Application of Mole Concept

CHEMISTRY TARGET IIT JEE 2014 XI (P)

APPLICATION OF MOLE CONCEPT It's a furry animal !! What is a mole?

A mole is something that my brother has on his face. Idiots ! Its chemistry A mole is a counting unit.

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Application of Mole Concept

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CHEMISTRY – STUDY OF MATTER Overview of Chemistry

Special Highlights BRAIN TEASERS:

GENERAL MISTAKE:



TEACHER’S ADVICE:

Application of Mole Concept

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KEY CONCEPTS 1. 1.1

LAWS OF CHEMICAL COMBINATION Law of conservation of mass [Lavoisier] In any physical or chemical change mass can neither be created nor be destroyed.

1.2

Law of constant composition [Proust] A chemical compound always contains the same element combined together in fixed proportion by mass.

1.3

Law of multiple proportions [Dalton] When two elements combine to form two or more compounds, the different masses of one element which combine with a fixed mass of the other element, bear a simple ratio to one another.

1.4

Law of reciprocal proportions [Richter] When two different elements combine with the same mass of a third element, the ratio in which they do so will be same or simple multiple if both directly combined with each other. In all chemical reactions, substances reacts in the ratio of their equivalent masses.

1.5

Gay Lussac law of combining volumes [Gay Lussac] When gases combined or produced in a chemical reaction they do so in a simple ratio by volume provided all the gases are at same temperature and pressure.

"Wonder these laws are useful?"

"These are no longer useful in chemical calculations now but gives an idea of earlier methods of analysing and relating compounds by mass." 2. 2.1

BASIC DEFINITION INVOLVED Atomic mass Atomic mass of an element can be defined as the number which indicates how many times the mass of one atom of the element is heavier in comparison to

Atomic mass =

2.2

1 th part of the mass of one atom of Carbon-12. 12

[ Mass of an atom of the element] Mass of an atom in amu = 1 1 amu  [ Mass of an atom of carbon - 12] 12

Atomic mass unit (amu) The quantity [

1 × mass of an atom of C–12] is known as atomic mass unit. 12

Application of Mole Concept

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Can you calculate value of 1 amu in gram?

Be clear in the difference between 1 amu and 1 gm. 2.3

Gram atomic mass The gram atomic mass can be defined as the mass of 1 mole atoms of an element.

2.4

Average atomic weight =  % of isotope X molar mass of isotope.

The % obtained by above expression (used in above expression) is by number (i.e. its a mole%) 2.5

Molecular mass Molecular mass is the number which indicates how many times one molecule of a substance is heavier in 1 th of the mass of one atom of C-12. comparison to 12 Molecular mass =

= 2.6

Mass of one molecule of the substance (in amu) 1  [ Mass of an atom of C - 12] 12

Mass of one molecule of the substance (in amu) 1 amu

Gram Molecular mass Gram molecular mass can be defined as the mass of 1 mole of molecules.

2.7

Average molecular weight =

 niMi  ni

where ni = no. of moles of any compound and mi = molecular mass of any compound.

Make yourselves clear in the difference between mole% and mass% in question related to above. Shortcut for % determination if average atomic weight is given for X having isotopes XA & XB.

Application of Mole Concept

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% of

XA

Average atomic weight  wt of X B = × 100 difference in weight of X A & X B

Try working out of such a shortcut for XA, XB, XC

2.8

Mole : One mole is a collection of that many entities as there are number of atoms exactly in 12 gm of C-12 isotope. or 1 mole = collection of 6.02 × 1023 species 6.02 × 1023 = NA = Avogadro's No. 1 mole of atoms is also termed as 1 gm-atom, 1 mole of ions is termed as 1 gm-ion and 1 mole of molecule termed as 1 gm-molecule.

3.

METHODS OF CALCULATIONS OF MOLE : Given no. NA

(a)

If no. of some species is given, then no. of moles =

(b)

If weight of a given species is given, then no of moles = or

(c)

=

Given wt. (for atoms), Atomic wt.

Given wt. (for molecules) Molecular wt.

If volume of a gas is given along with its temperature (T) and pressure (P) PV RT where R = 0.0821 lit-atm/mol-K (when P is in atmosphere and V is in litre.)

use n =

1 mole of any gas at STP occupies 22.7 litre.

Gases do not have volume. What is meant by "Volume of gas"?

Do not use this expression (PV = nRT) for solids/liquids.

How would I calculate moles if volume of a solid is given?

Application of Mole Concept

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4. 4.1

EMPIRICAL FORMULA, MOLECULAR FORMULA : Empirical formula : Formula depicting constituent atom in their simplest ratio. Molecular formula : Formula depicting actual number of atoms in one molecule of the compound

4.2

Relation between the two : Molecular formula = Empirical formula × n Molecular mass n = Empirical Formula mass

Check out the importance of each step involved in calculations of empirical formula. 4.3

Vapour density : Vapour density : Ratio of density of vapour to the density of hydrogen at similar pressure and temperature. Vapour density =

Molecular mass 2

Can you prove the above expression?

Is the above parameter temperature dependent?

5.

STOICHIOMETRY : Stoichiometry pronounced (“stoy – key – om – e – tree”) is the calculations of the quantities of reactants and products involved in a chemical reaction. Following methods can be used for solving problems. (a) Mole Method  Balance reaction required  (b) Factor Label Method  (c) POAC method } Balancing not required (d) Equivalent concept } to be discussed later

6. 6.1

CONCEPT OF LIMITING REAGENT. Limiting Reagent : It is very important concept in chemical calculation. It refers to reactant which is present in minimum stoichiometry quantity for a chemical reaction. It is reactant consumed fully in a chemical reaction. So all calculations related to various products or in sequence of reactions are made on the basis of limiting reagent.

