THE MOLE

UNIT

The Mole

How Can Particles be Counted by Weighing?  The first hypothesis hypo thesis to prese nt… is the supposition that t hat the number of integral molecules in any gases is always the same for equal volumes, or always proportional to the volumes.  Amadeo Avogadro (1776–1856) (1776–18 56)

Engage: What is the Mass of an Object in a Sealed Box?  A. On the periodic period ic table, the nu mber 12.01 is written beneath the symbol for carbon. The number 14.01 is beneath the symbol for nitrogen, and 16.00 is below oxygen’s symbol.  What do these nu mbers mean?

1.

Your teacher will provide you with a group group of containers partly filled filled with paperclips.  All paperclips in any given container ar e identical, but the size of the paperclips varies among the containers. One container in your group is empty, and all of the others contain exactly the same number of paperclips. Do not open the containers. Determine the mass of each container to ±0.1 gram.

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2.

What is the mass of the contents  of each container?

3.

There is the same number of paperclips in each container. Why do the contents of the containers have different masses?

4.

Let’s assign the lightest clip a mass of 1 relative clip mass unit, rcmu. What is the mass of the heavier clips in rcmu? Explain the reasoning you used to answer this question.

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Unit 5

5.

You do not know the number of paperclips in the containers, but you do know that there is the same number in each container. We can invent a term to describe that number. Since 12 is a dozen, let’s call the number of clips in each container a bozen  (rhymes with dozen   ). What is the mass of the lightest c lip in grams per bozen?

6.

What is the relationship between the rcmu and the gram?

7.

Assume that the size of a paperclip container is directly proportional to the number of clips it contains. What would be the mass of the contents of a container exactly twice the size of the one you worked with in this exercise? Answer in g and rcmu.

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The Mole

Montana High School Chemistry

Explore: How Can We Determine the Relative Masses of Elements? 8.

Imagine that you have a pair of magnets. What happens when you bring opposite poles together end-to-end? What happens when you bring the same poles together?

9.

When objects become electrically charged, they can have a positive charge or a negative charge. These charges act similar to magnets: like charges repel and opposite charges attract. If we create a negative charge on the surface of ultra-light ping pong balls, how  would these balls behave when we roll them toward one another?

10. Now imagine that we place 10 identically-charged balls in a large flexible-walled balloon.  The balloon is made o f a material that is so light, the interaction of the balls with its surface keeps it at a constant volume. The inner surface of the balloon also has the same charge. We send this balloon into outer space so that there is no gravitational effect. We then shake the balloon to get the balls to start moving, and the balloon expands until the force of the balls balances the elasticity of the material. Explain how the ping pong balls will behave inside of this balloon.

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Unit 5

The Mole

11. Scientists believe that our model of ping pong balls in a thin, flexible-walled balloon is similar to what happens when the particles that make up air are enclosed in a rubber balloon. The model that describes the behavior of gases is called the kinetic molecular theory. The term kinetic  refers to motion. The particles that make up a gas are constantly in motion. Additionally, the higher the temperature, the faster the particles move. The term molecular  refers to the particulate nature of matter. Gases consist of tiny molecular particles. In this context, theory  refers to a model. Thus, kinetic molecular theory is a model that depicts gases as tiny, molecular particles that are constantly in motion. 12. What will happen if you partially fill a balloon with air, and then you add more air, doubling the number of molecules within in it? No other variable is changed. Specifically, what happens to the volume of the balloon? Explain.

13. Use kinetic molecular theory to explain what happens at the particulate level to cause the macroscopic effect you described in the previous question.

Mental Models

14. Describe, using words, the relationship between the volume of a gas and the number of particles in the sample, when all other variables are held constant.

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15. Using the symbol V for volume and n for number of particles, write a mathematical expression stating the proportionality between the volume of a gas and the number of particles in the sample. The symbol " means “is proportional to.”

16. Using k as the proportionality constant, write the mathematical expression in the form of an equation that relates the volume and number of particles.

• The air we breathe is about 80% nitrogen and 20% oxygen.

