Preview A Problem Book in Chemistry for IIT JEE 1500 Selected Questions by Ranjeet Shahi (2020)

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Critical analysis of the situation is required whatever be format of the questions This book just gives emphasis on this, and it is hoped that it will give a boost to all the meritorious and hard-wroking students.

I shall like to thank Mr Yogesh Chand Jain, Chairman, Arihant Group,

for bringing the book in this nice form

The problems included in the book with their solutions, aim to give you the mastery required for solving the intricate problems asked in

the exams such as JEE

This work is the result of my teaching the JEE aspirants over the post decade and a half Often I have found that the students mess up with the chemical reactions given in the problem and get themselves entangled into them The reason is that they are not able to distinguish the relationships between the various chemical principles and concepts This book is an effort to make them master the fundamentals of Chemistry through problems-solving, and apply

them intelligently to arrive at a correct solution

Ranjeet Shahi

Suggestions for further improvement of the book are welcome.

PREFACE

22 Carboxylic Acids and Its Derivatives 193

M OLE C ONCEPT

P ROBLEM 1 A crystalline hydrated salt on being rendered anhydrous, loses 45.6% of its weight Thepercentage composition of anhydrous salt is: Al 10.5%= , K 15.1%= , S 24.8%= and O=49.6% Findthe empirical formula of the anhydrous and crystalline salt

P ROBLEM 2 How much quantity of zinc will have to be reacted with excess of dilute HCl solution toproduce sufficient hydrogen gas for completely reacting with the oxygen obtained by decomposing5.104 g of potassium chlorate?

P ROBLEM 3 A 1.85 g sample of mixture of CuCl2 and CuBr2 was dissolved in water and mixedthoroughly with 1.8 g portion of AgCl After reaction, the solid which now contain AgCl and AgBr wasfiltered, dried and weighed to be 2.052 g What was the % by weight of CuBr2in the mixture?

P ROBLEM 4 1.0 g of a sample containing NaCl, KCl and some inert impurity is dissolved in excess ofwater and treated with excess of AgNO3solution A 2.0 g precipitate of AgCl separate out Also sample

is 23% by mass in sodium Determine mass percentage of KCl in the sample

P ROBLEM 5 A one gram sample containing CaBr2, NaCl and some inert impurity was dissolved inenough water and treated with excess of aqueous silver nitrate solution where a mixed precipitate ofAgCl and AgBr weighing 1.94 g was obtained Precipitate was washed, dried and shaken with anaqueous solution of NaBr where all AgCl was converted into AgBr The new precipitate which containonly AgBr now weighed to be 2.4 g Determine mass percentage of CaBr2 and NaCl in the originalsample

P ROBLEM 6 Sulphur combines with oxygen to form two oxide SO2and SO3 If 10 g of S is mixed with

12 g of O2, what mass of SO2and SO3will be formed, so that neither S nor oxygen will be left at the end

of reaction?

P ROBLEM 7 An aqueous solution of ethanol has density 1.025 g/mL and it is 8.0 M Determine

molality m of this solution.

P ROBLEM 8 An aqueous solution of acetic acid has density 1.12 g/mL and it is 5.0 m Determine

molarity (M).

P ROBLEM 9 Octane is a component of gasoline Incomplete combustion of octane produces some COalong with CO2and H O2 , which reduces efficiency of engine In a certain test run, 1.0 gallon of octane isburned and total mass of CO, CO2 and H O2 produced was found to be 11.53 kg Calculate efficiency ofthe engine, density of octane is 2.65 kg/gallon

P ROBLEM 10 The formula of a hydrated salt of barium is BaCl2⋅xH O2 If 1.936 g of this compoundgives 1.846 g of anhydrous BaSO4 upon treatment with H SO2 4, calculate x.

P ROBLEM 11 A mixture of CuSO4⋅5H O2 and MgSO 7H O4⋅ 2 was heated until all the water wasdriven-off If 5.0 g of mixture gave 3 g of anhydrous salts, what was the percentage by mass ofCuSO 5H O4⋅ 2 in the original mixture?