It comes into picture when reaction involves two or more reactants. For solving any such reactions,first step is to calculate L.R.

Application of Mole Concept

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6.2

Calculation of Limiting Reagent : (a) By calculating the required amount by the equation and comparing it with given amount. [Useful when only two reactant are there] (b) By calculating amount of any one product obtained taking each reactant one by one irrespective of other reactants. The one giving least product is limiting reagent. (c) Divide given moles of each reactant by their stoichiometric coefficient, the one with least ratio is limiting reagent. [Useful when number of reactants are more than two.]

7.

PERCENTAGE YIELD actual yield The percentage yield of product = the theoretical maximum yield  100

For reversible reactions, the actual amount of any limiting reagent consumed in such incomplete reactions is given by [% yield × given moles of limiting reagent]

For irreversible reaction with % yield less than 100, the reactants is converted to product (desired) and waste. 8. 8.1

SOME EXPERIMENTAL METHODS : For determination of atomic mass : Dulong's and Petit's Law : Atomic weight × specific heat (cal/gm°C)  6.4

Gives approximate atomic weight and is applicable for metals only. Take care of units of specific heat. 8.2

Quantitative Analysis 1. Estimation of Carbon and Hydrogen 2. Estimation of Nitrogen (i) Dumas method (ii) Kjeldahl’s method 3. Estimation of Halogens 4. Estimation of Sulphur 5. Estimation of Phosphorus 6. Estimation of Oxygen

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8.3

For molecular mass determination : (a) Victor Maeyer's process : (for volatile substance) Procedure : Some known weight of a volatile substance (w) is taken, converted to vapour and collected over water. The volume of air displaced over water is given (V) and the following expressions are used. w w RT RT M= or M= (P  P' )V PV If aq. tension is not given If aq. tension is P'

Aqueous tension : Pressure exerted due to water vapours at any given temperature.

This comes in picture when any gas is collected over water. Can you guess why? (b)

Silver salt method : (for organic acids) Basicity of an acid : No. of replacable H+ atoms in an acid (H contained to more electronegative atom is acidic) Procedure : Some known amount of silver salt (w1 gm) is heated to obtain w2 gm of while shining residue of silver. Then if the basicity of acid is n, molecular weight of acid would be  w2 1      Msalt  w1 and molecular weight of acid = M – n(107) salt  108 n 

This is one good practical application of POAC. (c)

Chloroplatinate salt method : (for organic bases) Lewis acid : electron pair acceptor Lewis base :electron pair donor Procedure : Some amount of organic base is reacted with H2PtCl6 and forms salt known as chloroplatinate. If base is denoted by B then salt formed (i) with monoacidic base = B2H2PtCl6 (ii) with diacidic base = B2(H2PtCl6)2 (iii) with triacidic base = B2(H2PtCl6)3 The known amount (w1 gm) of salt is heated and Pt residue is measured. (w2 gm). If acidity of base is 'n'  w2 1  M  n (410)    M salt  w1 and M = salt then  base 2  195 n 

Application of Mole Concept

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EXERCISE # I LAWS OF CHEMICAL COMBINATION AND AVERAGE MOLAR MASS Q.1

2 isotopes of an element are present in 1 : 2 ratio of number, having mass number M and (M + 0.5) respectively. Find the mean mass number of element.

Q.2

Find the number of neutrons in 0.45 g water, assuming that all the hydrogen atoms are H1 atoms and all the oxygen atoms are O16 atoms

Q.3

A gaseous mixture contains CO2 (g) and N2O (g) in a 2 : 5 ratio by mass. Find the ratio of the number of molecules of CO2 (g) and N2O (g)

Q.4

1.61 gm of Na2SO4.10H2O contains same number of oxygen atoms as present in x gm of H2SO4. Calculate x.

Q.5

Ethanol, C2H5OH, is the substance commonly called alcohol. The density of liquid alcohol is 0.7893 g/ml at 293 K. If 1.2 mole of ethanol are needed for a particular experiment, what volume of ethanol should be measured out?

Q.6

What time in sec., it would take to spend Avogadro’s number of rupees at the rate of 10 lac rupees per second?

Q.7

Methane and propane are both constituent of natural gas. A sample of methane contains 5.7 gm of C atom and 1.9 gm of H atom combined in certain way. Whereas a sample of propane contain 4.47 gm of carbon atom and 0.993 gm of H atoms combined in different way. Show that two sample obey law of multiple proportion.

Q.8

Substance A and B are colourless gases obtained by combining sulphur with oxygen. Substance A results from combining 6 gm of sulphur with 6 gm of oxygen and substance B result from combining 8.6 gm of sulphur with 12.88 gm of oxygen. Show that the mass ratio in two substances are in simple multiple of each other.

Q.9

MOLE How many gm of HCl is needed for complete reaction with 69.6 gm MnO2 ? HCl + MnO2  MnCl2 + H2O + Cl2

Q.10

Nitric acid is manufactured by the Ostwald process, in which nitrogen dioxide reacts with water. 3 NO2 (g) + H2O (l)  2 HNO3 (aq) + NO (g) How many grams of nitrogen dioxide are required in this reaction to produce 25.2 gm HNO3 ?

Q.11

Flourine reacts with uranium to produce uranium hexafluoride, UF6, as represented by this equation U(s) + 3F2(g)  UF6(g) How many fluorine molecules are required to produce 7.04 mg of uranium hexafluoride, UF6, from an excess of uranium ? The molar mass of UF6 is 352 gm/mol. (NA = 6 × 1023)

Q.12

What total volume, in litre at 627°C and 1 atm, could be formed by the decomposition of 16 gm of NH4NO3 ? Reaction : 2 NH 4NO3  2N2 + O2 + 4H2O(g).