17. Consider four different elements that exist as gases at room temperature and pressure: nitrogen, oxygen, hydrogen, and chlorine. Four identical balloons are filled, one with each gas, to exactly the same volume. If these balloons are at the same temperature and pressure, can you draw conclusions about the relative number of particles in each? What can you say about the relative mass of the contents of each balloon?

18. In Unit 2, you used experimental evidence to show that the volume of a fixed amount of gas depends on temperature and pressure. When people communicate the results of investigations with gases that involve reporting the volume of the gas, they must also state the temperature and pressure at which that volume was measured. To simplify the literally infinite number of temperature and pressure conditions at which gas volumes can be measured, scientists have agreed to report gas volumes at standard temperature and pressure, 0°C and 760 mm Hg, whenever possible. The table below shows the mass and STP volume of balloons filled with four different elements. Element

Nitrogen Oxygen Hydrogen Chlorine

Mass of Empty Balloon (g)

Mass of Filled Balloon (g)

 Water Volume  Without Balloon (L)

 Water Volume  With Balloon (L)

1.46 1.57 1.32 1.31

29.48 33.57 3.34 72.21

6.78 3.64 5.90 7.23

29.18 26.04 28.30 29.63

 The volume of the balloon was determ ined by water displacement. A lar ge container  was partially filled with a mea sured volume of water. The balloon was then submersed in the water, and the resulting volume of the water plus balloon was measured. The  volume of the balloon is the difference in the two volume measurements. 5.6 Copyright ! 2006 Montana Partners

Unit 5

19. What is the volume of each gas? What is the relationship between these volumes? Why do they have this relationship?

20. Determine the density of each gas.

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The Mole

Montana High School Chemistry

Explain 21. Use the density data from the previous question to determine the relative masses of the four elements. Assign the lightest element a mass of 1 atomic mass unit, amu. What is the mass of the heavier elements in amu? Explain the reasoning you used to answer this question.

22. The symbols used to represent the elements whose relative masses you’ve calculated are: nitrogen, N oxygen, O hydrogen, H chlorine, Cl Locate these elemental symbols on the periodic table. What is the relationship between the atomic masses you calculated (to the ones place) and the numbers below the symbols of the elements on the periodic table?

23. What is the atomic mass of helium, He? neon, Ne? carbon, C? Explain how you answered these questions.

24. Scientists use the term mole to describe the number of particles in 22.4 L of a gas at 0°C and 760 mm Hg. They also use the term molar mass to describe the mass of a mole of a substance. Use the experimental data provided in this unit to determine the molar mass of nitrogen. Explain your reasoning.

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Unit 5

25. How does the molar mass of nitrogen compare with its atomic mass? What is the same and what is different?

26. What is the molar mass of oxygen, hydrogen, chlorine, helium, neon, and carbon?

27. Which sample has the greater number of particles: 39.95 grams of argon, symbol Ar, or 83.80 grams of krypton, symbol Kr? Explain your reasoning.

28. Which sample has the greatest mass: 2 moles of carbon or 2 moles of silicon, symbol Si? Explain your reasoning.

29. What is the mass of 3.0 moles of carbon? Explain.

30. How many moles of particles are in 80.72 grams of neon? Explain.

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Montana High School Chemistry

Elaborate: How is the Volume of a Gas Related to Its Other Measurable Properties? 31. In Unit 2, you used experimental data to show that the volume of a gas is proportional to its absolute temperature. You also showed that the volume is inversely proportional to its pressure. In this unit, you reasoned that the volume of a gas is directly proportional to the number of particles in a sample. The number of particles, by convention are counted in moles. Using symbols to express each of these relationships,  we have  V " T

V"

1 P

V " n

If one variable is proportional to two or more other variables, it is logical to assume that it is proportional to the product of those variables. For example, if A " X and A " Y,  we can assume that A " X # Y. Express the relationship between volume and temperature, the inverse of pressure, and number of particles in one proportionality.

32. Using R as the symbol for a proportionality constant, change the proportionality in the previous question to an equation.

33. Rearrange your equation so that pressure and volume are on one side of the equal sign, and the other three symbols are on the other side.