P ROBLEM 12 A sample of clay contain 15% moisture, and rest are CaCO3and non-volatile SiO2 This

on heating loses part of its moisture, but CaCO3 is completely converted into CaO The partially dried

sample now contain 7.35% moisture and 51.5% SiO2 Determine mass percentage of CaCO3 in theoriginal sample.

P ROBLEM 13 Chlorine dioxide (ClO )2 , has been used as a disinfectant in air conditioning systems Itreacts with water according to the reaction:

ClO + H O2 2 → HClO + HCl3

In an experiment, a 10.0 L sealed flask containing ClO2 and some inert gas at 300 K and 1.0atmosphere pressure is opened in a bath containing excess of water and all ClO2is reacted quantitatively.The resulting solution required 200 mL 0.9 M NaOH solution for neutralization Determine molefraction of ClO2 in the flask

P ROBLEM 14 Potassium salt of benzoic acid (C H COOK)6 5 can be made by the action of potassiumpermanganate on toluene as follows:

C H CH + KMnO6 5 3 4 → C H COOK + MnO + KOH + H O6 5 2 2

If the yield of potassium benzoate can’t realistically be expected to be more than 71%, what is theminimum number of grams of toluene needed to achieve this yield while producing 11.5 g of

C H COOK6 5 ?

P ROBLEM 15 Manganese trifluoride can be prepared by the following reaction:

MnI ( ) + F ( )2 s 2 g → MnF3 +IF5What is minimum number of grams of F2 that must be used to react with 12.0 g of MnI2if overallyield of MnF3 is no more than 75%

P ROBLEM 16 A compound containing Ca, C, N and S was subjected to quantitative analysis andformula mass determination A 0.25 g of this compound was mixed with Na CO2 3to convert all Ca into0.16 g CaCO3 A 0.115 g sample of compound was carried through a series of reactions until all its S waschanged into SO42– and precipitated as 0.344 g of BaSO4 A 0.712 g sample was processed to liberate all

of its N as NH3and 0.155 g NH3 was obtained The formula mass was found to be 156 Determine theempirical and molecular formula of the compound

P ROBLEM 17 A 0.2 g sample, which is mixture of NaCl, NaBr and NaI was dissolved in water andexcess of AgNO3 was added The precipitate containing AgCl, AgBr and AgI was filtered, dried andweighed to be 0.412 g The solid was placed in water and treated with excess of NaBr, which convertedall AgCl into AgBr The precipitate was then weighed to be 0.4881 g It was then placed into water andtreated with excess of NaI, which converted all AgBr into AgI The precipitate was then weighed to be0.5868 g What was the percentage of NaCl, NaBr and NaI in the original mixture

P ROBLEM 18 A mixture of NaI and NaCl when heated with H SO2 4produced same weight of Na SO2 4

as that of original mixture Calculate mass percentage of NaI in the original mixture

P ROBLEM 19 Ammonia is manufactured by the reaction of N2 and H2 An equilibrium mixturecontains 5.0 g of each N2, H2 and NH3 Calculate mass of N2 and H2 present initially and maximumamount of NH3 that can be produced

P ROBLEM 20 Consider the following reactions:

XeF + F2 2 → XeF6and XeF +6 —( CH2—CH )2—n → —( CF2—CF )2—n + HF + XeF4

Determine mass of F ( )2 g required for preparation of 1.0 kg fluorinated polymer.

P ROBLEM 21 2.5 g of a sample containing Na CO ; NaHCO2 3 3 and some non-volatile impurity ongentle heating loses 12% of its weight Residue is dissolved in 100 mL water and its 10 mL portionrequired 15 mL 0.1 M aqueous solution of BaCl2 for complete precipitation of carbonates Determinemass percentage of Na CO2 3 in the original sample.

