aq) From the above equation it can be seen that • •

HCl is completely converted into its ions and no amount of it remains in the undissociated form. One mole of HCl forms one mole each of hydrogen ions and chloride ions. Thus, concentration (molarity) of H+ ions is same as that of HCl in the solution.

(ii) Dissociation of weak acids Weak acids are only partially dissociated into ions in their aqueous solutions. Consider dissociation of acetic acid. H+(aq) + CH3COO–(aq)

CH3COOH(aq)

From the process depicted above it can be seen that: • • •

•

CH3COOH is only partially dissociated into ions. The process of dissociation is reversible and an equilibrium is established between dissociated and undissociated CH3COOH. The amount of hydrogen ions and acetate ions formed is less than the total amount of acetic acid taken initially. Thus, if one mole of acetic acid was dissolved in one litre of solution (concentration = 1 mol L-1) the concentration of hydrogen ions H+ formed in the solution would be less than 1 mol L-1. In fact acetic acid is such a weak electrolyte that less than 1% of it would dissociate in this solution. We can write expression of the law of equilibrium for the above equilibrium as [H+][CH3COO–] Ka = ________________________ [CH3COOH]

Here the symbol used for equilibrium constant is Ka in place of Kc. Here Ka is dissociation constant of acetic acid. 6.5.3b Dissociation of bases (i) Dissociation of strong bases Strong bases like sodium hydroxide are completely dissociated in their solutions. NaOH(aq)

Na+(aq) + OH−(aq)

From the above equation it can be seen that • •

NaOH is completely converted into its ions and no amount of it remains in the undissociated form. One mole of NaOH forms one mole each of sodium ions and hydroxyl ions. Thus concentration (molarity) of OH– ions is same as that NaOH of in the solution.

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(ii) Dssociation of weak bases Weak bases like ammonium hydroxide are only partially dissociated in their solutions. NH4OH(aq)

NH4+(aq) + OH–(aq)

NH4OH(aq)

NH4+(aq) + OH–(aq)

From the process shown above it can be seen that •

NH4OH is only partially dissociated.

•

The dissociation process is a reversible process and in the solution equilibrium is established between dissociated and undissociated NH4OH.

•

The amount of OH– ions and NH4+ ions formed is less than the total amount of ammonium hydroxide taken initially.

•

We can write expression of the law of equilibrium as Ka =

– + 4 __________________

[NH ][OH ] [NH4OH]

Here the symbol used for equilibrium constant is Kb in place of Kc. Kb is the dissociation constant of ammonium hydroxide. 6.5.4 Self-dissociation of water Pure water is neutral in nature. It ionizes to a small extent and releases an equal number of hydrogen and hydroxide ions. H2O(1)

H+(aq) + OH–(aq)

It can be seen from the above equation that in pure water [H+] = [OH−]

Also, for this equilibrium Kw = [H+]. [OH–] where Kw is known as ionic product of water. This is in fact the equilibrium constant for self dissociation process of water. The term in the denominator is [H2O] which by convention is taken as 1 for any pure solid or liquid (see section 6.2.5). The concentration of H+ and OH– ions in water has been measured and found to be 1 × 10–7 mol L-1 each at 25 0C. Instead of saying that the hydrogen ion concentration in pure water is 1 × 10–7 mol L-1, it is customary to say that the pH of water is 7.0 . The pH is the logarithm (see box) of the reciprocal of the hydrogen ion concentration. It is written: l pH = log _________ [H+] Alternately, the pH is the negative logarithm of the hydrogen ion concentration i.e. pH = - log [H+] Because of the negative sign in the expression, if [H+] increases pH would decrease and if it decreases the pH would increase.

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LOGARITHM Logarithm is a mathematical function. If, Then

x = 10y y = log x

You will study more about logarithm in your higher classes.

Similarly, we may define pOH and pKw as: pOH = –log [OH–] and pKw = –log Kw Since the concentration of OH- ions, [OH-] is 1 × 10–7 mol L–1 ; pOH = 7 The relationship between pKw, pH and pOH is pKw = pH + pOH = 7+7 = 14 The following points should be noted regarding self-dissociation of water: (i) Water produces H+ and OH- ions in equal amounts therefore: [H+] = [OH–] (ii) Water is a neutral liquid. (iii) pH of water is 7.0 at 25 0C temperature. (iv) The sum of pH and pOH of any aqueous solution is always 14 at 25 0C. 6.5.5 Neutral, acidic and basic solutions and their pH In the light of discussion on self-dissociation of water in the last section, we can now discuss the characteristics of neutral, acidic and basic aqueous solutions. 6.5.5a Neutral aqueous solutions Neutral solutions would be similar to water, which is also neutral in nature. Therefore, the following are the characteristics of neutral aqueous solutions: (i) [H+] = [OH–] (ii) pH = 7.0 at 25 0C 6.5.5b Acidic aqueous solutions Acidic solutions would have more [H+] than in water. Therefore the following are the characteristics of acidic aqueous solutions: (i) [H+] > [OH-] (ii) Since hydrogen ion concentration in acidic solutions is more than in water their pH would be less than that of water i.e. pH < 7.0 at 25 0C (iii) For calculation of pH of acidic solutions first the concentration of H+ ions i.e. [H+] is calculated. From it the pH is calculated by the relation pH = –log [H+] Such calculations have been shown in the next section.

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6.5.5c Basic aqueous solutions Basic solutions would have more [OH–] than in water. Therefore they would have less [H+] than water. The following are the characteristics of basic aqueous solutions: (i) [H+] < [OH–] (ii) Since hydrogen ion concentration in basic solutions is less than in water their pH would be more than that of water i.e. pH > 7.0 at 25 0C The pH of such solutions can be calculated indirectly. First pOH is calculated from the concentration of OH- ions using the relation (see next section). pOH = − log [OH−] Then pH is calculated by the relation pH = 14 –pOH Thus in brief we may conclude that at 25 0C: (i) Water has a pH of 7 and is neutral. (ii) Solutions with pH 7 are neutral. (iii) Solutions with pH less than 7 are acidic. (iv) Solutions with pH more than 7 are basic. 6.5.7 Calculations based on pH concept In the last section we learned the concept of pH and its relationship with hydrogen ion or hydroxyl ion concentration. In this section we shall use these relations to perform some calculations. It may be noted that the methods of calculation of pH used in this lesson are valid for solutions of strong acids and bases only. The method is not valid for solutions, which are extremely dilute. The concentration of H+ or OH– should not be less than 10–6molar. Example 6.6 : Calculate the pH of 0.001 molar solution of HCl. Solution: HCl is a strong acid and is fully dissociated in its solutions according to the process: H+(aq) + Cl−(aq) HCl(aq) From the above process it is clear that one mole of HCl will give one mole of H+ ions. Therefore the concentration of H+ ion would also be 0.001 molar or 1 x 10–3 mol L–1. Thus [H+] = 1x 10– 3 mol L–1 pH = −log [H+] = − ( − 3) =3 Thus pH= 3 Example 6.7 : What would be the pH of an aqueous solution of sulphuric acid which is 5 x 10–5 molar in concentration? Solution : Sulphuric acid dissociates in water as: H2SO4(aq) 2H+(aq) + SO42−(aq)

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Thus each mole of sulphuric acid gives two moles of H+ ions in solutions. One litre of 5 x 10−5 molar solution contains 5 x 10−5 moles of H2SO4, which would give 2 x 5 x 10-5 = 10 x 10-5 = 10-4 mol of H+ , therefore [H+] = 10–4 mol L–1 Therefore, pH = –log [H+] = –log 10– 4 = – (–4) =4

Example 6.8 : Calculate the pH of 1x10– 4 molar solution of NaOH. Solution: NaOH is a strong base and dissociates in its solutions as: NaOH(aq) Na+(aq) + OH– (aq) One mole of NaOH would give one mole of OH- ions. Therefore [OH−] = 1x10− 4 molar pOH = – log [OH−] = – (log 10−4) = − (− 4) pOH = 4 Since pH = 14 – pOH = 14 – 4 = 10 CHECK YOUR PROGRESS 6.5 1. Aqueous solution of a substance does not conduct electricity through it. What type of substance is it? 2. A substance completely dissociates in to ions when dissolved in water. What type of substance is it? 3. X is a strong acid while Y is a weak acid. In whose aqueous solution a dynamic equilibrium will be established? 4. In an aqueous solution [H+] = [OH–] What type of solution is it, acidic, basic or neutral? 5. pH of a solution is 4. What is the hydrogen ion concentration in it? •

•

• • •

LET US REVISE Based on the nature of chemical changes, reactions can be classified into five types (i) combination reactions, (ii) decomposition reactions, (iii) displacement reactions, (iv) double-displacement reactions, and (v) oxidation-reduction reactions. The reactions in which all the reactants and products are present in the same phase are called homogeneous reactions and the reactions in which reactants and products are present in different phases are called heterogeneous reactions. The reactions in which heat is evolved are called exothermic reactions and the reactions in which heat is absorbed are called endothermic reactions. The reactions that can occur in forward and reverse directions simultaneously under same set of conditions are called reversible reactions. A system is said to be in a state of equilibrium if none of its properties changes with time.

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• •

•

•

A. 1.

2.

3.

4.

5.

One mole of a gas occupies a volume of 22.7 L at STP (standard temperature and pressure) i.e. at 273 K temperature and 1 bar pressure. An acid is a substance that furnishes hydrogen ions, H+; a base is a substance that furnishes hydroxyl ions, OH– in its solutions and a salt is produced when an acid and a base react with each other. An electrolyte conducts electric current through itself in the molten state or through its solution. If it dissociates completely it is known as a strong electrolyte and if it dissociates only partially it is known as a weak electrolyte. pH of a neutral solution is 7, that of an acidic solution is less than 7 and that of a basic solution is more than 7 at 250C TERMINAL EXERCISES Multiple choice type questions. The reaction given below is: Zn(s) + CuSO4(aq) ZnSO4(aq) + Cu(s) (a) Combination reaction (b) Displacement reaction (c) Redox reaction (d) Displacement and redox reaction. The reaction given below is not a: CO2(g) C(s) + O2(g) (a) Heterogeneous reaction (b) Displacement reaction (c) Exothermic reaction (d) Redox reaction. In the reaction 2KClO3(s) 2KCl(s) + 3O2(g) (a) 1 mole of KClO3 produces 1.5 mole of O2 (b) 1 mole of KClO3 produces 3 moles of O2 (c) 2 moles of KClO3 produce 1 mole of KCl (d) when 1 mole of KCl is produced 3 moles of O2 are produced Which of the following statements about chemical equilibrium is not correct ? (a) It is dynamic equilibrium. (b) It can be established by a reversible reaction only. (c) It is established in any aqueous solution of a strong acid or a strong base. (d) On changing the temperature the equilibrium constant’s value would also change. pH of a solution is equal to (a) log [H+] (b) - log [H+] (c) log [OH–] (d) - log [OH–]

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6. In which of the following reactions H2O2 acts as a reducing agent? (a) H2O2 +2KI 2KOH + I2 (b) H2O2 + SO2 H2SO4 (c) H2O2 + Ag2O 2Ag + H2O + O2 (d) 4H2O2 + PbS PbSO4 + 4H2O B. Descriptive type questions. 1. Write electronic definitions of oxidation and reduction. 2. Give one example each of slow and fast reactions. 3. Give any two examples of quantitative information carried by a chemical equation. 4. What is an acid? 5. What is pH? 6. What is an exothermic reaction? Give one example. 7. Differentiate between displacement reactions and double displacement reactions. 8. What are weak electrolytes? Give one example. 9. In the reaction Cl2(g) + 2KBr(aq) 2KCl(aq) + Br2(aq) How much mass of Cl 2 is required to produce 1.5 moles of Br2? 10. What is the pH of 5x10–4 molar solution of H2SO4? 11. In the reaction: CuO(s) + H2(g) Cu(s) + H 2O(l) Identify the species that is getting (i) reduced (ii) oxidized. 12. What is the difference between dynamic and static equilibrium? Give example of each. 13. NH4OH is a weak base. Write down the equilibrium established in its aqueous solution and the expression of its dissociation constant Kb. 14. Given the following reaction 2Al(s) + Fe2O3(s) 2Fe + Al2O3(s) calculate the mass of Fe2O3 in grams required to produce 20.0 g of Fe. (Relative atomic masses: Fe = 55.8; O = 16). 15. Calculate the pH of (i) 10–5 mol L–1 HCl and (ii) 10–4 mol L–1 NaOH. 16. What are oxidation and reduction? Give one example with equation of a redox reaction. Identify the oxidizing agent and the reducing agent in it. 17. (i) What is a homogeneous reaction? Give one example each of gas phase and solution phase homogeneous reactions. (ii) What is a reversible reaction? Give one example. 18. In the reaction 3C3H6 + 2KMnO4 + 4H2O 3C3H8O2 + 2KOH + 2MnO2 Calculate, (i) the number of moles of MnO2 produced by 12 moles of C3H6. (ii) the number of moles of KMnO4 needed to react with 0.006 moles of C3H6. (iii) the number of moles of KMnO4 needed to produce 0.15 moles of C3H8O2. (iv) the mass of C3H6 required to produce 5.6 grams of KOH. (Atomic mass of K = 39)

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19. What is a neutralization reaction? A titration was started by taking 20 mL of 10–2 molar HCl. Then a solution of NaOH was gradually added from the burette. By mistake the student missed the end point and added excess of NaOH. When he finished the titration, the solution was 10−4 molar in NaOH. What was the pH of the solution present in the titration flask? (i) In the beginning of the titration (ii) at the end point when NaOH had just neutralized the HCl and (iii) at the end of the titration. 20. Sodium metal reacts with excess of water according to the reaction: 2Na(s) + 2H2O(l) 2NaOH(aq) + H2(g) (i) Calculate the mass of sodium required to produce 1 kg of NaOH. (ii) Find out the volume of H2 evolved at STP when 1.012 kg of sodium reacts with excess of water. ANSWERS TO CHECK YOUR PROGRESS 6.1 1. 2. 3. 4. 5. 6.2 1. 2. 3. 4. 5. 6.3 1. 2. 3. 4. 5. 6.4 1. 2. 3. 6.5 1. 2. 3. 4. 5.

D C B A E Heterogeneous Endothermic Irreversible Fast Non-equilibrium T F T T F Salt Y X Non-electrolyte Strong electrolyte In solution of Y Neutral 10–4 mol L-1

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GLOSSARY Acid: A substance containing hydrogen that furnishes hydrogen ions (H+) in its solutions. Base: A substance that furnishes hydroxyl ions, OH– in its solutions. Combination reaction: A reaction in which two or more substances react to form a new substance. Decomposition reaction: A reaction in which one substance breaks down into two or more substances. Displacement reaction: A reaction in which an ion present in a compound is displaced by another ion. Double displacement reactions: The reactions in which two ionic compounds exchange their ions. Electrolyte: A substance that conducts electric current through it in the molten state or through its solution. Endothermic reactions: The reactions in which heat is absorbed Equilibrium state: A state in which no property of system changes with time. Exothermic reactions: The reactions in which heat is evolved Heterogeneous reactions: Reactions in which reactants and products are present in more than one phase. Homogeneous reaction: Reactions in which all the reactants and products are present in the same phase. Molarity: It is the number of moles of a substance present in one litre volume. Neutralization: The reaction between an acid and a base to produce salt and water. Non-electrolyte: A substance that does not conduct electric current through it in the molten state or through its solution. Oxidation: A process which involves loss of electrons. pH: The negative logarithm of the hydrogen ion concentration. Reduction: A process which involves gain of electrons. Reversible reactions: The reactions that can occur in forward and reverse directions simultaneously under same set of conditions. Salt: A substance produced by the reaction of an acid with a base along with water. STP: Standard temperature and pressure i.e. when temperature is 273 K temperature and pressure is 1 bar. Strong electrolytes: The electrolytes that dissociate completely in their solutions. Synthesis reaction:The reaction in which a compound is formed by combination of its constituent elements. Weak electrolytes: The electrolytes that dissociate only partially into ions in their aqueous solutions.

7

Motion and Its Description In this world, we see many objects moving around us, for example, cars, buses, trucks, and bicycles moving on the road, aeroplanes flying in air and ships sailing on the sea, leaves falling from the trees and water flowing in the river. All these objects are changing their position with time. When an object changes its position with time, it is said to be in motion. In these examples, motion is easily visible to us. But in some cases, motion is not easily visible to us. For example, air moves in and out of our lungs and blood flows in our body. The moon moves around the earth, while the two together go around the sun. The sun itself with its planets travels through our own galaxy. An object that does not change its position with time is said to be at rest, for example a book lying on a table. In this lesson, you will learn how to describe motion. For this, we will develop the concepts of displacement, velocity and acceleration. You will also learn how these quantities are related to each other. For an object moving along a straight line with uniform acceleration, we will obtain simple equations (known as equations of motion) connecting these quantities with time. OBJECTIVES After completing this lesson, you will be able to: !