Application of Mole Concept

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Q.13

Q.14

Calculate mass of phosphoric acid required to obtain 53.4 gm pyrophosphoric acid. LIMITING REACTANT Titanium, which is used to make air plane engines and frames, can be obtained from titanium tetrachloride, which in turn is obtained from titanium oxide by the following process : 3 TiO2(s) + 4C (s) + 6Cl2 (g)  3TiCl4(g) + 2CO2(g) + 2CO (g) A vessel contains 4.32 gm TiO2, 5.76 gm C and; 7.1 gm Cl2, suppose the reaction goes to completion as written, how many gram of TiCl4 can be produced ? (Ti = 48)

Q.15

A chemist wants to prepare diborane by the reaction 6 LiH + 8BF3  6Li BF4 + B2H6 If he starts with 2.0 moles each of LiH & BF3. How many moles of B2H6 can be prepared.

Q.16

Carbon reacts with chlorine to form CCl4. 36 gm of carbon was mixed with 142 gm of Cl2. Calculate mass of CCl4 produced and the remaining mass of reactant.

Q.17

Sulphuric acid is produced when sulphur dioxide reacts with oxygen and water in the presence of a catalyst : 2SO2(g) + O2 (g) + 2 H2O(l) 2 H2SO4 . If 5.6 mol of SO2 reacts with 4.8 mol of O2 and a large excess of water, what is the maximum number of moles of H2SO4 that can be obtained ?

Q.18

Potassium superoxide, KO2, is used in rebreathing gas masks to generate oxygen : KO2(s) + H2O(l)  KOH (s) + O2 (g) If a reaction vessel contains 0.158 mol KO2 and 0.10 mol H2O, how many moles of O2 can be produced?

Q.19

PROBLEMS RELATED WITH MIXTURE 39 gm of an alloy of aluminium and magnesium when heated with excess of dil. HCl forms magnesium chloride, aluminium chloride and hydrogen. The evolved hydrogen collected at 0°C has a volume of 44.8 litres at 1 atm pressure. Calculate the composition of the aluminium by moles.

Q.20

A sample containing only CaCO3 and MgCO3 is ignited to CaO and MgO. The mixture of oxides produced weight exactly half as much as the original sample. Calculate the mass percentages of CaCO3 and MgCO3 in the sample.

Q.21

Determine the percentage composition of a mixture (by mass) of anhydrous sodium carbonate and sodium bicarbonate from the following data: wt. of the mixture taken = 2 gm Loss in weight on heating = 0.124 gm.

Q.22

A sample of mixture of CaCl2 and NaCl weighing 5.55 gm was treated to precipitate all the Ca as CaCO3 which was then heated and quantitatively converted to 1.68 gm of CaO. Calculate the mass percentage of CaCl2 in the mixture.

Q.23

When 4 gm of a mixture of NaHCO3 and NaCl is heated, 0.66 gm CO2 gas is evolved. Determine the percentage composition of the original mixture by mass.

Application of Mole Concept

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Q.24

PERCENTAGE YIELD AND PERCENTAGE PURITY A power company burns approximately 475 tons of coal per day to produce electricity. If the sulphur content of the coal is 1.2 % by weight, how many tons SO2 are dumped into the atmosphere each day?

Q.25

Calculate the percent loss in weight after complete decomposition of a pure sample of potassium chlorate. KClO3(s)  KCl(s) + O2(g)

Q.26

A sample of calcium carbonate is 80% pure, 25 gm of this sample is treated with excess of HCl.How much volume of CO2 will be obtained at 1 atm & 273 K?

Q.27

Cyclohexanol is dehydrated to cyclohexene on heating with conc. H2SO4. If the yield of this reaction is 75%, how much cyclohexene will be obtained from 100 gm of cyclohexanol ? H 2SO 4 C6H12O con .   C6H10

Q.28

Q.29

How many grams of 80% pure Na2SO4 can be produced from 130 gm of 90% pure NaCl ? SEQUENTIAL REACTIONS Sulphur trioxide may be prepared by the following two reactions : S8 + 8O2(g)  8SO2(g) 2SO2(g) + O2(g)  2SO3(g) How many grams of SO3 will be produced from 1 mol of S8?

Q.30

2PbS + 3O2  2PbO + 2SO2 3SO2 + 2HNO3 + 2H2O  3H2SO4 + 2NO According to the above sequence of reactions, how much H2SO4 will 1200 gm of PbS produce? (Pb = 208)

Q.31

Potassium superoxide, KO2, is utilised in closed system breathing apparatus. Exhaled air contains CO2 and H2O, both of which are removed and the removal of water generates oxygen for breathing by the reaction 4KO2(s) + 2H2O(l)  3O2(g) + 4KOH(s) The potassium hydroxide removes CO2 from the apparatus by the reaction : KOH (s) + CO2 (g)  KHCO3(s) (a) What mass of KO2 generates 48 gm of oxygen ? (b) What mass of CO2 can be removed from the apparatus by 63.9 gm of KO2 ?

Q.32

Sodium chlorate, NaClO3, can be prepared by the following series of reactions: 2KMnO4 + 16 HCl  2 KCl + 2 MnCl2 + 8H2O + 5 Cl2 6Cl2 +6 Ca(OH)2  Ca(ClO3)2 + 5 CaCl2 + 6H2O Ca(ClO3)2 + Na2SO4  CaSO4 + 2 NaClO3 What mass of NaClO3 can be prepared from 100 ml of concentrated HCl (density 1.28 gm/ml and 36.5% by mass)? Assume all other substances are present in excess amounts.

Application of Mole Concept

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Q.33

QUANTITATIVE ANALYSIS On complete combustion, 0.1 g of an organic compound gave 0.176g of carbon dioxide and 0.18 g of water. Determine the percentage composition of carbon and hydrogen in the compound.