P ROBLEM 22 2.0 g of a sample containing NaCl, NaBr and some inert impurity is dissolved in enoughwater and treated with excess of AgNO3 solution A 3.0 g of precipitate was formed Precipitate onshaking with aqueous NaBr gain 0.76 g of weight Determine mass percentage of NaCl in the originalsample

P ROBLEM 23 Based on the following information, determine value of x and y:

P ROBLEM 24 An organic compound containing C, H, O, N and Cl was analyzed and 0.15 g of sample

on combustion produced 0.138 g of CO2and 0.0566 g of H O2 All the nitrogen in different 2.0 g sample

of compound was converted into NH3which was found to weigh 0.238 g Finally the chlorine in a 0.125

g sample of compound was converted to Cl– and by reacting with AgNO3, 0.251 g AgCl was obtained.Deduce the empirical formula of the starting organic compound

P ROBLEM 25 A 5.0 g sample of felspar containing Na O2 , K O2 and some inert impurity is dissolved indilute HCl solution and NaCl and KCl formed are separated by fractional crystallization Duringcrystallization some less soluble impurities also comes out Mass of NaCl, KCl and impurityaccompanying these salts was found to be 6.47 g Solid crystal was then re-dissolved and required 300

mL of 0.3 M AgNO3for complete precipitation of chlorides The precipitate thus, obtained was found tocontain 4.23% insoluble impurity Determine mass percentage of Na O2 and K O2 in the original sample

P ROBLEM 26 Potassium chlorate (KClO )4 is made in the following sequence of reactions:

Cl ( ) + KOH2 g → KCl + KClO + H O2

KClO → KCl + KClO3KClO3 → KClO + KCl4What mass of Cl2 is needed to produce 1.0 kg of KClO4?

P ROBLEM 27 Titanium oxide (TiO2) is heated in stream of hydrogen to give water and a new oxide

Ti Ox y If 1.598 g TiO2 produces 1.438 g Ti Ox y, what is the formula of new oxide

P ROBLEM 28 A solution of copper sulphate that contain 15% CuSO4by weight has a density of 1.169g/mL 25 mL portion of this solution was reacted with excess of ammonia solution to form a dark bluesolution When cooled, filtered and dried, 6.127 g of dark blue solid was obtained A 0.195g solid wasanalyzed for ammonia and required 30.63 mL of 0.1036 M HCl solution to reach the equivalence point

In a separate analysis, 0.200 g was heated at 110°C to drive off water, producing 0.185 g of anhydrousmaterial Deduce formula of the compound crystallized out from blue solution assuming that it containonly one copper atom per formula unit Also determine the percentage yield of crystallization process

P ROBLEM 29 0.1152 g of a compound containing carbon, hydrogen, nitrogen and oxygen are burned inoxygen The gases produced are treated further to convert nitrogen containing product into N2 Theresulting mixture of CO2, H O2 and N2 is passed through a CaCl2 drying tube, which gains 0.09912 g.The gas stream was then bubbled through water where the CO2forms H CO2 3 Titration of this solutionrequired 28.8 ml 0.3283 M NaOH solution to reach the phenolphthalein end point The excess O2 was

removed by reaction with copper metal and the N2was collected in a 225 mL measuring bulb where itexerted a pressure of 65.12 mm of Hg at 25°C In a separate analysis, the molar mass of this compoundwas found to be 146 g mol–1 Deduce molecular formula of the starting compound.

P ROBLEM 30 Pb(NO )3 2and KI reacts in aqueous solution to form an yellow precipitate of PbI2 Inone series of experiments, the masses of two reactants varied, but the total mass of the two was heldconstant at 5.0 g What maximum mass of PbI2 can be produced in the above experiment ?

P ROBLEM 31 An element X react with hydrogen leading to formation of a class of compounds that is analogous to hydrocarbons 5 g of X forms 5.628 g of a mixture of two compounds of X, XH4and X2H6

in the molar ratio of 2 : 1 Determine molar mass of X.

P ROBLEM 32 The mineral Argyrodite is a stoichiometric compound that contain silver, sulphur (– 2)

and an unknown element Y (+4 The mass-ratio of silver and Y in the compound is,)

m(Ag): ( )m Y =11.88

Y forms a reddish brown lower sulphide on heating the mineral in stream of H ( )2 g , in which Y is in

+2 state The residue are Ag S2 and H S2 To convert 10 g Argyrodite completely, 0.295 L of H ( )2 g

measured at 400K and 1.0 atmosphere is required Determine molar mass of Y and empirical formula of

mineral

P ROBLEM 33 Uranium is isolated from its ore by dissolving it as UO (NO )2 3 2 and separating it assolid UO (C O )2 2 4 ⋅xH O2 A 1.0 g sample of ore on treatment with nitric acid yielded 1.48 g UO (NO )2 3 2which on further treatment with 0.4 g Na C O2 2 4 yielded 1.23 g UO (C O ) H O2 2 4 ⋅x 2 Determine weight

percentage of uranium in the original sample and x.