34. You’ve just written the most common form of the ideal gas law. It is the mathematical form of a model that describes an ideal gas, which is a gas that follows a relatively simple particulate-level model. The model closely describes the actual behavior of gases. 35. Experiments have been conducted to determine the value of R, which is called the universal gas constant. Use the following data to calculate the value of R: At 19°C and 721 mm Hg, 0.155 mole of a gas occupies 3.92 L.

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36. What is the value of the universal gas constant when the pressure is expressed in atmospheres?

37. What volume will a gas occupy when 0.33 mole of the gas is at 741 mm Hg and 15°C?

38. What is the pressure of 1.23 moles of oxygen gas with a volume of 675 mL at –11°C?

39. How many moles of gas particles are in a 55-liter nitrogen cylinder at 18°C and 2.20 atm pressure?

40. A balloon is filled with 0.0368 mole of air. The air is at the same pressure of the room in  which it is located, 7 55 mm Hg. It has a volume of 0.90 L. What is the tem perature (°C) of the air in the balloon?

41. A gas cylinder has a volume of 2.0 liters. It is filled with helium until the pressure is 5.5 atm and the temperature is 35°C. What mass of helium is in the cylinder?

42. A neon sign is filled with 0.50 grams of neon at 75°C and 1.1 atm. What is the volume of the gas within the sign?

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The Mole

Montana High School Chemistry

Appendix 1: Gas Properties and Kinetic Molecular Theory The air that surrounds us is a sea of mixed gases called the atmosphere. It is not necessary, then, to search very far to find a gas whose properties we may study. Some of the familiar characteristics of air—in fact, of all gases—are the following: 1.

Gases may be compressed.  A fixed quantity of air may be made to occupy a smaller volume by applying pressure. Figure 5.1(a) shows a quantity of air in a cylinder having a leakproof piston that can be moved to change the volume occupied by the air. Push the piston down by applying more force, and the volume of air is reduced (F ig. 5.1[b]).

2.

Gases expand to fill their con tainers uniformly. If less force were applied to the  piston, as shown in Figure 5.1(c), air would respond immediate ly, pushing the  piston upward, expanding to fill the larger volume uniformly. If the piston were  pulled up (Fig. 5.1[d]), air would aga in expand to fill the addition al space.

3.

 All gases have low density. The density of air is about 0.0012 g/cm . The density of water is 770 times greater than the density of air, and iron is 6000 times more dense than air, when all are at room temperature.

3

Figure 5.1 Compression and expansion properties of gases. The piston and cylinder show that gases may be compressed and that they expand to fill the volume available to them.

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Unit 5

4.

Gases may be mixed. “There’s always room for more” is a phrase that may be applied to gases. You may add the same or a different gas to a gas already occupying a rigid container of fixed volume, provided there is no chemical reaction between them.

5.

A confined gas exerts constant pressure on the walls of its container uniformly in all directions. This pressure, illustrated in Figure 5.2, is a unique property of a gas, independent of external fac tors such as gravitational forces.

The Mole

 What Particulate-Level Model is Used to Explain Gas Properties? As you study this section, work to achieve these learning goals: • Explain or predict physical phenomena relating to gases in terms of the ideal gas model. In trying to account for the properties of gases, scientists have devised the kinetic molecular theory. The theory describes an ideal gas model by which we can visualize the nature of the gas by comparing it with a physical system we can either see or readily imagine. As always, chemists explain observable macroscopic  phenomena in terms of  particulate behavior. The main features of the ideal gas model are as follows: 1.

Gases consist of particles moving at any given instant in straight lines (Fig. 5.3). Particle motion explains why gases fill their containers. It also suggests how they exert pressure. When an individual particle strikes a container wall, it exerts a force at the point of collision. When this is added to billions upon billions of similar collisions occurring continuously, the total effect is the steady force that is responsible for gas pressure.

Figure 5.3 Particle motion in a gas. Particles collide with each other and with the walls of the container, the latter being responsible for the pressure the gas exerts. Figure 5.2 Pressure in gases and liquids. Each container has four pressure gauges, one on top, one on bottom, and two on the side. Note how the four gauges on the gas container all read the same pressure, but the liquid gauges show that pressure increases with increasing depth. Gas pressures are exerted uniformly in all directions; liquid pressures depend on the depth of the liquid.