!

! !

! !

define the terms motion, scalar and vector quantities, displacement, speed, velocity and acceleration, distinguish between (a) rest and motion (b) scalar and vector quantities (c) speed and velocity; differentiate between uniform and non-uniform motion; plot and interpret the following graphs (a) displacement – time graph for uniform motion, (b) velocity – time graph for uniformly accelerated motion; establish three equations of motion; solve problems based on equations of motion.

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7.1 SOME BASIC ASPECTS OF MOTION 7.1.1 Types of motion In our daily life we see many objects moving. Some objects move in a straight line. For example, a ball rolling on a horizontal surface, a stone falling from a building and a runner on a 100m race track. In all these examples, objects change their positions with time along a straight line. This type of motion is called rectilinear motion. Observe the motion of a second’s hand of a clock, or motion of a child sitting on a marry-go round, or the motion of the blades of an electric fan. In such a motion, an object follows a circular path during motion. This type of motion is called circular motion. If you take a stone, tie a thread to it and whirl it with your hand, you will find that the stone moves on a circular path. In all such cases, though an object changes its position with time, it remains at a fixed distance from a point. Some objects move to and fro, such as a swing, a pendulum, the branches of a tree in the wind and the needle of a sewing machine. Such type of motion is called oscillatory motion. In such a motion, an object oscillates about a point, often called equilibrium position. 7.1.2 Scalar and vector quantities Each of the physical quantities you encounter in this book can be categorized as either a scalar or a vector quantity. A scalar is a quantity that can be completely specified by its magnitude with appropriate units; i.e. a scalar has only magnitude and no direction. A vector is a physical quantity that requires the specification of both magnitude and direction. Mass is an example of a scalar quantity. If someone tells you that mass of an object is 2 kg, that information completely specifies the mass of the object; no direction is required. Other examples of scalar quantities are, temperature, time interval, the number of students in a class, the volume of water in a bucket and the number of pages in this book. An example of a vector quantity is force. If your friend tells you that he is going to exert a force of 5N on an object, this is not enough information to let you know what will happen to the object. The effect of a force of 5N exerted horizontally is different from the effect of a force of 5N exerted vertically upward or downward. In other words, you need to know the direction of the force as well as its magnitude. Velocity is a vector quantity. If you wish to describe the velocity of a moving vehicle, you must specify both its magnitude (say, 30 m/s) and the direction in which the vehicle is moving (say, northeast). Other examples of vector quantities include displacement and acceleration, which are defined in this lesson. We use different symbols to represent scalar and vector quantities. A scalar quantity is represented by an ordinary letter (such as a) or number (such as 5) with appropriate unit. 3 cm, 6 L, and 12 kg represent scalar quantities. A vector quantity is represented by a symbol printed in boldface, such as a or A. Since in handwriting, this representation is not practical, a common notation is to indicate a r r vector quantity by an arrow over its symbol, a or A . When we are interested only in the magnitude of a vector quantity, such as a, we write it as a scalar (that is, a) indicating that its direction is not being considered. Graphically, a vector is represented by an arrow. The

Motion and Its Description : 123 :

length of the arrow is proportional to the magnitude of the vector and the arrow points in the direction of the vector. Fig. 7.1 a shows vector A and vector –A, both has the same magnitude but are in opposite directions. A

A

B

–A

Fig. 7.1 (a) Vectors in same direction

Fig. 7.1 (b) Vectors in different directions

Figure 7.1 (b) shows vector A and another vector B whose magnitude is same as that of A but direction is different. Scalars can be added and subtracted like ordinary numbers. Vectors follow different laws. However, vectors having same direction can be added easily. For example, sum of vector A and a vector C (Fig. 7.1c) is a vector D whose magnitude is the sum of the magnitudes of vector A and C and direction is the same as that of A. A

D=A+C

C Fig. 7.1 c Addition of vector

Subtraction of vector C from vector A can be seen as addition of vector – C to vector A as shown in Fig. 7.1d. The resultant has a magnitude equal to the difference of the magnitude of A and the magnitude of B. It points in the direction of A (the bigger of the two vectors). A A

E

C

(–C)

E = A–C = A+(–C)

–C

Fig. 7.1 (d) Subtraction of vectors

7.1.3 Distance and displacement Motion occurs when an object changes position. Therefore, in order to describe the motion of an object, one must be able to specify its position at all times. In this course, we shall consider motion of objects in which position changes along a straight line, known as rectilinear motion. Let us say that the object moves along x-axis as shown in Fig. 7.2 S – –100 –80

O

R –60

–40

–20

0

P 20

40

60

Q 80

100 +x (m)

Fig. 7.2 Movement of an object along x-axis

Then position of the object is specified with reference to a point, say O. This point is called origin of the axis. The position is taken to be positive if it is to the right of the origin and negative, if it is to the left. So, if a car is at P, its position is + 60m. If it is at R, its position is –40m.

: 124 : Motion and Its Description

Suppose a car starts from O, moves to Q and then comes back to P. During this motion, the actual path length covered by the car = OQ + QP = +100m + (40m) = 140m. This is known as distance. The total path length covered by an object irrespective of its direction of travel is called distance. It is a scalar quantity. In SI unit, it is measured in metres (m). In the above example, at the end of journey, the car is at P. So, its final position is P while its initial position was O. Therefore, change in position is OP +60m only. This is known as displacement. The displacement of an object is defined as the change in its position and is given by the difference between its final and initial position. Displacement of an object = final position – initial position. Displacement is a vector quantity. In SI units, it is measured in metres (m). In the above example, the displacement of the car is + 60m. The plus sign means that it is along + x-axis. The magnitude of this displacement is 60m and its direction is towards right or + x-axis. Consider another case. Suppose a truck moves from O to R and returns to O. What is the distance covered by the truck? What is its displacement? Though the truck is moving along – x-direction, the length of path covered is positive. (The minus or plus sign, as explained earlier, indicates the direction of travel). Distance covered by the truck

= Path length of OR + Path length of RO = 40 m + 40 m = 80 m

Displacement of the truck

= Final position – initial position = O (since it returns to origin O, its initial position)

Example7.1: What is the distance covered and displacement of a car, a) b)

If the car moves from O to P If the car moves from O to P and then back to R (see Fig. 7.2).

Solution : a) Distance covered in moving from O to P Displacement

=

Length of path OP = 60 m

= Final position – Initial position = + 60 m – (0 m) = + 60 m 60 m is the magnitude of the displacement and + sign indicates that it is directed towards right or towards P. Note that in this case magnitude of displacement is equal to the distance. This is so because the object does not change its direction during the course of motion. b) Distance covered in this case

=

Length of path OP + Length of path PR

Motion and Its Description : 125 :

= 60 m + (60 m + 40 m) = 160 m Displacement = Final position – Initial position = (–40 m ) – (0 m ) = – 40 m The minus sign shows that the direction of displacement is towards left or towards – x direction. Note that in this case, the magnitude of displacement (i.e. 40 m) is not equal to the distance (160 m). 7.1.4 Speed and velocity An object in motion travels a given distance in a certain time interval. How fast is the object moving? This is indicated by a quantity called speed. The speed of an object is defined as the length of the path travelled per unit time. Speed =

Path length or distance covered Time taken

…(7.1)

Its unit is m/s. It is also expressed in kmh-1. For example, if a car covers a distance of 61 km in 2h, its speed is 61km / 2h = 30.5 kmh-1. The velocity of an object is defined as the displacement divided by the time interval during which the displacement occurred: Displacement …(7.2) Time taken Since displacement is a vector quantity, velocity is also a vector quantity. Its unit is the same as that of speed, i.e. ms-1 or kmh-1. Velocity =

ACTIVITY 7.1 Aim : To calculate your average speed of walking. What is required ? A metre stick or a measuring tape; stop watch or a wrist watch with second’s hand. What to do? i) Take a stopwatch to a field. ii) Using the measuring tape mark two positions (in a straight line) on the field that are 50m apart. iii) Start the clock as you walk down the marked line and stop it as you reach the 50m mark. Find the time taken by you to cover this distance. iv) Calculate your average speed of walking. v) Measure the time it takes you to run the same distance. What is your average speed? To represent displacement and velocity, we must use vector notations. But in this class, we shall be considering motion along a straight line. As mentioned earlier, in such cases, direction can be represented by + or – signs. Therefore, we need not use vector notations.

: 126 : Motion and Its Description

For example, consider a car moving towards + x axis (Fig. 10.1). It moves from O to A position + 900 m in 1 minute. Then its displacement = + 900 m – (0 m ) = + 900 m. + 900 m = +15 ms–1 60 s The magnitude of velocity is 15 m/s and it’s direction (as indicated by + sign) is towards right or towards + x axis. Suppose the car travels back to origin O in 90 s. Then, speed for this motion = Distance covered/ time taken = (900 m + 900 m)/ (60 s + 90 s)

Therefore, velocity =

=

1800 m = 12 ms-1 150 s

Displacement 0m = = 0 ms-1 Time taken 150 s (Displacement is zero because final position coincides with the initial position). CHECK YOUR PROGRESS 7.1 1. If the average velocity of an object is zero in some time-interval, what can you say about the displacement of the object for that time interval? 2. If B is added to A, under what conditions does the resultant vector have a magnitude equal to A+B? Under what conditions is the resultant vector equal to zero? 3. Car A travelling from Delhi to Ghaziabad, has a speed of 25 ms-1. Car B, travelling from Delhi to Gurgaon, also has a speed of 25 ms-1. Are their velocities equal? Explain. 4. Give one example of circular motion and one example of motion in a straight line. 5. A body moves in a straight line from O to P and then to Q. What is the value of (i) distance travelled by the body, and (ii) displacement of the body.

Velocity for this motion

=

7.2 GRAPHICAL REPRESENTATION OF MOTION 7.2.1 Position time graph It is easy to analyze and understand motion of an object if it is represented graphically. To draw graph of the motion of an object, its positions at different times are shown on y – axis and time on x – axis. For example, positions of an object at different times are given in Table 7.1. Time (s)

Table 7.1 Position of different objects at different times 0 1 2 3 4 5 6 7 8 9

Position (m) 0

10

20

30

40

50

60

70

80

10

90 100

In order to plot position – time graph for data given in Table 7.1, we represent time on horizontal axis and position on vertical axis drawn on a graph paper. Next, we choose a suitable scale for this. For example, in Fig. 7.3, 1 cm on horizontal axis represent 2 s of time interval and 1 cm on vertical axis represent 20 m, respectively. If we connect different points representing corresponding position time data, we get a straight line as shown in

Motion and Its Description : 127 :

Fig. 7.3. This line represents the position-time graph of the motion corresponding to data given in Table 7.1.

100

Distance (m)

80

60

40

20

0

1

2

3

4

5

6

7

8

9

10

11

12

Time (s)

Fig. 7.3 Position-time graph for the motion of a particle on the basis of data given in table 7.1 Fi 7 3

We note from the data that displacement of the object in 1st second, 2nd second,………, 10th second is the same i.e. 10 m. In 10 second, the displacement is 100 m. Therefore, velocity is 100 m/10 s = 10 m/s for the whole course of motion. Velocity during 1st second = 10 m/ 1s = 10 ms-1 Velocity during 2nd second = 10 m/1s = 10 ms-1 and so on. Thus, velocity is constant i.e., equal to 10 m/s throughout the motion. The motion of an object in which its velocity is constant, is called uniform motion. As you see in Fig. 7.3, for uniform motion, position-time graph is a straight line. ACTIVITY 7.2 Aim : To plot and interpret the graph of the motion (walking) of your friend. What is required ? A metre stick, stop watch, and a marker (chalk, etc.) What to do? (i) Go out to your college field with your friend. (ii) Using a meter stick, mark positions, 0, 5m, 10m, 15m, 20m, 25m, 30m, 35m, 40m, 45m, and 50m. (iii)Ask your friend to walk down the line starting from position marked 0m. (iv)As your friend starts walking, start the stop watch and record the reading of the stopwatch as he touches the marks 5m, ................, 50m. What do you observe? (i) Record your data in the following table:

: 128 : Motion and Its Description

Displacement (m)

Time (s)

Displacement (m)

0

0

30m

5m

35m

10m

40m

15m

45m

20m

50m

Time (s)

25m

(ii) Plot a graph of distance (vertical axis) and time (horizontal axis). What do you infer? (i) Is the graph a straight line? If yes, what does it mean? If no, what does it mean? (ii) Did your friend travel this distance with uniform velocity? (iii)Calculate the average velocity of your friend for a dsiplacement of 20m, 40m and 50m. Are they same? Explain your result. Like position-time graph, one can also plot displacement-time graph. Displacement is represented on the vertical axis and time interval on the horizontal axis. Since displacement in each second is 10 m for data in Table 7.1, the same graph (Fig. 7.3) also represents the displacement-time graph if the vertical axis is labelled as displacement. How will the position-time graph look like for a stationary object or object at rest. Suppose an object is at rest at position x = 40 m. Then, its position-time graph will be a straight line parallel to the time axis as shown in Fig. 7.4 because at all times, it is at 40 m.

100

Distance (m)

80

60

40

20

0

1

2

3

4

5

6

7

8

9

10

11

12

Time (s)

Fig. 7.4 Position time graph of a particle at rest

7.2.2 Velocity – time graph Take time on the horizontal axis and velocity on the vertical axis on a graph paper. Let 1 cm on horizontal axis represent 2 s and 1 cm on vertical axis represent 10 ms-1. Plotting the data in Table 7.2 gives us the graph as shown in Fig. 7.5.

Motion and Its Description : 129 : Table 7.2 Velocity-time data of an object Time (s)

0

1

2

3

4

5

6

7

8

9

Position (m)

0

10

10

10

10

10

10

10

10 10

10 10

Velocity (ms–1)

50 40 30 20 10 2

4

6

8

10

Time (s)

Fig. 7.5 Velocity-time graph for the motion of a particle on the basis of data given in table 7.2

Thus, we see that the velocity-time graph of motion represented in Table 7.1 and Table 7.2 is a straight line parallel to time axis. This is so because the velocity is constant throughout the motion. The motion is uniform. Consider the area under the graph in Fig. 7.5. Area = (10 ms-1) x 10 s = 100 m. This is equal to the displacement of the object in 10s. Area under velocity-time graph = Displacement of the object during that time interval. Though, we obtained this result for a simple case of uniform motion, it is a general result. Let x be displacement of an object in time t, moving with uniform velocity v, then x = v t (Uniform motion ) …(10.3) In real life, objects usually do not move with constant velocity. We see that usually an object starts from rest, picks up motion, moves some distance, slows down and finally comes to rest. This means that the velocity during different time intervals of motion is different. In other words, velocity is not constant. Such a motion is called non-uniform motion. This change in velocity with time is a physical quantity called acceleration which we shall define next. 7.2.3 Acceleration The acceleration of an object is defined as the change in velocity divided by the time interval during which this change occurs. Acceleration =

Change in velocity Time interval

…(10.4)

Its unit is m/s2. It is a vector quantity. Suppose the velocity of a car changes from + 10 m/s to + 30 m/s in a time interval of 2.0 s. Note that both velocities are towards the right, as indicated by + signs. Therefore, Acceleration =

30 m / s − 10 m / s = + 10 ms-2 2 .0 s

: 130 : Motion and Its Description

The acceleration in the present case is +10 ms-2. This means that the car accelerates in the + x direction and its velocity increases at a rate of 10 ms-1 every second.

V (ms–1)

If the acceleration of an object during its motion is constant, we say that the object is moving with uniform acceleration. The velocity-time graph of such a motion is a straight line inclined to the time axis as shown in Fig. 7.6.

0

t (s)

Fig. 7.6 Velocity-time graph of a particle moving with uniform acceleration

For a given time interval, if the final velocity is more than the initial velocity, then according to Fig. 7.6, the acceleration will be positive. However, if the final velocity is less than the initial velocity, the acceleration will be negative. What is the acceleration corresponding to motion represented in Fig. 7.6? It is zero since there is no change in velocity with time. Thus, for uniform motion, the acceleration is zero and for non-uniform motion, the acceleration is non-zero.