P ROBLEM 34 When iodine was added to liquid chlorine in cold condition, orange crystal of acompound separate out The amount of chlorine in a sample of crystal was determined by precipitatingAgCl A 0.467 g sample of crystal gave 0.861 g of AgCl Deduce empirical formula of the crystal

P ROBLEM 35 Urea is manufactured on large scale by passing CO ( )2 g through ammonia solution

followed by crystallization CO2 for the above reaction is prepared by combustion of hydrocarbons Ifcombustion of 236 kg of a saturated hydrocarbon produces as much CO2 as required for production of

1000 kg of urea, deduce molecular formula of hydrocarbon

P ROBLEM 36 Sodium bicarbonate can be purified by dissolving it in hot water (at 60°C), filtering toremove insoluble impurities, cooling to 0°C to precipitate solid NaHCO3and the filtering to remove thesolid leaving soluble impurities in solution Some NaHCO3that remain in solution is not recovered Thesolubility of NaHCO3in water at 60°C is 164 g/L Its solubility in cold water at 0ºC is 69 g/L If a 250 gimpure sample of NaHCO3 was purified by this method by dissolving first in 250 mL water at 60°C andthen crystallizing NaHCO3 from 100 mL water at 0°C, 150 g NaHCO3 was recovered Determinepercentage purity of original sample

P ROBLEM 37 A 100 g solution was prepared by dissolving 46 g CuSO4⋅xH O2 in 54 g of water andmole fraction of CuSO4 in solution was found to be 0.05 Determine x.

P ROBLEM 38 An ore of iron contain FeS and non-volatile impurity Roasting of this ore converts allFeS into Fe O2 3 and a 4% loss in weight was observed Determine mass percentage of FeS in ore

P ROBLEM 39 Optical measurement is a very efficient method of determining molar mass of unknownmaterial In one experiment, 3.0 g of an unknown polymeric material was dissolved in 100 mL of CCl4and transmittance of this solution was found to be 72% Transmittance of a 0.001 M standard solution in

the same solvent, under identical experimental condition was 60% Determine molar mass of unknownpolymer.

P ROBLEM 40 A crystalline polymer molecule is uniform prismatic in shape with dimensions asshown below,

If density of this polymer is 1.2 g/cm3, determine molar mass

P ROBLEM 41 A mother cell disintegrate into sixty identical cells and each daughter cell furtherdisintegrate into 24 smaller cells The smallest cells are uniform cylindrical in shape with diameter of

120 Å and each cell is 6000 Å long Determine molar mass of the mother cell if density of the smallestcell is 1.12 g/cm3

P ROBLEM 42 A sample of rock taken for analysis weigh 1.0 g on air dried basis After drying for onehour at 110°C, the sample weigh 0.9437 g The calcium is precipitated as oxalate but weighed as CaSO4;that weigh 0.5g The magnesium is precipitated as MgNH PO4 4 which finally ignited to 0.5 g Mg P O2 2 7.Find the percentage of CaO and MgO on oven dried basis and percentage of them and H O2 on air driedbasis

P ROBLEM 43 A sample is a mixture of Mohr’s salt and (NH ) SO4 2 4 A 0.5 g sample on treatment withexcess of BaCl2 solution gave 0.75 g BaSO4 Determine percentage composition of the salt mixture.What weight of Fe O2 3 would be obtained if 0.2 g of the sample were ignited in air?

P ROBLEM 44 A chloride mixture is prepared by grinding together pure BaCl 2H O2⋅ 2 , KCl and NaCl.What is the smallest and largest volume of 0.15 M AgNO3 solution that may be used for completeprecipitation of chloride from a 0.3g sample of the mixture which may contain any one or all of theconstituents?