Q.34

In Dumas. method for estimation of nitrogen, 0.3g of an organic compound gave 24.93 mL of nitrogen collected at 300K temperature and 775mm pressure.Calculate the percentage composition of nitrogen in the compound. (Aqueous tension at 300K=15 mm)

Q.35

During estimation of nitrogen present in an organic compound by Kjeldahl’s method, the ammonia evolved from 0.5 g of the compound in Kjeldahl’s estimation of nitrogen, neutralized 10 mL of 1 M H2SO4. Find out the percentage of nitrogen in the compound.

Q.36

In Carius method of estimation of halogen, 1 g of an organic compound gave 0.094 g of AgBr. Find out the percentage of bromine in the compound.

Q.37

In sulphur estimation, 0.64 g of an organic compound gave 0.466 g of barium sulphate. What is the percentage of sulphur in the compound?

Q.38

A sample of 0.50 g of an organic compound was treated according to Kjeldahl's method. The ammonia evolved was absorbed in 50 ml of 0.5 M H2SO4. The residual acid required 60 mL of 0.5 M solution of NaOH for neutralization. Find the percentage composition of nitrogen in the compound.

Q.39

MISCELLANEOUS PROBLEM P4S3 + 8O2  P4O10 + 3SO2 Calculate minimum mass of P4S3 is required to produce at least 0.96 gm of each product.

Q.40

By the reaction of carbon and oxygen, a mixture of CO and CO2 is obtained. What is the mass ratio of the mixture obtained when 20 grams of O2 reacts completely with 12 grams of carbon ?

Q.41

In a determination of P an aqueous solution of NaH2PO4 is treated with a mixture of ammonium and magnesium ions to precipitate magnesium ammonium phosphate Mg(NH4)PO4. 6H2O. This is heated and decomposed to magnesium pyrophosphate, Mg2P2O7 which is weighed. A solution of NaH2PO4 yielded 3.33 gm of Mg2P2O7. What weight of NaH2PO4 was present originally?

Q.42

Calculate the amount of H2SO4 produced (in gm) when 40 ml H2O (d = 0.9 gm/ml) reacts with 49.26 l SO3 at 1 atm. and 300 K, according to the following reaction ? H2O + SO3  H2SO4

Q.43

2.40 gm of the chloroplatinate of a mono acid base on ignition gave 0.8 gm of Pt. Calculate the mol. wt of the base. (Pt = 195)

Q.44

0.75 gm of an organic compound gave on complete combustion 1.6 gm of carbon dioxide and 0.47 gm of water. A given weight of the compound when heated with nitric acid and silver nitrate gave an equal weight of silver chloride. 0.75 gm of the compound gave 58.57 ml of nitrogen at1 atm and 273 K. Deduce the empirical formula of the compound?

Q.45

10 gm of an organic compound on complete combustion gives 17.6 gm CO2, 3.6 gm water and 6.4 gm SO2. Deduce the empirical formula of compound.

Q.46

An organic compound contains C, H and O. 0.3 gm of this compound on combustion yielded 0.44 gm CO2 and 0.18 gm of H2O. If the weight of 1 mole of compound is 60, find molecular formula.

Application of Mole Concept

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EXERCISE # II Q.1

Nitrogen (N), phosporus (P), and potassium (K) are the main nutrients in plant fertilizers. According to an industry convention, the numbers on the label refer to the mass % of N, P2O5, and K2O, in that order. Calculate the N : P : K ratio of a 28 : 14.2 : 4.7 fertilizer in terms of moles of each elements, and express it as x : y : 1.0.

Q.2

A mixture of Ferric oxide (Fe2O3) and Al is used as a solid rocket fuel which reacts to give Al2O3 and Fe. No other reactants and products are involved. On complete reaction of 1 mole of Fe2O3, 200 units of energy is released. (i) Write a balance reaction representing the above change. (ii) What should be the ratio of masses of Fe2O3 and Al taken so that maximum energy per unit mass of fuel is released. (iii) What would be energy released if 16 kg of Fe2O3 reacts with 2.7 kg of Al.

Q.3

In one process for waterproofing, a fabric is exposed to (CH3)2SiCl2 vapour. The vapour reacts with hydroxyl groups on the surface of the fabric or with traces of water to form the waterproofing film [(CH3)2SiO]n, by the reaction n(CH3)2SiCl2 + 2nOH–  2nCl– + nH2O + [(CH3)2SiO]n where n stands for a large integer. The waterproofing film is deposited on the fabric layer upon layer. Each layer is 6.0 Å thick [ the thickness of the (CH3)2SiO group]. How much (CH3)2 SiCl2 is needed to waterproof one side of a piece of fabric, 1.00 m by 3.70 m, with a film 300 layers thick ? The density of the film is 1.0 g/cm3. (Si = 28)

Q.4

A 10 g sample of a mixture of calcium chloride and sodium chloride is treated with Na2CO3 to precipitate

calcium as calcium carbonate. This CaCO3 is heated to convert all the calcium to CaO and the final mass of CaO is 1.12gm. Calculate % by mass of NaCl in the original mixture. Q.5

124 gm of mixture containing NaHCO3, AlCl3 & KNO3 requires 500 ml, 8% w/w NaOH solution [dNaOH = 1.8 gm/ml] for complete neutralisation. On heating same amount of mixture, it shows loss in weight of 18.6 gm. Calculate % composition of mixture by moles. Weak base formed doesn't interfere in reaction. Assume KNO3 does not decompose under given conditions. AlCl3 + 3NaOH  Al(OH)3 + 3NaCl NaHCO3 + NaOH  Na2CO3 + CO2 + H2O

Q.6

If the yield of chloroform obtainable from acetone and bleaching powder is 58%. What is the weight of acetone required for producing 47.8 gm of chloroform ? 2CH3COCH3 + 6CaOCl2  Ca(CH3COO)2 + 2CHCl3 + 3CaCl2 + 2Ca(OH)2

Q.7

Chloride samples are prepared for analysis by using NaCl, KCl and NH4Cl separately or as mixture. What minimum volume of 5 % by weight AgNO3 solution(sp.gr, 1.02 g ml–1) must be added to a sample of 0.321 gm in order to ensure complete precipitation of chloride in every possible case?