CHECK YOUR PROGRESS 7.2 1. Look at fig. 7.7. (i) What kind of motion does the graph represent? (ii) What does the slope of the graph represent?

d (m)

Note: Please note that speed and velocity that we defined in the earlier section are, in fact, average speed and average velocity for the time-interval under consideration. Unless otherwise specified, terms ‘speed’ and ‘velocity’ wherever used refer to the ‘average speed’ and ‘average velocity’.

0

t (s)

Fig. 7.7

2. Look at fig. 7.8. (i) What kind of motion does the graph represent? (ii) What does the area under the graph represent? Fig. 7.8

3. Look at fig. 7.9. (i) What kind of motion does the graph represent? (ii) What does the slope of the line represent? (iii) What does the area under the curve represent?

V (ms–1)

Motion and Its Description : 131 :

t(s)

O

10

Fig. 7.9

4. A car starts from rest accelerates uniformly and attains a maximum speed of 20 ms-1 in 5 seconds. In the next 10 s it slows down uniformly and comes to rest at the end of 10th s. Draw a velocity time graph for the motion. Calculate from the graph (i) acceleration, (ii) retardation, and (iii) distance travelled. 5. A body moving with a constant speed of 10 ms-1 suddenly reverses its direction of motion at the 5th second and come to rest in the next 5 seconds. Draw a position - time graph of the motion. 7.3 EQUATIONS OF MOTION Consider an object moving with uniform acceleration, a. Let u be its initial velocity (at time t = 0), v, its velocity after time t and s, its displacement during this time interval. Let us see how these quantities are related to each other. 7.3.1 Relation between, v, u, a and t According to the definition of acceleration, we have Acceleration =

Change in velocity Time interval v −u t

or

a=

or,

v= u+at

…(10.5)

With the help of this equation, we can find velocity of a uniformly accelerated object after a given time interval. Or, given any three of these quantities, fourth can be found using this equation. Example 7.2: A car has an initial velocity of 25 ms-1. The brakes are applied and the car stops in 2.0 s. What is the acceleration of the car? Solution: Using (10.5),

v = 0, u = 25 ms-1, t = 2.0 s

O = 25 ms-1 + a (2.0s) hence, a = - 12.5 ms-2 It is negative. Negative acceleration is also called deceleration. 7.3.2 Relation between s, u, a and t From equation (10.3), we have Displacement = (average velocity) × ( time interval )

: 132 : Motion and Its Description

or,

v+u  s= t  2 

But,

v = u + at

Therefore, s =

1 (u + u + at ) t = u t + 1 a t 2 2 2

1 s = ut + a t 2 2

… (10.6)

If an object starts from rest, u = 0 and equation (10.6) reduces to s=

1 2 at 2

… (10.7)

Thus, we see that the displacement of an object undergoing a constant acceleration is proportional to t2, while the displacement of an object with a constant velocity (zero acceleration) is proportional to t (Equation 10.3). A body in free fall, falls with a uniform acceleration, called acceleration due to gravity (denoted by g) and having an average value 9.8 ms-2 near the surface of earth. For this motion the equations of motion become v = u + gt s = ut + ½ gt2 Use these concepts to do the following activity: ACTIVITY 7.3 Aim: To measure your reaction time. What is required? To do this activity, you need the help of your friend, a metre scale, and a stop watch. What to do? (i) Take a metre scale and ask your friend to hold it vertically between his index finger and thumb. (ii) Note the position of the metre scale with respect to his index finger. (iii)Ask your friend to release the ruler and you must catch it (without lowering your hand after catching it). (iv)Note the position of the metre scale, when you catch it and find the distance through which the ruler falls. Let it be d. (v) Repeat this activity 5 times and note the value of d each time.

Motion and Its Description : 133 :

What do you infer? (i) The ruler is a freely falling object with u = 0, a = g (acceleration due to gravity = 9.8 m/s2) 1 2 Using equation of motion, s = ut + a t 2

we have d = or t r =

1 2 g tr 2

2d g

(ii) Using the different experimentally values of d obtained, you can calculate tr find the mass of all these values. What you get is your reaction time. (iii)Similarly, you can measure the reaction time of your friend. It is usually about 0.2 s. Example 7.3: An object with an initial velocity of 4.0 m/s is accelerated at 6.0 m/s2 for 2.0 s. (a) How far does the object travel during this period? (b) How far would the object travel if it were initially at rest? Solution: a) Given u = 4.0 ms-1, t = 2.0 s, a = 6.0 ms-2 s = u t + ½ a t 2 = (4.0 ms-1) ( 2.0 s) + (1/2) (6.0 ms-2) (2.0 s)2 = 8.0 m + 12.0 m = 20 m. b) For u = 0, s = 0 + ½ (6.0 ms-2) (2.0 s) 2 = 12 m 7.3.3 Relation between u, v, and s We know that, u+v s= t  2  and,

v −u t On multiplying these two equations, we have a=

 v − u  v + u  v2 −u2 as =  t =   t  2  2 or, v2 = u2 + 2 a s

…(10.8)

Equations (10.5), (10.6) and (10.8) are the three equations of motion. Example 7.4: A bus starts from rest and moves with a uniform acceleration of 3ms-2. What will be its velocity after moving a distance of 37.5 m?

: 134 : Motion and Its Description

Solution : Given

u = 0, a = 3 ms-2, s = 37.5 m v = u2 + 2 a s = 0 + 2 (3 ms-2) (37.5 m) = 225 m2/s2 = (15 ms-1) 2 v = 15 ms-1

Example 7.5: A body is dropped from the top of a 3 story (h=15m) building. After how much time will it strike the ground? (g=10ms-2) 1 Solution: s = ut + _____ gt2 2 u = 0, g = 10 ms–2, s = 15m ∴ 15 =

⇒ t=

1 × 10t 2 2

15 = 3 = 1732 . s 5

CHECK YOUR PROGRESS 7.3 1. A ball is thrown straight up with an initial velocity of + 19.6 ms-1. It was caught at the same distance above ground from which it was thrown: (i) How high does the ball rise. (ii) How long does the ball remain in air? (g=9.8 m/s2) 2. A ball is thrown vertically upwards. (i) What are its velocity and acceleration when it reaches the highest point? (ii) What is its acceleration just before it hits the ground? 3. A body accelerates from rest and attains a velocity of 10 ms-1 in 5s. What is its acceleration? 4. A body starts its motion with a speed of 10 ms-1 and accelerates for 10 s with 10 ms-2. What will be the distance covered by the body in 10s? 5. A body starts from rest and covers a distance of 50m in 10 s. What is the average speed of the body?

!

!

LET US REVISE If a body stays at the same position with time, it is at rest.

!

If the body changes its position with time, it is in motion.

!

Motion is said to be rectilinear if the body moves in the same straight line all-the time, e.g, a car moving in a straight line on a level road.

!

The motion is said to be circular if the body moves on a circular path: e.g, the motion of the tip of the hand of a watch.

!

The total path length covered by a moving body is the distance travelled by it.

Motion and Its Description : 135 : !

The difference between the final and initial position of a body is called its displacement.

!

Physical quanities are of two types (i) scalar: which have magnitude only, no direction (ii) vector: which have magnitude as well as direction.

!

Distance, speed, mass, time, temperature etc. are scalar quantities, whereas displacement, velocity, acceleration, momentum, force etc. are vector quantities.

!

Distance travelled in unit time is called speed, whereas, displacement per unit time is called velocity.

!

Position-time graph of a body moving in a straight line with constant speed is a straight line sloping with time axis. The slope of the line gives the velocity of the motion.

!

Velocity-time graph of a body in a straight line with constant speed is a straight line parallel to time axis. Area under the graph gives distance travelled.

!

Velocity-time graph of a body in a straight line with constant acceleration is a straight line sloping with the time axis. The slope of the line gives acceleration.

!

For uniformly accelerated motion : v = u+at 1 s = ut + _____ at2 2 where u = initial velocity, v = final velocity, and s = distance travelled in t seconds. TERMINAL EXERCISES

1. Explain whether or not the following particles have an acceleration: (i) a particle moving in a straight line with constant speed, and (ii) a particle moving on a curve with constant speed 2. Consider the following combination of signs and values, for velocity and acceleration of an object with respect to a one-dimensional motion along x-axis: Velocity a. Positive b. Positve c. Positive d. Negative

Acceleration Positive Negative Zero Positive

Velocity e. Negative f. Negative g. Zero h. Zero

Acceleration Negative Zero. Positive Negative

Describe what an object is doing in each case, and give a real-life example for a car on an east-west one-dimensional axis, with east considered as the positive direction. 3. A car travelling initally at + 7.0 m/s accelerates at the rate of + 0.80 m/s2 for an interval of 2.0s. What is its velocity at the end of the acceleration? 4. A car travelling in a straight line has a velocity of + 5.0 m/s at some instant. After 4.0s, its velocity is + 8.0 m/s. What is its average acceleration in this time interval? 5. The velocity - time graph for an object moving along a straight line as shown in figure. 7.10.

: 136 : Motion and Its Description

8 6

V (ms–1)

4 2 t (s) –2

5

10

15

20

–4 –6 –8

Fig. 7.10

Find the average acceleration of this object during the time intervals 0 to 5.0 s, 5.0s to 15.0s, and 0 to 20.0s. 6. The velocity of an automobile changes over a period of 8 s as shown in the table given below: Time(s) 0.0 1.0 2.0 3.0 4.0

Velocity (m/s) 0.0 4.0 8.0 12.0 16.0

Time (s) 5.0 6.0 7.0 8.0

Velocity (m/s) 20.0 20.0 20.0 20.0

(i) (ii) (iii) (iv) (v)

Plot the velocity - time graph of motion. Determine the distance the car travels during the first 2s. What distance does the car travel during the first 4s? What distance does the car travel during the entire 8s? Find the slope of the line between t = 0s and t = 4.0s. What does this slope represent? (vi) Find the slope of the line between t = 5.0s and t = 7.0s. What does the slope indicate? 7. The position-time data of a car is given in the table given below: Time(s) 0 5 10 15 20 (i) (ii) (iii)

Position(m) 0 100 200 200 200

Time(s) 25 30 35 40 45

Position(m) 150 112.5 75 37.5 0

Plot the position-time graph of the car. Calculate the average velocity of the car during first 10 seonds. Calculate the average velocity between t = 10s to t = 20s.

Motion and Its Description : 137 :

(iv)

Calculate the average velocity between t = 20s and t = 25 s. What can you say about the direction of the motion of car?

8. Distance is always (a) less than; (b) greater than; (c) less than or equal to; (d) greater than or equal to, the magnitude of displacement. 9. The graph of x vs. t plot for an object with a uniform velocity in the x-direction is (a) a curved line; (b) a straight line; (c) a circle; (d) a point. 10. An object initially at rest moves for t seconds with a constant acceleration a. The average speed of the object during this time interval is (a) at/2; (b) 2 at; (c) 1/2 at2 (d) 1/2at. 11. A car starts from rest with a uniform acceleration of 4 m/s2. The distances travelled at the ends of each of the first 4 seconds are, respectively, (a) 4, 8, 16, 32m, (b) 2, 8, 18, 32m, (c) 2, 4, 8, 16m, (d) 4, 16, 32, 64m. ANSWERS TO CHECK YOUR PROGRESS 7.1 1. Zero 2. Both A and B should be along the same direction. B should be equal in magnitude and opposite in direction to A 3. No. Though the magnitudes of their velocites are the same (25 ms-1), their direction are different. Hence, VA ≠ VB. 4. Motion of a second’s hand of a clock is a circular motion. A ball rolling on a horizontal surface executes motion along a straight line. 5. (i) 25m, (ii) –5m 7.2 1. (i) uniform motion (ii) velocity of the object 2. (i) uniform motion (ii) displacement of the object 3. (i) uniformly accelerated motion (ii) accleration (iii) displacement 4. refer section 7.2.2 5. refer section 7.2.1 7.3 1. 2. 3. 4. 5.

(i) 19.6m (i) v = 0, a = g 2ms-2 600m 5ms-1

(ii) 4s (ii) g

: 138 : Motion and Its Description

Force & Motion INTRODUCTION: In the previous lesson, you have studied about the motion of bodies in a straight line. You have learnt that there are three equations of motion, with the help of which you can solve problems involving initial velocity, duration of motion and the acceleration with which a body travels. But what is the cause of change in motion or cause of acceleration which is responsible for producing an increase in the velocity of a moving body? Newton formulated three laws regarding the motion of bodies. These laws are called Newton’s laws of motion. In this lesson you will learn about these laws. These laws will tell you why a motion occurs. These will help you to find out more about moving bodies. If you push a body on a floor or ground, the body stops after moving through some distance. Why does it happen so? Why does a stone thrown upwards always come down to the earth? Why the edge of a knife is made sharp? Why do some bodies float on water whereas some other bodies sink in water? The answer to such questions will be discussed in the present lesson. OBJECTIVES

After completing this lesson, you will be able to: • explain the cause of motion; • define the terms inertia, force, mass and momentum; • state the three laws of motion and explain their significance; • establish a relationship between force, mass and acceleration; • explain friction and the factors on which it depends; • illustrate advantages and disadvantages of friction in day to day life; • explain how friction is increased or decreased in different situations; • state and explain the Newton’s law of gravitation; • distinguish between mass and weight, and express the relationship between them; • distinguish between thrust and pressure with suitable examples; • state the principle of Archimedes and apply it to solve problems.

Force and Motion If you put a ball on the ground, it will stay there. It does not move by itself. It will move only when you kick it. If you kick it hard, it moves faster. To move a heavy stone across a room lot of pushing has to be done. But to move a sheet of paper off your table requires a very little push. Can you think of a situation when a cart is moving without bullocks? No. It means something has to be done to move a body from rest or to make it move slow or fast. You can also stop a moving ball by catching it or putting an obstacle in its path. It means something is done to stop a moving body. Consider another example in which the volleyball players are hitting the ball from both sides. You will observe that in each hit the direction of the ball is changed. In this case also something is done to change the direction of motion of the body. What is this something that changes the state of rest, or of uniform motion of a body? This something is called force. Thus, we can say that the force is something which when applied on a body changes or tends to change the state of rest or uniform motion of the body. Kick, push, pull and hit are some of the different ways of applying force on a body. Each one is called an action. You must note that force is a vector quantity, because it is always applied along a particular direction and has magnitude. Newton's Laws of Motion 8.2.1 Newton’s first law of motion Therefore, we conclude that everybody continues in its state of rest or of uniform motion in a straight line unless and until it is compelled by some unbalanced force to change that state. This is the statement of Newton’s First Law of Motion. So, Newton’s first law of motion may be used to define force. It also defines another concept called inertia. The property of a body by virtue of which it is unable to change its state of rest or of uniform motion in a straight line is called inertia. You can do another activity to understand the concept of inertia. ACTIVITY 8.1 Aim: To study Newton’s first law of motion and inertia. What is required ? Two books and a smooth sheet of paper. What to do? (i) Place the sheet of paper on the table with some part of it coming out of the edge of the table. Now stack two books on the paper. (ii) Remove the paper with a jerk and see the effect on books. What do you observe? When the paper is removed with a jerk from below the books, the books do not change their position (Fig. 8.3).

Fig 8.3 Paper being removed with a jerk from below the books What do you infer? We find that the books remain in their position unless something external is done. Even removal of paper from below them with jerk does not change their position. ACTIVITY 8.2 Aim: To study the inertia of rest What is required? A coin, talcum powder, a table with sunmica top or glass top. What to do? (i) Strike the coin on a smooth floor and note the distance travelled by it. (ii) Now, sprinkle talcom powder on the floor and again strike the coin from the same place with the same force and note the distance travelled by it again. The distance travelled by the coin in straight line is different in the two situations. What do you infer? We find that coin travels through much longer distance along a straight line on the floor when powder is sprinkled. The floor exerts a resistive force on the motion of the coin. But this resistive force is much less when powder is sprinkled on the floor, so coin travels much farther. If we imagine a completely smooth floor which offers no resistive force, the coin will continue to move on it with constant velocity unless some net external force is applied to stop it. Inertia is a property common to all bodies in nature. You must have experienced that it is difficult to move a heavy body than a lighter one e.g., pushing a loaded box is more difficult than to push an empty box because heavy box has more inertia. So inertia of a body is characterized by the quantity called mass of the body. Thus, it can be said that the mass of a body is a measure of its inertia. Some illustrations of first law of motion (a) Why do you tend to fall while getting off a moving bus or why are you thrown forward when the moving bus stops suddenly and you are not cautious. What actually happens is that when a moving bus suddenly stops, your feet in contact with the bus are suddenly brought to rest while the rest of your body, which has acquired the same velocity as the bus, due to inertia of motion tends to move forward even after the bus has stopped.