P ROBLEM 45 A 1.5 g sample containing oxalic acid and some inert impurity was dissolved in enoughwater and volume made up to 250 mL A 20 mL portion of this solution was then mixed with 30 mL of analkali solution The resulting solution was then treated with stoichiometric amount of CaCl2just neededfor precipitation of oxalate as CaC O2 4 Solution was filtered off and filtrate was finally titrated against0.1 M HCl solution 8.0 mL of acid was required to reach the equivalence point At last, the above neutralsolution was treated with excess of AgNO3solution and AgCl obtained was washed, dried and weighed

to be 0.4305 g Determine mass percentage of oxalic acid in the original sample

P ROBLEM 46 A 1.5 g sample containing P O2 3and some inert impurity was dissolved in enough waterand boiled gently where P O2 3disproportionated quantitatively into PH3 and H PO3 4 The solution was

100Å

300 Å

further boiled for some time to let-off all PH ( )3 g and finally cooled to room temperature and diluted to

100 mL A 10 mL portion of this solution was then mixed with 20 mL 0.3 M NaOH solution Excessalkali required 11.0 mL 0.05 M H SO2 4solution for back titration Determine mass percentage of P O2 3inthe original sample

P ROBLEM 47 2.5 g of a mixture containing CaCO , Ca(HCO )3 3 2 and NaCl was dissolved in 100 mLwater and its 10 mL portion required 10 mL 0.05 M H SO2 4 solution to reach the phenolphthalein endpoint An another 10 mL portion of the same stock solution required 32.35 mL of the same acid solution

to reach the methyl orange end point Determine mass percentage of CaCO3 and Ca(HCO )3 2 in theoriginal mixture

P ROBLEM 48 A solution contain both Na CO2 3 and NaHCO3 10 mL portion of this solution is mixedwith few drops of phenolphthalein indicator and titrated against 0.08 M H SO2 4solution 7.0 mL of acidwas required to reach the end point A 5.0 mL portion of this solution was then taken for further analysisand a few drops of methyl orange was added to it and finally titrated against same acid solution 3.53 mL

of acid was required to reach the end point Determine mass of Na CO2 3 and NaHCO3 per litre ofsolution Ignore volume change due to addition of indicator

P ROBLEM 49 A mixture was known to contain both KNO3 and K SO2 3 To 0.486 g of the mixture,dissolved in enough water to give 50 mL solution, was added 50 mL of 0.15 M HCl solution Thereaction mixture was heated to expel all SO2and then 25 mL of the reaction mixture was titrated with 0.1

M KOH The titration required 13.11 mL of the base Calculate mass percentage of K SO2 3 in themixture

P ROBLEM 50 An amino acid isolated from a piece of animal tissue was believed to be glycine A 0.05 gsample was treated in such a way that all nitrogen in it was converted into ammonia This ammonia wasadded to 50 mL of 0.05 M HCl solution The excess acid remaining in the solution required 30.57 mL0.06 M NaOH solution for complete neutralization What was the percentage by mass of nitrogen? Howdoes this mass compare with percentage mass of nitrogen calculated from glycine (H NCH COOH)2 2 ?

P ROBLEM 51 In a reaction, calcium orthophosphate on heating with magnesium produced calciumphosphide, magnesium metaphosphate, calcium oxide and oxygen gas Phosphide on hydrolysisproduces PH3gas The PH3gas is burnt completely to P O2 5 using air, which contains 21%, by volume

of oxygen Calculate the volume of air at STP required for combustion, if 2.4 g Mg was initially reactedwith calcium orthophosphate All volumes are measured at STP

P ROBLEM 52 9.3 g of a mixture containing Li CO , NaHCO , Na CO2 3 3 2 3on strong heating produced7.37 g of solid residue The residue is dissolved in 200 mL water

A 10 mL portion of this solution is mixed with 15 mL of a normal HCl solution The excess acidrequired 12 mL 0.5 N NaOH solution to reach the equivalence point Determine the mass percentage ofNaHCO3 and Na CO2 3 in the original mixture Li = 7, Na = 23

P ROBLEM 53 4.0 g of a monobasic, saturated carboxylic acid is dissolved in 100 mL water and its 10

mL portion required 8.0 mL 0.27 M NaOH to reach the equivalence point In an another experiment, 5.0

g of the same acid is burnt completely and CO2produced is absorbed completely in 500 mL of a 2.0 NNaOH solution A 10 mL portion of the resulting solution is treated with excess of BaCl2to precipitateall carbonate and finally titrated with 0.5 N H SO2 4solution Determine the volume of the acid solutionthat would be required to make this solution neutral