Q.8

A mixture of nitrogen and hydrogen, in the ratio of one mole of nitrogen to three moles of hydrogen, was partially converted into NH3 so that the final product was a mixture of all these three gases. The mixture was to have a density of 0.46 g per litre at 27°C and 1.00 atm. What would be the mass of gas in 22.4 litres at 1 atm and 273 K? Calculate the % composition of this gaseous mixture, by volume.

Application of Mole Concept

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Q.9

In order to determine the composition of a mixture of halides containing MBr2 & NaI, 14 gm mixture was dissolved in water. To this solution AgNO3 solution of certain molarity was added gradually. The mass of precipitate produced (in gm) were measured and it was plotted against volume of AgNO3 solution added (in ml). If it known that AgI is precipitated first. Precipitation of Br– does not start until the already precipitating I– precipitates completely. Find out the value of ABCD where : AB = Atomic weight of metal 'M' CD = Mole percent of NaI in original mixture. 24.44 Total Mass of ppt. formed 9.4 (in gm) 40

120

Vol.of AgNO3 added (in ml)

Q.10

Equal weights of mercury and iodine are allowed to react completely to form a mixture of mercurous and mercuric iodide leaving none of the reactants. Calculate the ratio by mole of Hg2I2 and HgI2 formed (Hg = 200 , I = 127)

Q.11

Two substance P4 & O2 are allowed to react completely to form mixture of P4O6 & P4O10 leaving none of the reactants. Using this information calculate the composition of final mixture when mentioned amount of P4 & O2 are taken. P4 + 3O2  P4O6 P4 + 5O2  P4O10 (i) If 1 mole P4 & 4 mole of O2 (ii) If 3 mole P4 & 11 mole of O2 (iii) If 3 mole P4 & 13 mole of O2

Q.12

The chief ore of Zn is the sulphide, ZnS. The ore is concentrated by froth floatation process and then heated in air to convert ZnS to ZnO. % 2ZnS + 3O2 75    2ZnO + 2SO2 % ZnO + H2SO4 100   ZnSO4 + H2O

(a) (b) Q.13

% 2ZnSO4 + 2H2O 80    2Zn + 2H2SO4 + O2 What mass of Zn will be obtained from a sample of ore containing 292.2 kg of ZnS. Calculate the volume of O2 produced at 1 atm & 273 K, along with zinc. (Zn = 65.4)

4.9 gm sample of KClO3 was heated under such conditions that a part of it decomposed according to the equation (1) 2KClO3  2 KCl + 3O2 and remaining underwent change according to the equation. (2) 4KClO3  3 KClO4 + KCl If the amount of O2 evolved was 672 ml at 1 atm and 273 K., calculate the % by weight of KClO4 in the residue.

Application of Mole Concept

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Q.14

For a hypothetical chemical reaction represented by 3A(g)  C(g) + D(g) , the following informations are known. Information (i) At t = 0, only 1 mole of A is present and the gas has V.D. = 60. (ii) At t =30 min, the gaseous mixture consist of all three gases and has a vapour density = 75. (iii) Molecular Mass of C = 200 Calculate (a) Molecular weight of A and D. (b) Moles of each specie at t = 30 min.

Q.15

Consider the following set of reactions

(

)n

If 0.1 moles of silver salt is taken & wt. of residue obtained is 54 gms then what will be the molecular mass of CH 3 —  CH  — CH 3 |   Br   n Q.16

The molecular mass of an organic acid was determined by the study of its barium salt. The barium salt contains two moles of water of hydration per Ba+2 ion. 2.562 g of this salt reacts completely with 30 ml of 0.2 M H2SO4 to produce BaSO4 and the acid. The acid is mono basic. What is molecular mass of anhydrous acid ? 'x' M solution represent that there is 'x' mole of solute per litre of solution (Atomic mass of Ba = 137)

Application of Mole Concept

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EXERCISE # III Fill in the blank: Q.1 For the reaction, 2X + 3Y + 4Z  5W Initially if 1 mole of X, 3 mole of Y and 4 mole of Z is taken. If 1.25 mole of W is obtained then % yield of this reaction is _______. Q.2

The vapour density of a mixture of gas A (Molecular mass = 40) and gas B (Molecular mass = 80) is 25. Then mole % of gas B in the mixture would be ________.

Q.3

For the reaction 2A + 3B + 5C  3D Initially if 2 mole of A, 4 mole of B and 6 mole of C is taken. With 25% yield, moles of D which can be produced are _________.

Single Correct: Q.4 3.64 gram of the silver salt of an organic dibasic acid yields, on strong heating, 2.16 gm of silver. If the weight percentage of carbon in it 8 times the weight percentage of hydrogen and one-half the weight percentage of oxygen, determine the molecular formula of the acid. [Atomic weight of Ag = 108] (A) C4H6O4 (B) C4H6O6 (C) C2H6O2 (D) C5H10O5 Q.5

Maximum mass of sucrose C12H22O11 produced by mixing 84 gm of carbon, 12 gm of hydrogen and 56 lit. O2 at 1 atm & 273 K according to given reaction, is C(s) + H2(g) + O2 (g)  C12H22O11(s) (A) 138.5 (B) 155.5 (C) 172.5 (D) 199.5