(b) You would have noticed that when a moving trolley is stopped suddenly, sometimes the loaded goods fall from it. This is due to the inertia of motion of the goods. When the trolley stops suddenly, it comes at rest immediately. But because of inertia of motion, the goods placed in it try to remain in motion. Hence they fall from it. Now think, why does the ink comes out of a fountain pen when it is given a jerk? Newton's second law of motion You have seen that force changes or tends to change the state of motion of a body. When you throw a piece of stone in the air, you apply a force. Greater the force with which you throw the stone, the farther it goes, i.e., the greater the force, the greater is the change in motion of a particular body. But how does the motion of a body change when you apply some external force? To establish a relationship between the force and the acceleration produced in a body, Newton formulated his second law of motion. If you kick a football, it moves, but if you kick it very hard, it moves faster than before. Kicking harder means applying more force due to which football gains more acceleration and hence moves faster. It is seen that acceleration of a body is directly proportional to the force applied on the body.

Fig. 8.4 Passenger falling forward as the bus stops suddenly The mass of the football is greater than that of the plastic ball. For the same force the acceleration produced in the plastic ball is greater than the acceleration produced in the football. So it can be said that the acceleration produced in a body depends on its mass and is inversely proportional to the mass. Hence, we have, a = F/m ............... 8.1 Where, ‘a’ denotes the acceleration produced in a body of mass ‘m’ when a force ‘F’ is applied on it. Now, you know acceleration is a vector quantity and force is also a vector quantity, so the equation (8.1) may be expressed in the vector form as a = F/m ...................... 8.2

Fig 8.5 Motion of (a) foot ball (b) plastic ball when the same force is applied on them This shows that acceleration produced in a body is in the same direction as the applied force. Equation (8.2) represents Newton’s second law of motion which may be stated as the acceleration produced in a body is directly proportional to the unbalanced force acting on it and is inversely proportional to its mass. The direction of the acceleration is the same as that of the force. Unit of force: You can use equation (8.1) to define the unit of force. Equation (8.1) may be written as, F = ma ............................ 8.3 In SI system of units, if m = 1 kg and a = 1 ms-2 then, F = (1 kg *1 m)/1s2 = 1kgm/s2 1kgm/s2 is called as 1 Newton whose symbol is N. Hence, the SI unit of force is Newton.1 Newton force is that force which on acting on a body of mass 1 kg produces in it an acceleration of 1 ms-2 i.e., 1N = 1 kg ms-2 You must note that equation (8.3) can be used to find out the acceleration or force applied or mass of a body provided any two of the three quantities namely force, mass and acceleration are known. If you put F = 0 in equation (8.3), you will get, ma = 0 But, mass m of a body can never be zero. Therefore, or a = v – u = 0 or v = u i.e., a moving body continues to move with the same velocity if no force acts on it. This is nothing but the first law of motion. So first law can be derived from the second law. Let us solve some problems using Newton’s Law of motion. -2 Example 8.1: What force accelerates a 50 kg mass at 4m/s ?

Solution: Newton’s second law gives F = ma Here m = 50kg and a = 4ms-2 Therefore, F = 50 kg x 4ms-2 = 200 kg ms-2 = 200N (since 1N = 1kg ms-2 ) Example 8.2: If a force of 50 N acts on a body of mass 10 kg. then what is the acceleration produced in the body? Solution: Newton’s second law gives

F = ma or a = F/m Here, F = 50 N = 50 kg ms-2 and m = 10 kg a= 50kgms-2 * 1/10 kg = 5ms-2 Momentum You know that a moving body always has a mass and a velocity. These two quantities help us to define a new quantity called momentum. Thus, the momentum of a moving body is defined as the product of its mass and velocity, and its direction is same as that of its velocity. So, we can say that all moving bodies have momentum. i.e. Momentum = Mass x Velocity p = m x v = mv You know, velocity is a vector quantity, so momentum is also a vector quantity directed along the velocity. In vector notation, p = mv Momentum plays an important role in the motion of bodies. We know that the acceleration of a body is defined as rate of change of its velocity. v = Final velocity, u = Initial velocity and t = Time Newton’s second law of motion gives. F = ma Substituting (8.4) in the above equation we have, F = ( Final momentum – Initial momentum ) / Time (according to the definition of momentum) or F = ( Change in momentum ) / Time = Rate of change of momentum Hence the rate of change of momentum of a body is equal to the force acting on the body and is in the same direction. This is another way of stating Newton’s second law of motion. Unit of momentum: By definition, momentum is the product of mass and velocity. In SI units, the unit of mass is kg and that of velocity is m/s. Therefore, the unit of momentum is kg m/s or kgms-1 or Ns 8.2.5 Some illustrations of second law of motion According to the Newton’s second law of motion the force is defined as F = Rate of change of momentum Force is large when time is small and when time is large, force becomes smaller, for the same change of momentum. The following examples are based on this concept.

(a) If a bundle tied with a string is lifted quickly by holding the string, the string snaps. Why? This is because a large force must be exerted on the string to quickly increase the momentum of the bundle. (b) When a person falls on a cemented floor, why does he get hurt? The person has some initial momentum ‘mu’ which becomes zero when he comes to halt. Since the mass comes to rest within a very short time, very large force comes into action in order to produce a definite change in momentum (from ‘mu’ to zero), thereby hurting the person. On the other hand, if he falls on dry clay or husk or on a foam mattresses, he does not get hurt due to prolongation of time in making momentum zero and hence reduction of force. (c) Why does a cricket player while catching a ball moves his hands backward? By doing so he increases the time duration in which the momentum of the ball becomes zero. As time increases, smaller force comes into action to produce the desired change in momentum, so his hands do not get hurt. 8.2.6 Newton’s third law of motion You must have noticed that when you jump out of a boat suddenly, the boat moves in the backward direction. Why does this happen? While jumping, your foot exerts a backward force on the boat (Fig. 8.6). This force is called the action. At the same time, a force is exerted by the boat on your foot, which makes you move forward. This force is known as reaction. Action and reaction forces are, equal in magnitude but opposite in direction.

Fig 8.6 A boy jumping out of a boat Also you must have noticed that when an air-filled balloon is released, the balloon moves opposite to the direction of the air coming out of it. In this case the air coming out of the balloon exerts a force of reaction on the balloon and this force pushes the balloon backwards. If the air rushes out vertically downwards (action) the balloon moves vertically upwards (reaction). You can try it yourself at your home.

Therefore, forces always exist in pairs and they act on two different bodies. Newton’s third law of motion very clearly states that to every action there is always an equal and opposite reaction, and the action-reaction forces act on different bodies. There are three significant features of this law: (i) We cannot say which force out of the two forces is the force of action and which one is the force of reaction. They are interchangeable. (ii) Action and reaction always act on two different bodies. (iii) The force of reaction appears so long as the force of action acts. Therefore, these two forces are simultaneous. 8.2.7 An illustration of third law of motion Working of jet plane and rockets: A jet plane takes in air, the fuel burns and then releases the burnt gases from the tail. As the burnt gases come out, the plane moves in the forward direction. If the force with which the gases escape is the action, then the force enabling the plane to move forward is the reaction. Friction in Motion You might have noticed that a moving car begins to slow down the instant its engine is switched off. Why does it happen? In fact the car is slowed down by a force called friction, which exists between the surfaces of all materials which rub against each other. 8.3.1 Factors affecting friction Friction is caused due to the irregularities i.e., elevations and depressions in the surfaces of sliding objects. These irregularities act as obstructions to motion. The direction of the frictional force is always in a direction opposite to the motion. Thus, if an object is to move at a constant velocity, a force equal to the opposing force of friction must be applied. In that condition the two forces exactly cancel one another and the net force on the body is zero; hence the acceleration produced in the body is zero. But zero acceleration does not mean zero velocity. Zero acceleration means that the body maintains its velocity, it neither speeds up nor slows down. The resistive force before the body starts moving on a surface is called static friction. So it may be concluded that force needed to overcome friction, is necessary to maintain the uniform motion of a body. Air resistance is one type of frictional force. It is a common experience that it is difficult to walk on sand, but it is easier to walk on a metalled road. Greater the roughness, greater is the friction. More power is needed to develop same speed on the same road for a heavy truck than for a lighter truck. It is so because the heavy truck has greater normal reaction (reaction of road on the truck against the action or weight of the loaded truck) and hence greater frictional force.

8.3.2 Sliding and Rolling Friction Once a body starts moving on a surface the friction between them is called sliding or kinetic friction. This friction is less than the static friction discussed above. You might have used a slide in your school or a park in your childhood to play with. Here force of friction is much less. You may be using a bicycle or a scooter to go from one place to another. The wheels are round and these roll over the road. Friction between wheels and road is rolling friction. This type of friction is least of all other types. Ball bearings do have rolling friction. 8.3.3 Advantages and disadvantages of friction (a) Advantages of friction • It helps vehicles to move. If there were no friction between vehicle tyres and the ground, the wheels of the vehicle might spin but the vehicle would stay where they were. Thus, vehicle tyres are designed to give as much friction as possible in all conditions. • It helps us to walk. When you are walking, a force of friction is developed between the soles of your feet or shoes and the ground. This force causes us to move. Can you now tell, why we find it difficult to walk on slippery ground or even on the sand? • We can easily walk, write on a page or black board due to friction. (b) Disadvantages of friction • Friction produces heating of the rubbing surfaces. • Friction reduces efficiency of the machines as considerable amount of energy is wasted in overcoming friction. • Friction causes wear and tear of surfaces and machine parts. 8.3.4 Control of friction • Oil reduces friction by helping the surfaces slide over each other, move smoothly. • Wheels of vehicles are usually mounted on ball or roller bearing to reduce friction. • Some time friction is increased by making surface rough as in case of tyres of vehicles, stairs and ramps. From what has been stated above one may conclude that the friction plays an important role in our daily life. This is the reason why friction is often termed as a necessary evil.

Force of Gravitation It is every day experience that bodies like a ball thrown vertically upward comes back to the earth. Why does it happen so? We are even today fascinated how planets move around the sun and how various stars are there in their orbits or positions? All this has been possible due to the force of attraction between any two masses. Newton called it force of gravitation and he formulated a law connecting the force and masses of the two bodies involved. The interesting aspect of this gravitational force is that it is always attractive whatever may be the size of bodies. 8.4.1 Newton’s law of gravitation On the basis of some observations, Newton found that the force of gravitation is directly proportional to the product of masses of the two bodies and inversely proportional to the square of the distance between the bodies. Mathematically, F = G (m1*m2) / r2 Where G is called the universal gravitational constant. In S.I. units where m is measured in kilogram, F in newton and r in metre, G has a value 6.67 x 10-11 N m2/kg2. At once we see that for appreciable value of force, masses should be very large. The gravitational force due to earth is also known as gravity. 8.4.2 Acceleration due to gravity Stand at the roof top of a three or more storeyed building with stones of different masses in your two hands and drop these together (Be careful don’t hurt anyone). Ask another person (an observer) to observe falling of the stones. You will find that both the stones fall simultaneously. The earth’s gravity accelerates the bricks down. Since both reach ground together, this acceleration, called acceleration due to gravity (g), is same for both pieces and is same for any mass. That is ‘g’ is independent of the mass of the freely falling body. Its value changes from place to place on the Earth and it is 9.81 ms -2 at the equator. Its value is maximum at the poles. 8.4.3 Mass and weight We know that acceleration due to gravity varies with geographical latitude and the gravitational force is an inverse square of force i.e. Fµ 1/r2 . However, the ratio of the gravitational force to the free fall acceleration for a given body at any point on the Earth is a constant.

The ratio F/g is a characteristic of a body and is known as the mass of the body according to Newton’s second law of motion. Thus, mass of a body is defined as the

ratio of the force of gravity acting on the body to the free fall acceleration. m = F/g. Mass is a scalar quantity and is measured in kilogram (kg). Mass is also defined as the matter contained in the body. At a given place the value of acceleration due to gravity is same for all masses-big or small. Hence force of gravity is proportional to the mass of the body.

The weight of a body at a given place is the force with which the Earth attracts the body towards it. The unit of weight is Newton. More massive a body is, more weighty it will be. Thus, the weight of the body W is W = mass x acceleration or W = mg Mass : Mass is the amount of matter contained in a body. It is a scalar quantity. Mass of a body is a constant quantity. Mass is measured with a beam balance. Unit of mass is kg. It is gravitational force with which Earth attracts a body towards it. It is the ratio of gravitational force on the body to the acceleration due to gravity. Weight: Weight is force, hence a vector quantity. Weight of the body changes from place to place. Weight is measured with a spring balance. Unit of weight is N. Example 8.3: A body weighs 49 N at a place where g=9.8 ms-2. What will be its weight at the pole where g=9.82 ms-2. Solution: w=mg

weight at pole w = mg = 5 kg x 9.8 ms-2 = 49.10 N Example 8.4: A 1kg body falls from a height of 60 m from rest on a planet where acceleration due to gravity is 120 ms-2. Calculate the velocity of the body when it touches the planets surface. Solution : Initial velocity of the, body, u = 0 acceleration, a = g = 120 ms-2 height through which body falls = h = 60m. Using the equation of motion v2 = u2 + 2gh we have on substitution of values 2 2 -2 v = 0 +2 x 120 ms x 60 m

= 1,4,400 m2 s-2 v = 120 ms-2 Example 8.5: Two bodies A and B weighing, 2N and 6N are dropped from the roof of a 10 m high building together. Which A or B will reach the Earth first? Solution : Since the two bodies have same initial velocity (i.e. zero) and have same acceleration (g) i.e. acceleration due to gravity acts on both A and B, hence, both will reach Earth together irrespective of their masses. 8.4.4 Motion under gravity and free fall The force with which Earth attracts a body, stationary with respect to Earth, is called the weight of the body. When a body falls freely from some height (say, top of a building) it does so due to a force called weight. When no other force like air resistance except gravity, acts on a falling body, it is called a free fall and body acquires acceleration under its weight. There are many situations, like a person in a lift or satellite which has some acceleration with respect to the earth other than ‘g’, the weight of the person is not same. He exerts less or more force on his support than his actual weight. If the system, somehow, has acceleration a =g, the person feels no weight. This is known as the weightlessness. It has several implications for an astronaut. Thrust and Pressure Rockets and jet planes eject burnt gases with force. The gas in turn react on the rocket or jet plane with force called thrust. Similarly water coming out of a plastic or rubber pipe exert thrust on it. Thrust and pressure are properties of fluids (gases and liquids). The total force exerted by a fluid (liquid or gas) on any surface in contact with it, is called thrust. Thrust is measured in newton (N). The thrust exerted by fluid at rest per unit area of the surface in contact with the fluid (liquid/gas) is called pressure. The air exerts pressure, you fill air in cycle or scooter/motor cycle tyres upto a certain pressure, the astronaughts and soldiers in places like Siachin wear pressure suits to avoid bleeding. Blood pressure becomes higher than atmospheric pressure at high attitudes. Under sea water, pressure put by it on the body is quite high. The normal atmospheric pressure is one atmospheric pressure and according to the definition -2 p = F/A, its value in Nm is 1 atmosphere = 1.014 x 105 Nm-2 Normal atmospheric pressure is also measured in terms of centimetre or milimetre of mercury, 1 atm = 76 cm = 760 mm of mercury. The SI unit of pressure is Nm-2. Pressure is measured in pascal (Pa)

1 Pa = 1 Nm-2 The air or gas pressure is also measured in bar or torr. 1 atmos = 1.014 bar and 1 torr = 1 m m of mercury – 133.3 N m-2 1 atmos = 760 torr A practical application of pressure is the shape of a paper pin, needle and nail. The tip of these is made very narrow so that these pierce the object with greater pressure. Buoyancy : How a ship floats on sea? If there is no water below or insufficient water, the ship will sink to the sea bottom. The weight of the ship acts downward and water pushes it upward. Similarly a diver in a swimming tank is also pushed up when he jumps from the board into the water. The force exerted by water or any liquid or gas on a body immersed in it, in the upward direction, is called the up-thrust or buoyant force or simply buoyancy. In the early days of space flights, buoyancy of Earth’s atmosphere posed a big problem in the re-entry of space vehicles in Earth’s atmosphere and their safe landing on Earth. The principle of buoyancy comes from Archimedes principle. 8.5.1 Archimedes principle When you put a piece of stone on the surface of water it sinks but boat can float on it. Why does this happen? Greek scientist Archimedes gave the principle which could explain such things. According to Archimedes principle when a body is immersed, wholly or partially in a liquid (or fluid), it undergoes an apparent loss in its weight, which is equal to the weight of the liquid displaced by the body. 8.5.2 Applications of Archimedes principle (i) Flotation of bodies : Suppose the weight of a body is W and weight of liquid or fluid displaced is w then body will float immersed or partially immersed when W = w or W < w. (ii) To determine the specific gravity of the body (iii) To find the volume of a body. Example 8.6: The mass of a body in air is 1 kg. What will be its weight in the liquid -2 of specific gravity 1.2 if it displaces 100 ml of this liquid? (Take g = 10ms ). Solution : Weight of the body in air = 1 kg x 10ms-2 – 10N. Density of liquid = 1.2 x 103 kgm-3 Volume of the liquid displaced – 100 ml = 100 x 10-6 m3 Buoyant force = 100 x 10-6 m3 = 1.2 N Loss in weight of the body =1.2 N Weight of body in the liquid = 10N – 1.2N = 8.8 N.