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Figure 5.4 An ideal gas particle collides with the walls of the container without losing energy. The energy of the particle is the same before (E1), during (E2), and after (E3) the collision with the container wall: E1 = E2 = E3.

2.

 Molecules collide with each other and with the container walls without loss of total kinetic energy (Fig. 5.4). If gas particles lost energy or slowed down as a result of these collisions, the combined forces would become smaller, and the  pressure would gradually decreas e. Furthermore, because of the relationsh ip  between temperature and average molecular speed, temperature would drop if energy were lost in collisions. Any enclosed gas would eventually become a liquid because of this loss of energy. But these things do not happen, so we conclude that energy is not lost in molecular collisions, either with the walls or  between molecules .

3.

Gas molecules are very widely spaced (Fig. 5.5). Gas molecules must be widely spaced; otherwise the densities of gases would not be as low as they are. One gram of liquid water at the boiling point occupies 1.04 cm3. When changed to 3 steam at the same temperature, the same number of molecules fills 1670 cm , an expansion of 1600 times! If the water molecules were touching each other in the liquid state, they must be widely separated in the gaseous state. Compressing and mixing gases are possible because of the open spaces between gas molecules.

4.

The actual volume of molecules is negligible compared to the space they occupy. The total volume of the actual molecules in one gram of water is the same regardless of its state of matter. The 1.04-cm3 volume mentioned previously for one gram of water in the liquid state is 0.06% of the 1670-cm 3 total volume the molecules occupy as a gas, which qualifies as negligible.

5.

Gas molecules behave as independent particles; attractive forces between them are negligible.  The large distances between gas particles ensure us that attractions between these molecules are n egligible.

Figure 5.5 Suppose you were to select a sample of liquid water that contained 100 molecules. If you then selected 15 more samples—total 16—of the same volume, each sample would contain 100 molecules. This would be a total of 1600 molecules in the 16 samples. If you were to then select 16 separate samples of steam, each sample having the same volume as each sample of liquid water, how many water molecules would be in each sample? On average, 15 of the sample volumes of steam would be empty—no molecules—and the 16th sample volume would contain only one water molecule.

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Unit 5

The Mole

Homework Questions Mass, Molar Mass, and Moles

1.

What is the molar mass of iron, Fe, and copper, Cu?

2.

The atomic mass of an element is 22.99 amu. What is the elemental symbol of that element?

3.

What is the mass of 0.248 mole of helium, He?

4.

How many moles of magnesium (Mg) atoms are in a 12.5-gram sample of the pure metal?

5.

How many moles of neon gas, Ne, are in 44.8 L at 0°C and 760 mm Hg? What is the mass of the gas?

6.

What volume will be occupied by 119.85 grams of argon gas at 0°C and 760 mm Hg?

Ideal Gases

7.

What is the temperature (°C) of a 3908-mL sample of hydrogen at 744 mm Hg if there are 0.55 moles of particles in the sample?

8.

How many moles of helium, He, are in 18.3 L of the gas at 188°C and 0.559 atm? What is the mass of the gas?

9.

What volume will be occupied by 0.056 mole of oxygen at –22°C and 885 mm Hg?

10. In the United States, pressure is often expressed in pounds per square inch, psi. One atmosphere is equal to 14.7 psi. What is the volume occupied by 3.38 moles of an ideal gas when it is at a pressure of 15.5 psi and a temperature of 72°F? 11. Gauge pressure is the pressure of a gas above atmospheric pressure. For example, if a tire pressure gauge reads 28 psi, it indicates that the pressure in the tire is 28 psi above atmospheric pressure. On a day when the atmospheric pressure is 14.7 psi, a 40.0-L auto tire is inflated to 28 psi. If the temperature is 65°F, what is the number of moles of gas particles in the tire? If the molar mass of air is 29 g/mol, what is the mass of air in this tire? 12. What will be the gauge pressure of a 41.3-L tire at 54°F that contains 151 grams of air?

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A gauge for measuring tire pressure. A typical tire gauge measures the pressure above atmospheric pressure. Image courtesy of Goulds Pumps/ITT Industries.