Q.6

40 gm of a carbonate of an alkali metal or alkaline earth metal containing some inert impurities was

made to react with excess HCl solution. The liberated CO2 occupied 12.315 lit. at 1 atm & 300 K. The correct option is (A) Mass of impurity is 1 gm and metal is Be (B) Mass of impurity is 3 gm and metal is Li (C) Mass of impurity is 6 gm and metal is Li (D) Mass of impurity is 2 gm and metal is Mg Q.7

The percentage by mole of NO2 in a mixture of NO2(g) and NO(g) having average molecular mass 34 is : (A) 25% (B) 20% (C) 40% (D) 75%

Q.8

The minimum mass of mixture of A2 and B4 required to produce at least 1 kg of each product is : (Given At. mass of 'A' = 10 ; At. mass of 'B' = 120)

 2AB2 + 4A2B 5A2 + 2B4  (A) 2120 gm (B) 1060 gm

(C) 560 gm

(D) 1660 gm

Q.9

74 gm of a compoud on complete combustion gives 132 gm CO2 and 54 gm of H2O. The molecular formula of the compound may be (A) C5H12 (B) C4H10O (C) C3H6O2 (D) C3H7O2

Q.10

An iodized salt contains 0.5 % of NaI by weight . A person consumes 3 gm of salt everyday. The number of iodide ions going into his body everyday is [Atomic weight I =127] (A) 10–4 (B) 6.02 ×10–4 (C) 6.02 × 1019 (D) 6.02 × 1023

Application of Mole Concept

[17]

Q.11

The mass of CO2 produced from 620 gm mixture of C2H4O2 & O2, prepared to produce maximum energy is (Combustion reaction is exothermic) (A) 413.33 gm (B) 593.04 gm (C) 440 gm (D) 320 gm

Q.12

In the quantitative determination of nitrogen, N2 gas liberated from 0.42 gm of a sample of organic compound was collected over water. If the volume of N2 gas collected was

100 ml at total pressure 11

860 mm Hg at 250 K, % by mass of nitrogen in the organic compound is [Aq. tension at 250 K is 24 mm Hg and R = 0.08 L atm mol–1 K–1 ] (A)

10 % 3

(B)

5 % 3

(C)

20 % 3

(D)

100 % 3

Q.13

The mass of P4O10 produced if 440 gm of P4S3 is mixed with 384 gm of O2 is P4S3 + O2  P4O10 + SO2 (A) 568 gm (B) 426 gm (C) 284 gm (D) 396 gm

Q.14

Calculate percentage change in Mavg of the mixture, if PCl5 undergo 50% decomposition. PCl5  PCl3 + Cl2 (A) 50% (B) 66.66 % (C) 33.33 % (D) Zero

Q.15

The mass of Mg3N2 produced if 48 gm of Mg metal is reacted with 34 gm NH3 gas is Mg + NH3  Mg3N2 + H2 (A)

200 3

(B)

100 3

(C)

400 3

(D)

150 3

Q.16

The number of carbon atoms present in a signature, if a signature written by carbon pencil weights 1.2 × 10–3 gm is (A) 12.04 × 1020 (B) 6.02 × 1019 (C) 3.01 × 1019 (D) 6.02 × 1020

Q.17

The average atomic mass of a mixture containing 79 mole % of 24Mg and remaining 21 mole % of 25Mg and 26Mg , is 24.31. % mole of 26Mg is (A) 5 (B) 20 (C) 10 (D) 15

Q.18

Air contains 20% oxygen by volume, calculate the theoretical volume of air which will be required for burning 200 m3 of acetylene gas completely. All volumes are measured under the same conditions of temperature and pressure. (A) 2500 m3 (B) 500 m3 (C) 2000 m3 (D) 3000 m3

Q.19

All alloy of iron (54.7%), nickel (45%) and manganese (0.3%) has a density of 8.17 g/cm3. How many iron atoms are there in a block of alloy measuring 10 cm × 20 cm × 15 cm? (A) 2.201 × 1026 (B)1.442 × 1026 (C) 8.41 × 1025 (D) 6.19 × 1026

Q.20

Aspartame, an artificial sweetener contains 9.52 wt. % nitrogen. There are two nitrogen atoms per molecule. What is the molecular weight of aspartame? (A) 147 (B) 294 (C) 588 (D) 266

Application of Mole Concept

[18]

Q.21

The specific gravity of the stainless steel spherical balls used in ball-bearings are 10.2. How many iron atoms are present in each ball of diameter 1 cm if the balls contain 84% iron, by mass ? The atomic mass of iron is 56. (A) 4.12 × 1021 (B) 4.82 × 1022 (C) 3.82 × 1022 (D) None of these

Q.22

An organic compound contains 8 % Oxygen and 4 % Sulphur by mass. Find the minimum possible molecular weight of compound? (A) 400 (B) 200 (C) 800 (D) 1600

Assertion Reason: Q.23 Statement -1 : 2A + 3B  C 4/3 moles of 'C' are always produced when 3 moles of 'A' & 4 moles of 'B' are added. Statement -2 : 'B' is the liming reactant for the given data. (A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1. (B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (C) Statement-1 is false, statement-2 is true. (D) Statement-1 is true, statement-2 is false. More than one correct: Q.24 For the following reactions 40%  Na2SO4 + H2O + NH3 (NH4)2SO4 + NaOH 

Yield = 40%

80%  NH4Cl NH3 + HCl  Yield = 80% Choose correct option(s). [Assuming all other reactants required are in sufficient amount] (A) Produced mass of NH4Cl is 2.71 gm if 4 gm of NaOH is taken (B) 41.25 gm (NH4)2SO4 is required to produce 10.7 gm NH4Cl (C) 25 gm of NaOH is required to produce 10.7 gm NH4Cl (D) Produced moles of NH4Cl (in IInd reaction) are 1.6 times of produced moles of Na2SO4 (in Ist reaction.) if 4 gm of NaOH is taken