In Text Questions 1. Is there any force applied when (i) you push the wall of a house? (ii) the speed of the cycle is increased? (iii) the player changes the direction of football by using his head? 2. What is the property by virtue of which a body tends to remain stationary? 3. When a bus suddenly starts, the passengers feel a backward jerk. Why? 4. If forces of same magnitude are applied on two bodies of masses 2 kg and 4 kg, which of the bodies will have more acceleration? 5. If a body of mass 5 kg moves with a velocity of 10 ms-1, then what is the momentum of the body? 6. If a force of 10N produces an acceleration of 2 ms-2 in a body, how much force would be required to produce an acceleration of 4 ms-1 in the same body? 7. What is the acceleration of an aeroplane moving in a circle around the Earth, if the passenger in it feels weightlessness? 8. Does any force act on a body in a free fall. 9. Density of kerosene is 0.8 g cm-3 and density of water is 1 g cm-3. Which one will exert greater buoyant force on a body? 10. A body is immersed in a liquid. If the liquid displaced by the body weighs 20g then what is the buoyant force acting on the body? 11. If the weight of a body is 10 g and the buoyant force is 7g, will the body sink or float? 12. Why is straw used to drink a soft drink? 13. Sailors generally say that a person is easily drowned in a river than in sea, why? Terminal Questions 1. Define force. Is it a vector quantity? What is its unit? 2. State Newton’s first law of motion. 3. Explain why is it dangerous to jump (or alight) from a fast moving bus or train? 4. Why do the dust particles from the hanging blankets fall off by beating with a stick?

5. Which law helps you to find the magnitude of the force acting on a body of mass ‘m’moving with an acceleration ‘a’? State the law. 6. Define momentum. Is it a vector quantity? What is the unit of momentum? 7. How is the rate of change of momentum related to force? 8. Which will have greater momentum—a truck moving with a speed of 60 km/ h or a train moving with the same speed? Justify your answer. 9. Find the acceleration produced in a body of 2 kg mass when a force of 10N acts on it. 10. What force accelerates a 50 kg mass at 6 m/s? 11. A force of 60N accelerates a mass of 15 kg from rest. Find the velocity at the end of 6 seconds. 12. Explain the effect of friction on motion. 13. Give an example to show that friction is useful as well as harmful to us. 14. What is an inverse square law of gravitation? What you have learnt

- If a body stays at the same position with time, it is at rest. - If the body changes its position with time, it is in motion. - Motion is said to be rectilinear if the body moves in the same straight line all-the time, e.g, a car moving in a straight line on a level road. - The motion is said to be circular if the body moves on a circular path: e.g, the motion of the tip of the hand of a watch. - The total path length covered by a moving body is the distance travelled by it. - The difference between the final and initial position of a body is called its displacement. - Physical quantities are of two types (i) scalar: which have magnitude only, no direction (ii) vector: which have magnitude as well as direction. - Distance, speed, mass, time, temperature etc. are scalar quantities, whereas displacement, velocity, acceleration, momentum, force etc. are vector quantities.

- Distance travelled in unit time is called speed, whereas, displacement per unit time is called velocity. - Position-time graph of a body moving in a straight line with constant speed is a straight line sloping with time axis. The slope of the line gives the velocity of the motion. - Velocity-time graph of a body in a straight line with constant speed is a straight line parallel to time axis. Area under the graph gives distance travelled. - Velocity-time graph of a body in a straight line with constant acceleration is a straight line sloping with the time axis. The slope of the line gives acceleration. - For uniformly accelerated motion : v = u+at s = ut + 1/2 at2 where u = initial velocity, v = final velocity, and s = distance travelled in t seconds.

10

Thermal Energy You are aware that energy is required for all types of activities. In the previous lesson you have learnt about mechanical form of energy. Heat is also a form of energy, called thermal energy. Fire has heat in it . When fuels like coal, petrol, wood, kerosene-oil are burnt, heat is produced. You would have noticed that in winter season, when it is cold, generally people rub their palms to warm up. Here, doing mechanical work against friction produces heat. You must have learnt that in ancient times man used to produce fire by rubbing two pieces of stone together. Even now a days we produce fire by the same method when we rub the tip of a matchstick on the special surface of the matchbox. Why do we need heat? We require heat to cook, to iron clothes, to have hot water for bathing in winter season, to melt solids, to vaporize the liquids, etc. Why do the wet clothes get dried when hanged in sunlight? Have you seen an iron smith heating an iron rod red hot and then beating it to give the required shape of a knife or a scissor? You must have got a chance to see a gold smith working with flames of a lamp in designing an ornament. What is the use of flame? In thermal power plants coal is burnt to generate electricity. In steel industry and glass industry, iron and glass are melted to give them definite shapes. Steam engine can pull a train due to the power of steam. In all these activities heat is used. Let us learn all about heat and its effects in this lesson. OBJECTIVES After completing this lesson, you will be able to • differentiate between heat and temperature; • explain that heat is transferred from one body to another when there is a temperature difference between the two bodies; • describe construction, calibration and use of thermometers; • explain the effect of heat on matter resulting in thermal expansion of solids, liquids and gases; • explain the constancy of temperature of a substance during change of phase even though heated continuously; • state the factors upon which the total transferable heat of a body depends; • calculate heat flow from a hotter body to a colder body in contact; • predict the variation in melting point and boiling point of materials due to the presence of impurities and with variation in pressure; • explain why the food gets cooked easily and quickly in a pressure cooker.

: 172 : Thermal Energy

10.1 WHAT IS HEAT? Heat is a form of energy. We call it thermal energy. It is measured in joule. Sunrays have heat in them. This heat is called radiant heat. It travels with the speed of light i.e. 3 x 10 8 m s -1. 10.1.1 How is heat produced? Rub your palms together. What happens? They become warmer, indicating generation of heat. Here friction is generating heat. When you burn coal, wood or kerosene oil, fire is produced. Fire has heat energy in it. Here, the chemical energy gets converted into heat by the process of burning.

Fig. 10.1 Rubbing the palms together makes them warmer

Fig. 10.2 Fire has heat energy

10.1.2 Heat is energy of molecular motion Every material is made up of molecules, which are in a state of continuous random motion. This is due to the heat in them. When we heat up this material, this molecular motion increases. This Fig. 10.3 Molecular motion increases suggests that heat is kinetic energy of molecular with absorption of heat motion. Kinetic energy of a body in motion can be utilized in doing work against frictional forces. This results in the heating up of the body. It is due to transfer of kinetic energy from the moving body to the molecules. Let us perform an activity to demonstrate conversion of mechanical energy into heat energy. ACTIVITY 10.1 Aim: Demonstration of conversion of mechanical energy into heat What to do? i) Keep bicycle on its stand and rotate the paddle with hand so that the rear wheel rotates very fast. ii) With the help of a pad of cloth on your finger tip, touch the rim of the wheel to stop the wheel.

Brake rubber

Fig. 10.4 Conversion of mechanical energy into heat energy

Thermal Energy : 173 :

What do you observe? At the finger tip you feel that cloth has become hot. What do you conclude? The kinetic energy of motion of the wheel has been transferred to the cloth due to friction and it appears in the form of heat. 10.1.3 Heat can lead to work You might have seen water boiling in a kettle. Due to steam formed in the kettle, its lid moves up and down. This shows that heat can do work. You must have seen a steam engine pulling a long array of coaches. Thus, heat can be utilized to do work. Thus, we can conclude that heat is a form of energy since it can do work. Also, heat and work are inter convertible. The device that converts thermal energy into mechanical work is called heat engine.

Fig. 10.5 Heat can do work

10.1.4 Temperature and need for its measurement How will you measure the hotness of a given body? You may suggest that this can be done simply by touching the body. It means feeling of hotness by our hand can be used to estimate how hot a body is. But sometimes it may be difficult (if the body is very hot and may cause burns) and sometimes the conclusion may be confusing. Can you have a wrong sensation of hotness by touch? ACTIVITY 10.2 Aim: Our sense of touch may be misleading What to do? i) Take three bowls A, B and C. Fill ice cold water in bowl A, ordinary tap water in bowl B and hot water in bowl C (Fig. 10.6). ii) Now dip your left hand in bowl C containing hot water and right hand in bowl A containing ice cold water and let them remain there for two minutes. iii) Now take your hands out of both bowls and put both of them in bowl B containing tap water.

R

(a)

R

L

(b)

Fig. 10.6 Sense of touch may be misleading

L

(c)

: 174 : Thermal Energy

What do you feel? You will be surprised to note that your left hand will give you the sensation that this water is cold, while the right hand will give you the sensation that it is warm. Thus, confusing sensations can be felt by skin. The difficulty in using the sensation as a measure of hotness arises because of the fact that the terms hot and cold are relative terms and cannot be used in the absolute measurement of hotness. Therefore, there is a need of some standard for the measurement of the hotness of a body. The degree of hotness of a body is called its temperature. It is measured by devices called thermometer. It is represented as a number on a thermometric scale. 10.1.5 Difference between heat and temperature Heat is energy in transit, which is transferred from one body to another due to temperature difference between them. While heat is a form of energy, the temperature is the degree of hotness of a body. Heat is measured in Joule while the temperature is measured in degree Fahrenheit (o F), degree Celsius (o C) or Kelvin (K). 10.1.6 Various types of scales for measurement of temperature The thermometers in common use have two different types of scales of measurements namely Fahrenheit and Celsius scales of temperature. For scientific work, Kelvin scale of temperature is more often used. However, the construction and working of these thermometers is same. It is obvious that a hotter body would show higher temperature and a colder body a lower temperature on the same scale. The thermometers cannot have confusing or wrong sensations. 10.1.7 Construction and use of a thermometer Mercury thermometers are the most common thermometers in use. Mercury is filled in a thin walled glass bulb joined at the end of a capillary tube by the process of repeated heating and cooling. The mercury is seen in the form of a thin dark thread in the capillary. The space above the mercury level in capillary is evacuated. The other end is now sealed. Mercury has the property of uniform thermal expansion over a wide range of temperatures. This means, the length of the mercury thread in the thermometer increases by same amount for each degree rise in its temperature. The tip of the mercury thread can be easily seen in the transparent glass tube as shown in Fig 10.7. Calibration of mercury thermometer To calibrate a scale on a thermometer, two fixed points are marked, the lower fixed point or ice point and upper fixed point or steam point. To mark the ice point, the bulb of thermometer is placed in a vessel containing mixture of water and crushed ice. When the level of the mercury becomes stable, a mark is put at the position of the tip of

Capillary tube

Constriction

Mercury in bulb

Fig. 10.7 Mercury thermometer

Thermal Energy : 175 :

mercury thread in the glass tube. This is called ice-point. Next, the same bulb is placed in steam just above boiling water in a vessel. The position of the tip of mercury thread changes due to thermal expansion of mercury in the bulb. A mark is again made on the glass tube at this new position of the tip of the mercury thread. This is called steam point. Now to mark a Celsius scale on this thermometer, zero is written at the ice point mark and 100 is written at the steam point mark. The length between these two marks is then divided into 100 equal parts. This now becomes a Celsius thermometer. To mark a Fahrenheit scale, 32 is written on the ice-point mark and 212 is written on the steam point mark. The length between these two marks is then divided into 180 equal parts. This now becomes a Fahrenheit thermometer. Steam point

Ice point

Fig. 10.8 Method of calibration of a thermometer

In a clinical thermometer, the marks are shown only in the range 95 0F to 110 0F. [These are the two limits of human body temperature beyond which human beings cannot survive]. Kelvin scale can be marked on a Celsius scale F C by writing 273 at ice point and 373 at steam point. 212 212 Steam point 44 110 Thus, each mark is calibrated with a value higher by 273 than on Celsius scale. The Kelvin scale 98.6 37 begins with the lowest possible temperature as its zero, which is –273.15 0C. This temperature is also 32 95 Ice point 35 32 called absolute zero. To measure the temperature of a hot body, the bulb of the thermometer, is put in contact with Fig. 10.9 Calibration of thermometers in that body. Mercury in the bulls expands, resulting different scales in the increase of the length of the mercury thread in the glass capillary. The position of the tip of the mercury thread on the scale (calibrated on the capillary) is read. This gives the value of temperature. When you measure temperature of a cooler body, mercury contracts, length of mercury thread decreases and it gives the value of temperature. As mercury does not stick to glass, the receding tip of mercury thread does not leave any mercury in empty part of capillary, which could cause error in the reading.

: 176 : Thermal Energy

ACTIVITY 10.3 Aim: To measure the temperature of a patient What to do? i) Take a clinical thermometer (also called Doctor’s thermometer) (Fig. 10.7). ii) Wash the thermometer in running cold water under a tap, rinse carefully and give a few jerks to bring tip of the mercury thread below 95 0F. iii) Now put the bulb end of the thermometer in the mouth Fig. 10.10 To measure the under the tongue of the patient for about 2 minutes. temperature of a pateint iv) Now take it out gently and read it. This gives the body temperature of the patient. v) Is it more than 98.6 0F? If yes! The patient has fever. It may be somewhere in between 97 0F and 98.6 0F, if the patient does not have fever. vi) Wash it again in running tap water; hold it from the other end and give it 3-4 jerks so that the thermometer reading reduces to 95 0F. vii) Now put the bulb of the thermometer under the armpit of the patient inside the shirt and keep it slightly pressed. Hold it for about 2 minutes. viii) Take it out gently and note the thermometer reading. ix) Is it about 1.0 0F lower than before? What do you conclude? The mouth temperature called the body temperature is about 10 higher than armpit temperature. To know the body temperature of an infant who cannot keep the bulb of the thermometer in his mouth, the temperature of the armpit is measured and then 10 is added to this reading to find the body temperature and decide if he has fever. 10.1.9 Relation between Fahrenheit and Celsius scales of temperature Let us solve the following examples: Example 10.1: A thermometer reads the temperature of some hot liquid as 100 0F. What would be the reading of the Celsius thermometer used to measure this temperature? Solution : You have known that Fahrenheit scale starts from 32 0F instead of 0 0C. Both of these are the ice points. Also steam points on these scales are marked as 212 0F and 100 0C, respectively. Thus, 180 divisions of F scale are equivalent to 100 divisions of C scale. Hence, 1 division of F scale = 100/180 divisions of C scale Now if F is the reading on the F scale, then Number of divisions above ice point are = F – 32 Therefore, value of (F – 32) divisions of F scale = (100/180) x (F – 32) divisions of C scale

Thermal Energy : 177 :

i.e. reading of Celsius thermometer will be = (100/180) (F – 32) = C or

F − 32 C = 180 100 F − 32 C = 9 5

This becomes the required formula to convert any reading of F scale to C scale or vice versa. In the present case F = 100 340 5 C = (100 − 32) = = 37.78 degree Celsius 9 9 ≈ 37.8 0C Example 10.2: Which temperature has same numerical value on Fahrenheit scale and Celcius scale of temperature ? Solution: Here, we are given F = C Therefore, in the conversion formula

F − 32 C = , 9 5

put F = C, we get C − 32 C = 9 5

5C – 160 = 9C

→ C = – 400

Thus –40 0C = –40 0F Example 10.3: What would be the value of 80 0C on Kelvin scale? Solution: Since Kelvin scale readings are higher by 273 than on Celsius scale, the value on Kelvin scale is 80+273 = 353 K Kelvin scale is used in system international (SI) to report the temperature. However, in laboratory we use only Celsius scale for measuring temperature. On Kelvin scale, the temperature is mentioned in Kelvin only and not degree Kelvin. CHECK YOUR PROGRESS 10.1 State whether the following statements are True or False. 1. Heat can be measured in Kelvin. (T/F) 2. –30 0F is a lower temperature than – 30 0C. (T/F) 3. The numerical value of temperature of any hot body measured on Kelvin scale is always higher than measured on Fahrenheit Scale. (T/F) 4. Thermal energy can be measured either in calories or Joules. (T/F)