Match the column: Q.25 One type of artifical diamond (commonly called YAG for yttrium aluminium garnet) can be represented by the formula Y3Al5O12.[Y = 89, Al =27] Column I Column II Element Weight percentage (A) Y (P) 22.73% (B) Al (Q) 32.32% (C) O (R) 44.95% Q.26

The recommended daily dose is 17.6 milligrams of vitamin C (ascorbic acid) having formula C6H8O6. Match the following. Given : NA = 6 × 1023 Column I Column II (A) O-atoms present (P) 10–4 mole (B) Moles of vitamin C in 1 gm of vitamin C (Q) 5.68 × 10–3 (C) Moles of vitamin C in recommended daily dose (R) 3.6 × 1020

Application of Mole Concept

[19]

Q.27

Br2 reacts with O2 in either of the following ways depending upon supply of O2. Br2 +

1 O  Br2O 2 2

3 O  Br2O3 2 2 Match composition of the final mixture for initial amount of reactants. Column I Column II (Initial reactants) (Final product) (A) 320 gm Br2 is mixed with 64 gm of O2 (P) 1 mole Br2O3

Br2 +

(B)

160 gm Br2 is mixed with 8 gm of O2

(Q)

(C)

80 gm Br2 is mixed with 32 gm O2

(R)

(D)

160 gm Br2 is mixed with 48 gm O2

(S)

1 1 mole (Br2O), mole (Br2) 2 2 1 mole (Br2O), 1 mole (Br2O3)

1 1 mole (Br2O3) , mole (O2) 2 4

Comprehension:

Q.28

Paragraph for question nos. 28 to 30 24 gm pure sample of magnesium is burned in air to form magnesium oxide and magnesium nitride. When products are treated with excess of H2O, 3.4 gm of gaseous NH3 is generated according to given reactions. Mg + O2  MgO Mg + N2  Mg3N2 Mg3N2 + 6H2O  3Mg (OH)2 + 2NH3 Calculate the amount of magnesium oxide (in gm) in products. (A) 28 (B) 20 (C) 16.8 (D) 32

Q.29

Calculate the amount of Mg(OH)2 (in gm) produced in above reaction. (A) 11.6 (B) 17.4 (C) 23.2 (D) 15.8

Q.30

Calculate the mass % of Mg converted into Mg3N2. (A) 20 (B) 30 (C) 35

Q.31

(D) 40

Paragraph for question nos. 31 to 33 NaBr, used to produce AgBr for use in photography can be self prepared as follows : Fe + Br2  FeBr2 ....(i) FeBr2 + Br2  Fe3Br8 ....(ii) (not balanced) Fe3Br8 + Na2CO3  NaBr + CO2 + Fe3O4 ....(iii) (not balanced) Mass of iron required to produce 2.06 × 103 kg NaBr [Atomic weigth Br = 80, Fe = 56 ] (A) 420 gm (B) 420 kg (C) 4.2 × 105 kg (D) 4.2 × 108 gm

Q.32

If the yield of (ii) is 60% & (iii) reaction is 70% then mass of iron required to produce 2.06 × 103 kg NaBr (A) 105 kg (B) 105 gm (C) 103 kg (D) None

Q.33

If yield of (iii) reaction is 90% then mole of CO2 formed when 2.06 × 103 gm NaBr is formed (A) 20 (B) 10 (C) 40 (D) None

Application of Mole Concept

[20]

Q.34

Q.35

Q.36

Q.37

Paragraph for question nos. 34 to 36 Water is added to 3.52 grams of UF6. The products are 3.08 grams of a solid [containing only U, O and F] and 0.8 gram of a gas only. The gas [containing fluorine and hydrogen only], contains 95 % by mass fluorine. [Assume that the empirical formula is same as molecular formula.] (U = 238, F = 19) The empirical formula of the gas is (A) HF2 (B) H2F (C) HF (D) HF3 The empirical formula of the solid product is (A) UF2O2 (B) UFO2

(C) UF2O

(D) UFO

The percentage of fluorine of the original compound which is converted into gaseous compound is (A) 66.66 % (B) 33.33 % (C) 50 % (D) 89.9 % Paragraph for question nos. 37 to 39 An organic compound contains 69.4 % C, 5.8 % H. A sample of 0.303 g of this compound is analysed for nitrogen by Kieldahl's method. The ammonia evolved was absorbed in 50 mL of 0.05 M H2SO4. The excess acid required 25 mL of 0.1 M NaOH for neutralization. Molecular weight of organic compound is 121. What is percentage of 'N' in the compound? (A) 7.4 % (B) 11.55% (C) 19.4 % (D) 21.6 %

Q.38

Number of hydrogen atoms in the molecular formula of the compound? (A) 7 (B) 10 (C) 5 (D) 12

Q.39

0.303 g of the organic compound, in Duma's method on combustion gave 32.27 mL of moist nitrogen at 27°C and at P mm Hg pressure. If the vapour pressure at 27°C is 21 mm of Hg. Find the value of 'P'? (A) 725 mm (B) 746 mm (C) 710 mm (D) 760 mm Paragraph for question nos. 40 to 41 1.0 g of an alloy of Al and Mg when treated with excess of dil HCl forms MgCl2, AlCl3 and hydrogen. The evolved hydrogen, collected over Hg at 0°C has a volume of 1.218 litre at 0.92 atm pressure. 3 H 2 2 Mg + HCl  MgCl2 + H2

Al + 3HCl  AlCl3 +

Q.40

Q.41

Weight percentage of Al in the mixture is: (A) 60% (B) 40%

(C) 55%

(D) 45%

Moles of MgCl2 produced will be? (A) 0.025 (B) 0.0167

(C) 0.0125

(D) 0.0114

Application of Mole Concept

[21]

EXERCISE # IV Q.1

An evacuated glass vessel weighs 50 gm when empty , 148.0 g when completely filled with liquid of density 0.98 gml1 and 50.5 g when filled with an ideal gas at 760 mm at 300 K . Determine the molecular weight of the gas. [JEE '98,3]

Q.2

A plant virus is found to consist of uniform cylindrical particles of 150 Å in diameter and 5000 Å long. The specific volume of the virus is 0.75 cm3 / g. If the virus is considered to be a sinlge particle, find its molar mass. [JEE 1999]

Q.3

At 100º C and 1 atmp , if the density of liquid water is 1.0 g cm 3 and that of water vapour is 0.0006 g cm 3 , then the volume occupied by water molecules in 1 L of steam at that temperature is : (A) 6 cm3 (B) 60 cm3 (C) 0.6 cm3 (D) 0.06 cm3 [JEE '2001 (Scr), 1]

Q.4

How many moles of e— weigh one Kg (A) 6.023 ×1023

(B)

1 ×1031 9.108

[JEE'2002 (Scr), 1] (C)

6.023 × 1054 9.108

(D)

1 × 108 9.108  6.023

Q.5

Calculate the amount of Calcium oxide required when it reacts with 852 gm of P4O10. [JEE 2005] 6CaO + P4O10  2Ca3(PO4)2

Q.6

20% surface sites have adsorbed N2. On heating N2 gas evolved from sites and were collected at 0.001 atm and 298 K in a container of volume is 2.46 cm3. Density of surface sites is 6.023×1014/cm2 and surface area is 1000 cm2, find out the no. of surface sites occupied per molecule of N2. [JEE 2005]

Q.7

Silver (atomic weight = 108 g mol–1) has a density of 10.5 g cm–3. The number of silver atoms on a surface of area 10–12 m2 can be expressed in scientific notation as y × 10x. The value of x is [JEE 2010]

Q.8

A decapeptide (Mol. Wt. = 796) on complete hydrolysis gives glycine (Mol. Wt.= 75), alanine and phenylalanine. Glycine contributes 47.0 % to the total weight of the hydrolysed products. The number of glycine units present in the decapeptide is [JEE 2011] [Given : Decapeptide consumes nine molecules of H2O for hydrolysis]

Application of Mole Concept

[22]

ANSWER KEY EXERCISE # I 1 3

Q.2

1.2 × 1023

2:5

Q.4

1.78

Q.5

70 ml

Q.6

6.023 × 1017

Q.9

116.8 gm

Q.10

27.6 gm

Q.11

3.6 ×1019

Q.12

51.723 litre

Q.13

58.8 gm

Q.14

9.5 gm

Q.15

0.25 mole

Q.16

w CCl = 154 gm ; w = 24 gm c 4

Q.17

5.6

Q.18

0.1185

Q.19

Al = 66.6%

Q.20

CaCO3 = 28.4%; MgCO3 = 71.6%

Q.21

NaHCO3 = 16.8 %; Na2CO3 = 83.2 %

Q.22

60%

Q.23

NaHCO3 = 63 % , NaCl = 37%

Q.24

11.4

Q.25

39.18%

Q.26

4.48 litre

Q.27

61.5 gm

Q.28

177.5 gm

Q.29

640.0 gm

Q.30

490 gm

Q.31

(a) 142 gm (b) 39.6 gm

Q.32

14.2 gm

Q.33

42 %, 20 %

Q.34

9.3 %

Q.35

56%

Q.36

4%

Q.37

10 %

Q.38

56%

Q.39

1.1 gm

Q.40

mco : m co 2 = 21 : 111

Q.41

3.6 gm

Q.42

196 gm

Q.43

87.5 g/mol

Q.44

C7H10NCl

Q.45

C4H4SO

Q.46

C 2H 4O 2

Q.1

M+

Q.3

EXERCISE # II Q.1

20 : 2 : 1

Q.2

(i) Fe2O3 + 2 Al  Al2O3 + 2Fe; (ii) 80 : 27; (iii)10,000 units

Q.3

1.161 gram

Q.5

AlCl3 = 33.33%; NaHCO3 = 50%; KNO3 = 16.67%

Q.6

40 gm

Q.8

11.33gm, N2 = 16.67 % H2 = 50%, NH3 = 33.33%

Q.9

4050

Q.4 Q.7 Q.10

%NaCl = 77.8% 20 ml 1 : 2.70

Application of Mole Concept

[23]

Q.12

(a) 117.72 kg ; (b) 20.16 × 103 lit.

Q.11

(i) 0.5 , 0.5 ; (ii) 2, 1 (iii) 1, 2

Q.13

52.72%

Q.14

(a) MA = 120, MD = 160; (b)nA = 0.4, nC= 0.2 , nD =0.2

Q.15

495

Q.16

128

EXERCISE # III Q.1

50%

Q.2

25%

Q.3

0.75

Q.4

B

Q.5

B

Q.6

A

Q.7

A

Q.8

A

Q.9

C

Q.10

C

Q.11

C

Q.12

A

Q.13

B

Q.14

C

Q.15

A

Q.16

B

Q.17

C

Q.18

A

Q.19

B

Q.20

B

Q.21

B

Q.22

C

Q.23

C

Q.24

BCD Q.25

(A) R, (B) P, (C) Q

Q.26

(A) R, (B) Q, (C) P

Q.27

(A) R, (B) Q , (C) S , (D) P

Q.28

A

Q.29

B

Q.30

B

Q.31

B

Q.32

C

Q.33

B

Q.34

C

Q.35

A

Q.36

A

Q.37

B

Q.38

A

Q.39

B

Q.40

A

Q.41

B

EXERCISE # IV Q.1

123 g/mol

Q.2

7.092 × 107 g

Q.3

C

Q.4

D

Q.5

1008 gm

Q.6

2

Q.7

7

Q.8

6

Application of Mole Concept

[24]