: 178 : Thermal Energy

5. Pure alcohol can also be used as thermometric liquid. (T/F) 6. When we touch a cold body, heat flows from our hand to the cold body. (T/F) 10.2 EFFECTS OF HEAT When objects are heated, they may show a change in their shape, size, colour or sometimes in their state. However, the magnitude of change depends upon the quantity of heat absorbed by the object. 10.2.1 Solids expand on heating Have you ever faced a problem of opening the jammed metallic cap of an inkpot? Sometimes, it is too much tightly closed. Place the inkpot in a wide vessel containing hot water for few minutes. Now take it out Fig. 10.11 Method to open tightly closed and try to open the cap. It opens easily. Why? metallic cap of an inkpot Metallic cap undergoes thermal expansion in its size (more than the mouth of inkpot which is made of glass) due to absorption of heat from the hot water and therefore, gets loosened. The phenomenon of expansion of solids is used for various purposes. (i) Fitting of tyres on wheels: Do you know, how is the iron ring mounted on the wooden wheel of a horse-cart? The radius of the iron ring is slightly less than that of the wooden wheel. It, therefore, cannot be easily slipped on to the rim of wooden wheel. The iron ring is, therefore, first heated to a higher temperature so that it expands in size and the hot ring is then easily slipped over to the rim of the wooden wheel. Cold water is now poured on the iron ring so that it contracts in size and holds the wooden wheel tightly (Fig. 10.12a)

Iron ring expands on heating

(a) Fitting of tyres on wheels

(b) Gaps in railway tracks at joints

Aluminium Aluminium expands more

Brass

(c) Thermostat in electrical appliance Fig. 10.12 Some applications of thermal expansion

Thermal Energy : 179 :

(ii) Gaps in the railway track at joints: You must have noticed gaps at the joints in a railways track. Why is it left like that? If this gap is not left then during summer the iron rail will expand due to hot weather and will get bent at the joints (Fig. 10.12b). (iii) Thermostat in electrical appliances: Thermostat is a temperature control device. It is a bi-metallic strip made up of two different metals having different expansivity. As the temperature rises, due to unequal thermal expansion, the strip bends. Due to this the contact breaks and the circuits gets disconnected. Similarly, it can be used to make contact as temperature rises and thus, to switch on a circuit, as in case of a fire-alarm (Fig. 10.12c). Thus, bimetallic strip is a technical application of differential expansion of metals. 10.2.2 How to measure the expansivity of the material of a body? All substances do not expand by the same amount when heated through the same difference of temperature. Also it is seen that the same substance expands by a different amount when heated to a different temperature. It is found that larger the rise in temperature, larger is the expansion. It is understood that the ratio of change in length (∆L) to the original length (L) is directly proportional to the rise in temperature (∆t) of solid bodies ; i.e. ∆L ∝ ∆t L ∆L = α ∆t L

or

α is a constant and depends on the nature of the material of the body. It is called linear coefficient of thermal expansion of the material. It is measured in per degree celsius. It is defined as fractional increase in length for each degree rise in temperature. Example 10.4: The length of a steel rod at room temperature of 25 0C is 20.00 cm. What would be its length when its temperature is raised to 325 0C? [Given linear coefficient of thermal expansion of steel as 0.000012 0C-1 ]. Solution : Since ,

or

∆L ∝ = α ∆t and t = 300 °C L ∆L = L α t = 200 x 0.000012 x 300 = 0.072 cm

Therefore, the increased length will be 20.00 + 0.072 = 20.07 cm. Please note that the result is rounded off to 2nd decimal place because 20.00 cm, the term with smallest decimal place in addition has 2 decimal places.

: 180 : Thermal Energy

ACTIVITY 10.4 Aim: To study the expansion of water What to do? i) Take a small glass bottle (say a used medicine/ injection bottle). Fill it with water up to the rim. ii) Take the thin plastic tube of a used, empty ball-pen refill. Warm it, bend it and pass through a cork into the mouth of the bottle. iii) Now heat the bottle gradually. Do you find droplets of water coming out of the bent tube? What do you conclude? Liquids expand on heating

Fig. 10.13 Expansion of liquids

Mercury is a liquid. The property of thermal expansion of mercury has been used in the construction of a thermometer. Different liquids expand by different extent for the same rise in temperature. Gases also expand on heating. It is important to know that unlike solids and liquids all gases expend by same amount for the same rise in temperature. Thus heating causes expansion of solids, liquids and gases. However, in case of liquids and gases we measure their volume expansivity. It is found that fractional increase in volume of liquids or gases is directly proportional to rise in their temperatures, i.e. ∆V ∝t V

or

∆V =γt V

Where, γ is a constant called volume coefficient of thermal expansion, which is different for different liquids. It is defined as the fractional increase in volume for each degree rise in its temperature. It is also measured in per degree Celsius. For gases this constant has the unique value 1/273 per Kelvin. It is interesting to note that unlike other liquids, water expands when it freezes into ice. Also when water is heated from 0 0C to 4 0C, its volume decreases. But further heating beyond 4 0C results in volume expansion. You must have noticed that if water bottles or cold drink bottles are left in the freezer of a refrigerator for some days, they crack. Similarly, there is bursting of water pipes under extreme cold conditions at hill stations. This is due to the fact that water expands on freezing into ice. Table 10.1 shows the values of linear and volume coefficients of thermal expansion of some materials. It is seen that volume coefficient of thermal expansion is equal to three times the linear coefficient of thermal expansion.

Thermal Energy : 181 :

Table 10.1: Coefficients of linear expansion and volume expansion for some substances Material

Coefficient of linear expansion (oC-1)

Coefficient of volume expansion (oC-1)

Quartz

0.4 x 10 -6

1.2 x 10 –6

Steel

8 x 10 -6

24 x 10 -6

Iron

11 x 10 –6

33 x 10 -6

Silver

18 x 10 –6

54 x 10 -6

Brass

18 x 10 –6

54 x 10 -6

Aluminium

25 x 10 –6

75 x 10 -6

Lead

2.9 x 10 –6

8.7 x 10 -6

10.2.3 Heating causes change of state of matter When a solid material is heated, its temperature rises. When the temperature reaches a certain value, the solid starts melting. The temperature remains constant till whole of the solid material gets melted. This temperature is called the melting point (M.P.) of the material. It is a characteristic temperature for the material. It does not depend upon the shape or size of the solid. Different materials have different melting points. ACTIVITY 10.5 Aim: Determination of melting point of ice What to do? i) Take some crushed ice in a cooking utensil. Place a thermometer in it and note down its temperature (it should be 0 0C) (Fig. 10.14). ii) Now heat it on a gas stove slowly. Do you see conversion of ice into water? Keep an eye on the level of mercury thread of the thermometer. Does it change? Fig. 10.14 Determination of iii) Keep on heating till whole of the ice gets melting point of ice melted. What is the temperature? Is it constant at 0 0C. Heat further. Do you find that the temperature of water is now increasing? What do you conclude? You will find that the ice melts at 0 0C and the temperature of ice-water mixture remains constant at 0 0C till whole of ice gets melted. Repeat this activity for other solids to find their melting points. You can perform a similar activity with boiling water to find its boiling point. You have to take care that

: 182 : Thermal Energy

thermometer measures the temperature of steam a little above water surface. If it dips in boiling water the water must be quite pure. Whenever there is a change of state between solid and liquid or liquid and gaseous states, the temperature does not change even though the heat is either continuously absorbed (as in the process of melting or boiling) or continuously given out (as in the process of freezing and liquefaction) by the material under observation. Table 10.2: Melting points and boiling points of some materials Material

Melting point (oC)

Latent heat of fusion (kj/kg)

Boiling point (oC)

Latent heat of evaporation (kJ/kg)

Helium

-271

-

-268

25.1

Hydrogen

-259

58.6

-252

452

Air

-212

23.0

-191

213

Mercury

-39

11.7

357

272

Pure water

0

335

100

2260

Aluminium

658

322

1800

–

Gold

1063

67

2500

–

10.2.4 Effects of impurities on melting point and boiling point Pure substances have definite melting points and boiling points characteristics of the material. But on addition of impurities their values change. Let us study this with the help of some activities. ACTIVITY 10.6 Aim: To find out effect of impurities on melting point of ice What to do? i) Take two containers A and B. In container A, put some pure water and crushed pure ice. In container B, ice is mixed with about 1/3rd its weight of powdered salt. Observe that in B some ice melts and a saturated solution of salt is formed. ii) Measure the temperature of liquid in both the containers. Obviously, temperature of ice in any container is same as that of its liquid. In which container is temperature lower? iii) The temperature is lower in B. What do you conclude? Presence of impurities lowers the freezing point/melting point.

Thermal Energy : 183 :

Activity 10.7 Aim: To find out effect of impurities on boiling point of water What to do? i) In the above activity 10.6, heat both the containers until the water starts boiling. ii) Note the boiling point of water in the both containers, keeping the bulbs of the two thermometers inside the levels of respective boiling liquids. What do you observe? The boiling point of salted water is higher than that of pure water. What do you conclude? Presence of impurities increases the boiling point. 10.2.5 Effect of pressure on melting point and boiling point The melting and boiling points of a material also change with the change in atmospheric pressure. Let us study the effect of pressure on melting point and boiling point with the help of some activities. ACTIVITY 10.8 Aim: To study the effect of pressure on the melting point of a substance What to do? i) Take an ice block, a wooden block and a wire. ii) Press the wire to first cut the ice block and then the wooden block. You cannot cut a wooden block by pressing a wire on it though wood is softer. Why does the wire pass through the ice block easily? What do you conclude? The pressure applied through the wire melts the ice in immediate vicinity allowing the wire to pass through it. Thus, the melting point of ice is lowered with increase in pressure. It should be noted that in case of all solids other than ice, the volume of liquid obtained on melting is generally larger than solid volume. Water is an exceptional case. In such solids, which increase in volume on melting, the melting point increases with increase of pressure. All liquids expand on evaporation. Hence, increase in pressure will obstruct the change of phase on boiling. This results in an increase in the boiling point of liquids with increase in pressure. 10.2.6 Cooking is easier in pressure cooker In a pressure cooker, (which is air tight from all sides), when water together with vegetables is heated, its temperature rises. Initially, when valve of the cooker is open, water boils to form steam at 1000 C. This steam so formed occupies larger volume than what it had in liquid state. Now the valve is closed. The steam, having no exit to come out, exerts pressure

: 184 : Thermal Energy

on the surface of water in the cooker, which stops boiling. More heat is now supplied. This increases the temperature of water without allowing the remaining water to boil any more. Thus, inside a pressure cooker, there is steam and water at higher temperature and at high pressure. The higher temperature and pressure quickly softens the vegetable and causes the quicker cooking of food. Fig. 10.15 Cooking is easier There is always a certain weight put on the in a pressure cooker nozzle of the lid of the pressure cooker. If the force due to the pressure of the steam exceeds this weight, the weight gets lifted and some of the steam leaks out and reduces pressure. Do you now understand why it is called pressure cooker?

The importance of pressure cooker for persons living at hill stations is very great. The atmospheric pressure in hilly areas is lower due to the high altitude, and thus, water starts boiling at a lower temperature. In such a situation if the ordinary utensil is used for cooking food (especially food like rice and pulses), it will take a long time, resulting in wastage of precious fuel. 10.2.7 Latent heat We have already discussed in the previous parts of this section that the temperature does not change during the change state even though heat is continuously supplied to the material. What happens to this heat supplied? It is used up wholly in changing the state of the substance. Therefore, it does not appear in the form of rise in temperature of the body. This is, therefore called latent heat (or hidden heat). Its value is constant and is different for different materials. Latent heat of a material is defined as the amount of heat required to completely change the state of unit mass of that substance either from solid to liquid or liquid to gaseous state. It is generally denoted by capital letter L and is measured in Joules per kilogram (J/kg). When material changes from solid to liquid, it is called as latent heat of fusion and when the state changes from liquid to vapours it is latent heat of evaporation. Do you understand why does water filled in a clay pitcher become cold even when placed inside a room? In this case, water drops leaking through the fine pores of clay pitcher absorb heat for evaporation from the water inside. Therefore, the inside water gets cooled. Example 10.5: How much thermal energy is required for complete melting of 10 kg of ice at 0 0C to form water at 0 0C? Solution: Thermal energy for melting m kg ice at its melting point =mL = 10 x 335 kJ = 3350 kJ

Thermal Energy : 185 :

Heat required for a mass m kg of a substance for change in state at its melting point or boiling point is = mL joule. 10.2.8 Sublimation Some solid substances when heated directly change to gaseous state without becoming liquid. This process is called sublimation. ACTIVITY 10.9 Aim: To study the sublimation of camphor What to do? Take some camphor tablets in a spoon and heat the spoon slowly over a gas stove. What to observe? Do you see fumes coming out and camphor gradually vanishing without melting?

Fig. 10.16 Camphor sublimates on heating

What do you conclude? This shows that camphor sublimates on heating. Naphthalene balls (used for preserving woolen clothes) and iodine are also sublime substances. CHECK YOUR PROGRESS 10.2 Fill in the blanks with the correct choice. 1. A bimetallic strip is used as a thermostat in the electrical device named ___________ (geyser, camera, T.V.) 2. If the mass of a substance is doubled, its melting point will _____________ (be lowered, be raised, remains same) 3. When solid ice is heated, the volume of the water formed on melting is _________ the initial volume of the solid ice. (more than, less than, same as) 4. Latent heat of evaporation is measured in _______________ (J, J/k, J/kg) 5. The water containing little salt dissolved in it boils at a temperature _______ 100 0C. (higher than, lower than, equal to) 10.3 THERMAL EQUILIBRIUM When two bodies at different temperatures are brought in contact heat energy will always flow from the body at higher temperature to the body at lower temperature, till both the bodies acquire the same temperature. The two bodies are then said to be in thermal equilibrium.

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ACTIVITY 10.10 Aim: To study the state of thermal equilibrium What to do? i) Take a steel tumbler. Fill it 2/3rd with tap water. Put a thermometer in it and measure its temperature. ii) Now take a large heavy metallic spoon which can be inserted in the tumbler. Heat it on a flame and put it in the tumbler and keep an eye on the temperature scale of the thermometer. What do you observe? Does the temperature of the water rise? Does the temperature stops rising after some time? Touch the spoon with the thermometer bulb and note the temperature of the spoon. Is the temperature of spoon same as that of water? What do you conclude? The heat energy keeps on flowing from the hot body to the cold body till both acquire same temperature. This is called state of thermal equilibrium. 10.3.1 Can we measure the amount of heat transferred? Heat gets transferred from a hotter body to a cooler body in contact. The larger the quantity of heat transferred, larger would be the rise in the temperature of the colder body before a state of thermal equilibrium is achieved. Therefore, the heat energy transferred is proportional to the rise in temperature of the cold body. Similarly, heat energy lost by the hot body is proportional to the fall in temperature of the hot body. ACTIVITY 10.11 Aim: To study the factors on which the heat transferred from a hot body to a cold body depends What to do? i) Take two identical vessels A and B and put equal amount of tap water in both of them. ii) Now take another larger vessel C containing some water and heat it on a gas stove till it boils. Note its temperature. iii)Now pour a small quantity of water from vessel C into vessel A and larger quantity of water into vessel B. Note the new temperatures of water in vessels A and B. What do you observe? The temperature of water in vessel B is more than that of water in vessel A. What do you conclude? The vessel B, in which larger quality of boiled water was added, has been given larger quantity of heat. Thus, the quantity of heat transferred not only depends on the temperature of the hot body but also depends upon its mass.

Thermal Energy : 187 :

The quantity of heat (H) transferred from a hot body is proportional to (i) mass (m) and also to (ii) fall in temperature (t). or

H∝mxt H=sxmxt

Where, s is a constant of proportionality and is called specific heat of the material of the body. It is a characteristic constant of the material of the body and does not depend upon the shape or size or mass of the body. Since s = H/m x t, specific heat of a material can be defined as the amount of heat required to raise the temperature of unit mass of that substance through unit degree. In S.I., it is measured in J/kg 0C or Jkg-1 0C -1. Using the concept of conservation of energy Heat given by hot body = Heat received by colder body Example 10.6: How much thermal energy is required to raise the temperature of 10 kg of water form 25 0C to 100 oC? [Given specific heat of water s = 4200 J kg-1 C-1]. Solution: Heat required = m x s x t = 10 x 4200 x (100 –25) J = 315 0 kJ Example 10.7: A hot iron ball of mass 1.0kg and specific heat 3000 J kg-1 0C-1 at temperature 60 0C is placed in water of mass 3.0kg at a temperature 25 0C. Calculate the final temperature when thermal equilibrium is achieved. Neglect the heat sharing by the vessel containing water. Solution: Let the final temperature of the mixture be θ 0C Then, heat given by the iron ball = ms t = 1 x 3000 (60- θ)J Heat taken by water = 3 x 4200 (θ – 25) J Since heat given = heat taken 1 x 3000 x (60- θ) = 3 x 4200 (θ – 25) or 180000 – 3000 θ = 12600 θ – 315000 or 15600 θ = 495000 0 This gives θ = 31.7 C CHECK YOUR PROGRESS 10.3 Which of the following is the correct alternative? 1. Two iron balls of radii r and 2r are heated to same temperature. They are dropped into two different ice boxes, A and B, respectively. The mass of ice melted (a) will be same in the two boxes (b) in A will be twice than in B (c) in B will be twice that melted in A (d) in B will be 8 times that melted in A 2. An iron ball A of mass 2 kg at temperature 20 0C is kept in contact with another iron ball B of mass 1.0 kg at 20 0C. The heat energy will (a) flow from A to B only (b) flow from B to A only (c) not flow form A to B or B to A (d) flow from B to A as well as A to B

: 188 : Thermal Energy

3. When solid ice at 0 0C is heated, its temperature (a) rises immediately. (b) falls (c) does not change until whole (d) first rises then falls back to 0oC of it melts 4. Which of the following bodies when gently dropped in a vessel containing water at 200C will cause highest rise in the temperature of water? a) An iron ball of mass 1.0 kg at temperature 50 0C. b) A brass ball of mass 2.0 kg at temperature 40 0C with specific heat half that of iron. c) A block of ice of mass 0.1 kg at temp –10 0C. 5. When steam at 100 0C is heated its temperature a) does not change b) increases c) decreases

• • •

•

LET US REVISE Heat is a form of energy while the temperature is the degree of hotness of the body. Heat energy is measured in joule while the temperature is measured either in degree Fahrenheit (0F) or degree Celsius (0C) or in Kelvin (K). Mercury is used as a thermometric substance, because it is opaque and does not stick to the walls of the glass capillary. Also it has uniform coefficient of thermal expansion over a wide range of temperature. A Fahrenheit scale of temperature is related to Celsius scale of temperature by the relation

• • • •

• • • • •

F − 32 C = 9 5

The Kelvin scale is related to Celsius scale by the relation K = 273 + °C All substances expand on heating i.e. a rise in temperature. Linear coefficient of thermal expansion of a solid material is defined as the increase in length per unit length per degree Celsius rise in temperature. It is measured in 0C-1. Volume coefficient of thermal expansion of a solid material or a liquid or gaseous material is defined as the change in volume per unit volume per unit rise in temperature. It is also measured in 0C-1 . Volume coefficient of thermal expansion of a solid material is equal to three times its linear coefficient of thermal expansion. Different substances expand to different extents when heated for same rise in temperature. Bi-metallic strip is a technical application of differential expansion of solid metals. It can be used as an on/off switch in electrical circuits in response to a rise in temperature. Melting point and boiling point of a material are characteristic temperatures for that material. They do not depend upon their shape or size. Melting point of a substance decreases while its boiling point increases with mixing of impurities.

Thermal Energy : 189 :

•

•

•

• •

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

16.

Melting point and boiling point change with rise in pressure. The solids (like ice) which contract in volume on melting show a fall in their melting point with rise in pressure. The boiling point of all liquids increases with rise in pressure. The temperature of substances remains constant when heat energy is supplied at their Melting point and boiling point. This is used in changing their phases and is called latent heat. It is measured in joule per kg. Heat always flows from a body at higher temperature to another body in contact at lower temperature. It keeps on flowing till both the bodies acquire a common final temperature and a state of thermal equilibrium is achieved. Heat transferred is equal to mass × specific heat × change in temperature. In all heat transfer cases; heat given by hot body is equal to heat taken by cold body. TERMINAL EXERCISES Descriptive type questions. What is the difference between the temperature of a hot body and its thermal energy? What happens to the temperature of a body when it changes its state from liquid to solid? On what factors does the thermal expansion in a wire depend? What is the difference in the units of specific heat and latent heat of substances. Name any two uses of a bimetallic strip. If you have a mercury thermometer without any calibration, how will you make a (i) Celsius scale (ii) Fahrenheit scale for it? Why is the mercury used as a thermometric substance? Why does a bimetallic strip bend on heating? Heats of fusion and vaporization of substances are often referred to as latent heats. Why? When some water in a tea kettle is heated on a gas stove, it always takes a much lesser time for the water to start boiling than for all the water to vaporize? Why is it so? Why is the steam-burn far more serious than the one obtained from a spilling hot water. A solid substance expands on melting. What will happen to its freezing point when the pressure is reduced, just like at a hill station? At what temperature the numerical value of Fahrenheit scale will be just double of that on Celsius scale? (Ans. 160 0C or 320 0F) A 50 cm silver bar becomes shorter by 1.0 mm when it is cooled. How much was it cooled. Given coefficient of linear expansion for silver = 18 x 10-6 C –1. The iron rim of a wagon wheel has an internal diameter of 1.000 m when the temperature is 150 0C. What would be its diameter when it cools off to 25 0C? (Coefficient of linear expansion for iron = 12 x 10-6 0C -1) How much heat energy is required to change 200 g of ice at –20 0C to water at 70 0C? [Given latent heat of fusion of ice = 335 kJ/kg and specific heat of ice = 2100 j/kg 0C]

: 190 : Thermal Energy

17. A 2.0 kg block of iron at 100 0C is dropped into a 0.75 kg of water contained in a 0.325 kg copper Calorimeter. If the initial temperature of water and Calorimeter was 12 0C, what will be the final temperature. Given specific heat of iron = 105 cal kg -1 °C-1; specific heat of water = 1000 cal kg–10C-1; specific heat of copper = 93 cal kg–10C-1 (use 1.0 cal = 4.25J) 18. A heavy box of mass 200 kg is pulled along the floor for 15 m. If the coefficient of sliding friction is 0.4, how much heat energy is developed? 19. A 50 g bullet of lead at 27 0C fired form a rifle moves with a velocity of 200 m s-1. What temperature would it attain when it stops after the impact? [Given specific heat of lead = 130 J/kg 0C]. Assume that entire heat generated by impact goes to the bullet and not to target. ANSWERS TO CHECK YOUR PROGRESS 10.1 1. F

2. T

3. F

10.2 1. hot water geyser

4. T

5. F

6. T

2. remains same

3. less than

10.3 1. (d) 2. (c) 3. (c) 4. (a) 5. (b) GLOSSARY Heat: A form of energy which gives us sensation of warmth. Latent heat of fusion of a solid: The amount of heat required (in joules) to convert 1 kg mass of the solid into its corresponding liquid state at its melting point. Latent heat of vaporization of a liquid: The amount of heat required to convert 1 kg of the liquid into its corresponding gaseous state at a constant temperature. Principle of Calorimetry: In case no heat is lost to the surroundings and no change of state is taking place, the heat lost by hot body is equal to the heat gained by the cold body, when these are brought into contact. Specific heat of a substance: Defined as the amount of heat required (in joule) to raise the temperature of 1 kg of a substance by 1 0C (or 1 K). Sublimation: The process in which a solid changes into its gaseous state directly without passing through liquid state. Temperature: A numerical measure of hotness of a body which determines the direction of flow of heat. Heat always flows from a body at higher temperature to a body at lower temperature. Thermal equilibrium: Implies that the two bodies are at the same temperature and hence no net heat transfer is taking place between them. Thermal expansion: Implies the increase in the size of an object on heating.Principle of Calorimetry: In case no heat is lost to the surroundings and no change of state is taking place, the heat lost by hot body is equal to the heat gained by the cold body, when these are brought into contact. Thermometer: A device used for measuring temperature. Thermostat: A temperature control device usually made of a bimetallic strip.

11

Light Energy Can you read a book in the dark? If you try to do so, then you will realize, how much we are dependent on light. Light is very important part of our daily life. We require light for a number of activities. Even the plants on which we depend, need light for their food production. Without light we feel helpless. Truly speaking, life is not sustainable without light. It is an experience from our early childhood that objects become visible in presence of light. You see the objects when the light after reflection from them falls on your eyes and thus makes their image at the retina of your eye. In fact, light is a form of energy and hence it is invisible, although the presence of light gives us the ability to see the things around us. You may have seen in torches that there is a curved sheet of metal around the bulb. Can you think why is it so? We are very fond of looking at the image of our face in a looking glass. Do you know how the image is formed? You would also have noticed that when a rod is placed in a tumbler of water, it appears bent. What has caused the rod to bend ? We see that the stars twinkle on a clear night, that on a clear day the sky appears blue, at the time of sunset or sunrise the sky near horizon appears orange red. Have you ever tried to find out the reason for such natural events? In the present lesson you will find the answers to all such questions. You will also study about some man-made otpical instruments like microscope and telescope in this lesson. OBJECTIVES After completing this lesson, you will be able to: • recognise the importance of light in day to day life; • define the reflection of light and state the laws of reflection; • describe the image formation by plane and curved mirrors with suitable ray diagrams; • use mirror formula and define magnification; • define refraction of light and state the laws of refraction; • give some examples from nature showing refraction of light; • explain the refraction of light through prism and rectangular glass slab; • describe the types of lenses and explain the image formation by convex and concave lenses with the help of ray diagrams; • use lens formula and define magnification; • explain the power of lens and define dioptre; • describe briefly the construction and working of the instruments, like simple microscope, compound microscope and astronomical telescope.

: 192 : Light Energy

11.1 REFLECTION OF LIGHT Can you think how does an object become visible to you. When we see an object, we do so because light from the object enters our eyes. Some objects such as sun, stars, candle, lamp etc. may emit their own light, called luminous objects. Some other objects may bounce back a part of the light falling on them from other luminous objects. This bouncing back of the light after falling on any surface is called reflection of light. The light bounced back from the surface is called reflected light. Normal

Angle of incidence

N

I

In

on

ray

cti

fle

cid ent

l

r

Re

ray

Some objects having smooth and shiny surfaces reflect light better than others. A smooth shining surface, which reflects most of the light incident on it is mirror. The reflection of light from a plane mirror is shown in Fig 11.1

R

f le o Ang ction refle

Thus, when a beam of light travelling through a medium comes in contact with an object, a part of it gets bounced back (however, a part of it is absorbed and some part of it is able to penetrate through the object). This phenomenon is called reflection of light.

O

Fig. 11.1 Reflection of light from a plane mirror

While studying the reflection of light, you will come across different terms related to it. They are given below : • • • • •

Ray can be defined as the direction of propagation of light. Beam of light consists of a number of rays. Incident ray is the ray of light that falls on the reflecting surface. Normal is the name given to a line drawn at 900 to the surface at the point where the incident ray strikes the surface. Angle of incidence is the angle between the normal and the incident ray.

11.1.1 Laws of reflection of light Suppose, a ray of light (IO) falls on a reflecting surface AB at O, after reflection it goes along OR, as shown in Fig 11.1. The reflection of light from the surface takes place according to the following two laws: (i) First law of reflection: The incident ray, the reflected ray and the normal at the point of incidence, all lie in the same plane. (ii) Second law of reflection: The angle of incidence is equal to the angle of reflection i.e., ∠i = ∠r 11.1.2 Types of reflection Depending on the nature of the surface the reflection of light can be of two types: (i) Regular reflection: When the reflecting surface is very smooth and the rays of light falling on it are reflected straight off it, then it is called regular reflection, as shown in Fig. 11.2.

Incident rays

Reflected rays

Smooth plane surface

Fig. 11.2 Regular reflection

Light Energy : 193 :

(ii) Diffused reflection : When the reflection of light takes place from rough surfaces, the light is reflected off in all directions, as shown in Fig. 11.3. It depends on the angle of the incidence on the part of the surface it hits. This is called diffused reflection.

Incident rays

Normal

Reflected rays

Normal

Rough surface

Fig. 11.3 Diffused reflection

Do you know ? The rough surface diffuse or scatter the light falling on it and prevent the formation of image. Light is reflected from the paper of this book also but the surface of paper is much rougher than mirrors. That is why no image is formed by the paper. You might have seen people putting frosted window glass pane? Have you ever thought why are frosted glass used? The frosted glass has a rough surface which does not allow the light to form clear images. Instead, the rough surface of glass diffuses the light and no clear image can be seen through it . How do we see non-luminous objects? Sunlight or light from a lamp incident over non-luminous objects undergo regular as well as diffuse reflection. When these reflected rays strike the retina of our eyes, an image of that object is formed in the eye, and thus we are able to see the objects. 11.1.3 Formation of images due to reflection You know that a mirror is a good reflector of light rays. Daily at least once a day, you must be using a mirror to see your face. What do you actually see in the mirror? You see your image. The images are of two types – real and virutal. (i) Real image: The images which are obtained by the actual intersection of reflected rays, are called real images. The real images can be cast on a screen. In case of spherical mirrors real images are formed on the same side of the mirror as the object. (ii) Virtual image: The image obtained when the rays appear to meet each other but actually do not intersect each other, are called virtual images. They cannot be cast on a screen. Virtual images are formed behind the mirror. To understand the formation of image by a plane mirror, let us do an activity. ACTIVITY 11.1 Aim : Image formation by a plane mirror What is required? A plane mirror, a few pins and a sheet of paper. What to do? (i) Spread the sheet of paper over a soft, smooth wooden plank or a piece of card board.

: 194 : Light Energy

(ii)

Put the mirror M1 M2 in a vertical position over the sheet as shown in figure 11.4 (iii) Put two pins, one at ‘A’ little far from the mirror and the other one very near to the mirror at ‘B’ so that, the line AB makes an angle with the line M1 M2 showing the position of the mirror. (iv) Look at the images A and B of the two pins through the mirror, put two other pins at C and D so that all four pins A, B, C and D are in the same straight line. A (v) Now, look at the images of all these pins closing one of your eyes and moving your face in side ways. If the image of the two earlier pins and the two pins you have put just now, B B O C O M appear to be moving together you can say your a b c observation is free-from parallax error. b c (vi) Join the positions of pins by straight lines. a A (vii) Keeping the first pin as it is, take out other Fig. 11.4 Image formation by a three pins and repeat the experiment described plane mirror above by putting the pins in new positions. This way take a few more readings. 2

What do you observe? Besides the formation of image of the pins by the mirror, you are able to trace the directions of various incident and reflected rays. To understand the formation of image, you may consider the light rays emerging out of the object A. We have drawn only three rays namely (a), (b) and (c). These rays after striking the mirror M1 M2 get reflected in the directions (d), (e) and (f), respectively, (as shown in the figure 11.4) obeying the laws of reflection. It is clear that these reflected rays never meet with each other in reality. However, they appear to be coming (emerging) out from the point A´, inside the mirror i.e., if the reflected rays (d), (e) and (f) are extended in the backward direction, they will all meet with each other at A´. Thus, at A´ we get the image of object A. From the above activity we find that the image formed by a plane mirror has the following characteristics: This image is virtual (i.e., not real), erect and same in size as the object. • The object distance and the image distance from the mirror are found to be equal i.e., OA = OA´. Hence, the image of a point in a plane mirror lies behind the mirror along the normal from the object, and is as far behind the mirror as the object is in front. It is an erect and virtual image of equal size. 11.1.4 Few important facts about reflection Put your left hand near a plane mirror. What do you see? You will find that on reflection, the image of the hand appears as right hand as shown in Fig. 11.5 (a). Similarly, the number 2 will appear in an inverted fashion on reflection as shown in Fig. 11.5 (b).

Light Energy : 195 :

Hence, due to reflection in a plane mirror left handedness is changed into right handedness and vice-versa. This is known as lateral inversion. For example a left handed screw will appear to be right handed screw on reflection as shown in Fig. 11.5(c).

mirror (a)

mirror

mirror

(b)

(c)

Fig. 11.5 Lateral inversion in image formed by a plane mirror

Do you know ? (i) If you are approaching towards a plane mirror, even your image will also appear to be approaching towards you. (ii) A woman can see her full image in a plane mirror whose height is half of her height. See the ray diagram in Fig. 11.6 and try to understand why this happens. H

G

A

h

E

C

B

f

F

Fig. 11.6 Size of plane mirror to see full image

CHECK YOUR PROGRESS 11.1 1. Name four luminous objects. 2. Name the phenomenon of bouncing back of light from a rigid surface. 3. What is the relationship between the angle of incidence and the angle of reflection? 4. Although the light is reflected from the book you read, why is your image not visible in it? 5. Give two differences between diffused and regular reflection. 11.2 REFLECTION AT CURVED MIRRORS A curved mirror is a section of a hollow sphere whose inner or outer surface has been polished. Thus, there are mainly two types of spherical mirrors-convex mirror and concave mirror.

: 196 : Light Energy

(i) Convex mirror: It is a mirror in which the reflection takes place from the outer or the bulging side (i.e. the polishing is on the inner side) as shown in Fig 11.7 (a). (ii) Concave mirror: It is a mirror in which the reflection takes place from the hollow side (i.e., the polishing Inci dent is on the outer-side) as shown in Fig. 11.7 (b). ray For understanding the reflection at spherical mirrors, Angle of certain important terms are very useful. They are as shown i incidence Curved r f o e l mirror in Fig 11.8 and defined below. g n n A ctio refle ray (i) Pole (P): It is the mid-point of the spherical mirror. cted e

Refl

(ii) Centre of curvature (C): It is the centre of the hollow sphere of which the spherical mirror is a part.

Fig. 11.7 Reflection of light by curved mirrors

(iii) Radius of curvature (R): It is the distance between the pole and the centre of curvature of a spherical mirror. (iv) Principal axis: It is the imaginary line joining the pole with the centre of curvature. (v) Principal focus (F): The rays of light parallel and close to the principal axis of the mirror after reflection, either pass through a point (in concave mirror) or appear to be coming from a point (in convex mirror) on the principal axis; this point is called principal focus of the mirror. (vi) Focal Length (f): It is the distance between the pole and the principal focus of the mirror. Hollow glass sphere

x

Hollow glass sphere

x

y

Principle axis

Principle axis R

R Radius of curvature

Radius of curvature

Fig.

y

11.8Concave Some mirror terms

in image formation by

Convex mirror spherical mirrors

Relationship between focal length and radius of curavture Focal length (F) of a spherical mirror is equal to half of the radius of curvature (R) of that mirror. In mathematical terms it can be written as, f=

R 2

11.2.1 Rules of image formation by spherical mirrors The ray diagram for image formation by mirrors can be drawn by taking any two of the following rays : (i) Central ray: The ray of light striking the pole of the mirror is reflected back at the same angle on the other side of the principal axis (Ray no. 1 in Fig. 11.9).

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(ii) Parallel ray: For a concave mirror the ray parallel to the principle axis is reflected in such a way that after reflection it passes through the principal focus. But for a convex mirror the parallel ray is so reflected that it appears to come from principal focus (Ray no.2 in Fig 11.9). (iii) Ray through centre of curvature: A ray passing through the centre of curvature hits the mirror along the direction of the normal to the mirror at that point and retraces its path after reflection (Ray no.3 in Fig 11.9). 1

2

1 2

2 F

3

P

C

P

2 3 1 1 (a)

(b)

Fig. 11.9 Image formation by spherical mirrors (a) Concave mirror (b) Convex mirror

Now, let us see how images are formed by concave and convex mirrors when the object is placed in different positions. (a) Formation of image by concave mirror Using the above said rules of image formation, the ray diagram for the image formed for different positions of object are given below: (b) Object beyond c

(a) When the object is situated at a

(c) Object at c

D P C

B

(b)

A

F

B

F

C

A

(c)

A

B B ’

F

A '

Real, inverted, highly diminished image at focus

Real, inverted highly diminished between C and F

(d) Object between then c and f

Real, inverted highly image of the same size as object at C

(e) Object at f

(f) Object between f and p

A' A B'

C B

Real, inverted, enlarged image beyond C

D P

(e)

C

A B F

Real, inverted, highly enlarged image at infinity

D P

C F

B

Virtual, erect, enlarged image behind the mirror

Fig. 11.10 Formation of image by a concave mirror

D P

B '

: 198 : Light Energy

In all these diagrams we have considered two rays starting from a point at the top of the object. The image is formed where these rays intersect after reflection. (b) Formation of image by convex mirror In case of convex mirror, the formation of the image is shown in Fig 11.11. The incident ray AQ parallel to principal axis is reflected such that it appears to come from focus F. The incident ray AN towards the centre of curvature being normal to the mirror is reflected back along the same path. A A' These two reflected rays appear to be coming from N the common point A´, which is the image of point A. C P B F B '

The image formed by convex mirror is between pole P and focus F, virtual, diminished, and erect. Fig. 11.11 Formation of image by convex mirror In convex mirror, whatever may be the position of the object infront of the mirror, the image formed is always virtual, erect, diminished, (i.e, smaller than the pize of the object) and is situated between the pole and the focus. 11.2.2 Uses of mirrors The different types of mirrors have different uses in our daily life. Let us study them one by one. (i) Plane mirror is used • in looking glasses, • in construction of kaleidoscope, telescope, sextent, and periscope etc., • for seeing round corners, • as deflector of light. (ii) Concave mirror is used • as shaving and makeup mirrors, • as a reflector in search light, head light of motor cars and projectors etc, • for converging solar radiation in solar cookers, • as mirror for the dentists, • in flood lights to obtain a divergent beam of light to illuminate buildings, • in reflecting telescopes large concave mirrors are used. (iii) Convex mirror is used • as a rear view mirror in motor cars, buses and scooters, etc, • as safety viewers at dangerous corners and on upper deck buses 11.2.3 Sign convention and mirror formula To measure distances with respect to a curved mirror, following convention is followed: (i) All distances are measured from the pole of the mirror. (ii) The distances measured in the same direction as incident light, are taken as positive. (iii) The distances measured against the direction of incident light, are taken as negative. (iv) The distances above the principal axis are taken positive, whereas, below it are taken negative. Using the sign convention, the relationship between object distance (u), image distance (v) and the focal length for a curved mirror is given by,

Light Energy : 199 :

1 1 1 = + f u v

You can use this formula to find out any of the quantities, provided the other two are given. 11.2.4 Magnification in spherical mirrors Often we find that a spherical mirror can produce an enlarged or magnified image of any object. The ratio of the size of the image to the size of the object is called linear magnification. i.e., linear magnification (M) =

size of image (I) v =− size of object (O) u

Where, v = image distance from mirror, and u = object distance from mirror Positive value of M tells that image formed is erect while negative value of M indicates that an inverted image is formed. CHECK YOUR PROGRESS 11.2 1. What is the focal length of a plane mirror? 2. Write the position and nature of image formed by a concave mirror when the object is placed between the focus and centre of curvature. 3. List any two differences between real and virtual images. 4. What type of mirror is used to view the rear objects by an autodriver? 5. If an object of 5cm size is placed infront of a concave mirror, the size of the image formed by it is 7.5 cm, what is the linear 3 magnification of the mirror? 1 3 1 i Air 11.3 REFRACTION OF LIGHT i When a light ray passes from a less dense medium r to a more dense medium (e.g., from air to glass), it r 2 bends towards the normal (Fig. 11.12) and when it 2 passes from a denser medium to a less dense medium (a) (b) Fig. 11.12 Refraction of light (e.g., from glass to air) it bends away from the normal (Fig. 11.12). This phenomenon of deviation of light rays from their original path, when they pass from one medium to another, is called refraction of light.

ACTIVITY 11.2 Aim : To study the refraction through a glass slab What is required ? A glass slab, drawing sheet, pencil, drawing board, alpins, protector, and a scale. What to do? (i) Place glass slab on a drawing sheet fixed on a wooden drawing board, sketch a

: 200 : Light Energy O

pencil boundary. Draw a line OC meeting the boundary line obliquely. (ii) Fix the pins A and B on that line. Now look for these pins through the other side of the glass slab. (iii) Take a pin and fix it on the sheet such that A, B and E are in a straight line. (iv)Now fix another pin F such that it is in a straight line with pins A, B and E. Remove the slab and the pins. (v) Draw a line joining the points F to E to meet the boundary at D. (vi)Join point C to D by a dotted line.

A B

C

D

E F

Fig. 11.13 Refraction through a glass slab

What do we observe? As shown in Fig. 11.13, the line ABC gives the direction of incident ray on the glass slab while the line DEF gives the direction of emergent ray. The line CD gives the direction of refracted ray. Draw normals N1CN2 at C and N3DN4 at D to the boundaries. Now check the indication of these rays. Do you find that the refracted ray D has slightly bent towards the normal to the boundary at C? What do you conclude? The ray of light when goes from a rarer (air) to a denser (glass) medium, it bends towards the normal. Also, the ray of light when goes from denser (glass) to rarer (air) mediums it bends away from the normal. 11.3.1 Refractive index of the medium When the light travels from one medium to another medium, the speed of light changes.A ray of light from a rarer medium to a denser medium slows down and bends towards the normal. On the other hand the ray of light going from a denser medium to a rarer medium, is speeded up and bends away from the normal. It shows that the speed of light in different substances varies. Therefore, different substances have different abilities to bend or refract light. We call this bending ability of a material as the index of refraction or refractive index of that material. The refractive index (µ) of a material is defined as the ratio of the speed of light in vacuume to that in the material medium. speed of light in vacuum speed of light in medium The refractive index of a rarer medium is less as compare to that of a denser medium. Therefore, refractive index of a medium (µ) =

11.3.2. Laws of refraction The extent to which a ray bends, depends not only on the refractive index of medium, but also on the angle of incidence. The laws of refraction are : (i) First law of refraction: The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.(see fig. 11.13)

Light Energy : 201 :

(ii) Second law of refraction: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant and it is equal to the refractive index of the medium. This law is also called as the Snell’s law of refraction. Refractive index (µ) =

sine of angle of incidence sin i = sine of angle of reflection sin r

Air 11.3.3 Application of refraction of light Actual Apparent depth depth (i) If you look at a coin placed at the bottom of a container full of water, you will notice that it appears to be raised as shown in Fig. 11.14. You know that an object is visible C´ only when the rays of light from the object reach your eyes. In the first case, when Water there is no water in the container, the coin C will not be visible to you from the side of Fig. 11.14 (a) Apparent depth of a coin in the container as shown in Fig. 11.14(a), water because the rays of light traveling in a straight line do not reach your eyes. But on pouring the water into the container, the rays of light from the coin change their direction as they travel from water (denser medium) into air (rarer medium) and thus, reach your eyes. Thus, the coin becomes visible to your eyes. The rays now appear to be coming from C1 instead of C. In this way, the coin appears to be raised. The ratio of the actual depth of the coin to the apperent depth of the coin is equal to the refractive index of the liquid of the container. 1 Rupee

1 Rupee

Refractive index (µ) =

actual depth apparent depth

(ii) Another example of refraction observed in our daily life is the twinkling of stars. Visibility of the sun before actual sunrise or after actual sunset can also be explained on the basis of refraction of light. Position of the pencil (ii) You would have observed that a pencil as it appears when seen half kept in water in a glass appears to fom above Air be bent. When the part of a pencil is kept inside the water in a glass, it appears to Water be broken or bent with respect to the part Ray of light suffers outside the water as shown in Fig 11.14 Actual position bending here of the pencil (b). This is also due to the bending of Fig. 11.14 (b) The pencil inside water appears light rays when they pass from water to bent air. Try to explain these events and discuss your answer with your teacher or fellow students. CHECK YOUR PROGRESS 11.3 1. What happens when a ray of light passes from one medium to another of different density?

: 202 : Light Energy

2. Why do the stars twinkle at night? 3. What happens to a ray of light, if it enters a glass block along its normal? 11.4 REFRACTION THROUGH CURVED SURFACE In the present discussion under this section, we will confine ourselves to the refraction of light through lenses only. Do you know what is a lens? A lens is a portion of a transparent refracting medium bounded by two spherical surfaces. Because the lenses are made from spheres, they are called as spherical lenses. They are mainly of two types : • Convex lens • Concave lens (i) Convex lens: A convex lens is thick in middle and thin at the rim. It makes the parallel rays of light to converge and come to a point. Hence, it is also called a converging lens. The conveging property of a convex lens is shown in Fig. 11.15(a). (ii) Concave lens : A concave lens is thin in the middle and thick at rim. It makes (a) Convex lens (b) Concave lens the parallel rays of light to spread from Fig. 11.15 Types of lenses a point. Hence it is also called a diverging lens. The diverging property of concave lens is shown in Fig. 11.15(b). The point at which the incident rays parallel to principal axis will converge upon after refraction in a convex lens is called its principal focus. Where as in a concave lens the point from where incident rays parallel to the principal axis of the lens appear to be coming, is called as its principal focus (F). 11.4.1 Rules of image formation by lenses In order to draw the image formed by any lens only two rays are required. These two rays are: (i) A ray parallel to the principal axis of the lens after refraction, converges upon (appears to diverge off) the principal focus of a convex (concave) lens. (ii) A ray towards the optical center falls on the lens symmetrically and after refraction passes through it undeviated. Let us now see the image formation in cases of convex and concave lens in different situations of the objects. (a) Image formation by convex lens According to the above said rules of image formation, the position and nature of the image formed for different positions of object is shown by the following ray diagrams: (see Fig. 11.16). (i) If the object is placed between the optical centre O and first focus F1, the image is formed on the same side of lens and it is virtual, upright and magnified. (ii) If the object is at first focus F1 ,the image is at infinity and it is real, inverted and very much magnified.

Light Energy : 203 :

Rays coming from the object at Infinity F

F (Object at F)

O

I (Image formed at F)

Fig. 11.16 (a) Object placed between optical centre and first focus

F

(Refracted parallel rays meet at infinity. So , image is formed at infinity.

Fig. 11.16 (b) Object at the first focus

(iii) If the object is between F1 and 2F1, the image is beyond 2F2 on the other side of the lens and it is real, inverted and larger in size. (iv) If the object is at 2F1, the image is at 2F2 on the other side of the lens and it is real, inverted and is of same size as object. O

O 2F

2F

F

F

2F

2F

F

O

F

Image is formed at 2F

I

Fig. 11.16 (c) Object is between F1 and 2F1

Fig. 11.16 (d) Object is at 2F1

(v) If the Object is beyond 2F1, the image is inbetween F2 and 2F2 on the other side of the lens and is real, inverted and diminished. (vi) If the object is at infinity, the image is at F2 on the other side of the lens and is real, inverted and very much diminished. O O

2F 2F (Object beyond 2F)

F

O

F F

Image between F and 2F

(Object is O between F and O)

F

Eye of the observer

Fig. 11.16 (e) Object is beyond 2F1

(b) Image formation by concave lens The image formed by a concave lens is always smaller than the object, erect and virtual and is formed between focus and optical centre on the same side as the object whatever be the position of object as shown in Fig. 11.17. 11.4.2 Sign convention and lens formula In case of the spherical lenses,

Fig. 11.16 (f) Object is at infinity

P P' O Q

Q'

Fig. 11.17 Image by concave lens

(i) all distances in a lens are to be measured from optical centre of the lens, (ii) distances measured in the direction of incident ray are taken to be positive, (iii) distances opposite to the direction of incident ray are taken to be negative.

: 204 : Light Energy + P (iv) the height of the object or image measured above – the principal axis are taken positive whereas below + it, are taken negative. Q' O Using the above mentioned sign convention, in Fig. C F C Q F 11.18 let us assume, distance of object PQ from the f optical center O = OQ = (-u), distance of iamge P´Q´ u v from the optical center O = OQ´ = (+V), and focal length – P' Fig 11.18 Sign convention in lenses of lens = OF´2 = (+f). The relationship between u,v and f for a lens is as shown below: 1

1

2

2

1 1 1 − = v u f

This is called lens formula. Focal length for convex lens is positive, whereas, for concave lens it is taken negative. 11.4.3 Magnification You would have noticed that in case of some lenses, the size of the image of an object is enlarged whereas in some other cases it is diminished. If we take the ratio of the size of the image to the size of the object for a particular lens it remains constant for that lens. This ratio of the size of the image to that of the object is called as the magnification of the lens. i.e., magnification (m) =

size of image I = size of object O

I v = O u A positive value of m tells that the image is erect and negative value of m tells that the image is inverted.

also, m =

CHECK YOUR PROGRESS 11.4 1. If an object is placed at the focus of a convex lens, what will be the position and nature of the image? 2. Draw the ray diagram to show the image formed by a concave lens. 11.5 DISPERSION OF WHITE LIGHT We are sure, you must have observed seven brillient colours of light in your surrounding. The separation of white light into its constituent seven colours is called dispersion of light. 11.5.1 Dispersion of light through glass prism When the white light passes through a glass prism, it gets splitted into seven different colour rays. In fact, the white light is supposed to be made up of seven colours. Different coloured light have different wavelengths. The refractive media like glass have different values of refractive indices for different colours. You should know that as we go from violet to red wavelength of light increases . The violet part of incident white light get refracted of the surface PQ at angle