P ROBLEM 54 5.0 g of a mixture containing NaHCO3, NaCl and Na CO2 3is dissolved in 500 mL waterand its 10 mL portion required 12.4 mL 0.1 M HCl solution to reach the equivalence point In an another

experiment, 10 mL portion of the same stock solution is mixed with 10 mL 0.15 M NaOH solution.Excess NaOH required 12.6 mL 0.1 M HCl solution for back titration Determine the mass percentage ofeach component in the original mixture.

P ROBLEM 55 6.4 g of a pure monobasic organic acid is burnt completely in excess of oxygen and CO2evolved is absorbed completely in one litre of an aqueous solution of NaOH A 10 mL portion of thissolution required 14.5 mL of a normal HCl solution to reach the phenolphthalein end point An another

10 mL portion of the same solution required 18 mL of the same HCl solution to reach the methyl orangeend point If the organic acid contains 25% oxygen by weight, deduce the empirical formula of this acidand strength of original NaOH solution

P ROBLEM 56 A complex of cobalt with ammonia is analyzed for determining its formula, by titrating itagainst a standardized acid as follows:

Co(NH ) Cl (3 3 ) + HCl NH (4+ ) + Co (3+ ) + Cl (– )

A 1.58 g complex required 23.63 mL 1.5 M HCl to reach the equivalence point Determine formula

If the reaction mixture at equivalence point is treated with excess of AgNO3solution, what mass of AgClwill precipitate out?

P ROBLEM 57 One litre solution of alkali is prepared by dissolving impure solid of alkali which contain5% Na CO2 3and 8% CaCO3and 10% NaCl A 10 mL portion of this solution required 9.8 mL of a 0.5 M

H SO2 4 solution for neutralization Calculate weight of alkali dissolved initially

P ROBLEM 58 40 g of a sample of caustic soda containing NaOH, Na CO2 3 and inert impurity isdissolved in water to prepare 1.0 litre solution A 25 mL portion of this solution required 23.15 mL 1.022

N HCl for complete neutralization To 25 mL another solution, excess of BaCl2 is added, and resultingsolution required 22.55 mL HCl of same strength to reach the end point Calculate mass percentage ofNaOH and Na CO2 3 in the original sample

P ROBLEM 59 1.5 g of a sample containing Na CO2 3 and NaHCO3is dissolved in 100 mL of water A

25 mL portion of this solution required 22.45 mL 0.202 N HCl using methyl orange as indicator In aseparate analysis, 25 mL portion of the same stock solution is mixed with 30 mL 0.204 N NaOH and thenexcess of BaCl2 is added resulting in precipitation of all carbonate as BaCO3 Filtrate required 9.98 mLHCl of same strength Calculate mass percentage of Na CO2 3and NaHCO3 in the mixture

P ROBLEM 60 One gram sample of a saturated hydrocarbon is burned completely and liberated CO2was absorbed in a 1.0 L 0.2 N NaOH solution To the resulting solution, excess of BaCl2 crystals wasadded and the solution was filtered off to free from BaCO3 A 10 mL portion of the extract required 12

mL 0.025 M H SO2 4 solution for neutralization Determine molecular formula of the hydrocarbon

P ROBLEM 61 2.0 g of a saturated, monobasic carboxylic acid was burned and liberated CO2was passedthrough a concentrated solution of NaOH The resulting solution was separated into two equal half andanalyzed One half required 71.72 mL 1.0 N HCl to reach the end point in presence of phenolphthaleinindicator The other half required 123.44 mL 1.0 N HCl to reach the end point in presence of methylorange indicator Deduce formula of acid and determine mass of NaOH present initially

P ROBLEM 62 2.5 g of a mixture containing NaHCO , Na CO3 2 3and NaCl is dissolved in 100 mL waterand its 50 mL portion required 13.33 mL 1.0 N HCl solution to reach the equivalence point On the otherhand its other 50 mL portion required 19 mL 0.25 M NaOH solution to reach the equivalence point.Determine mass percentage of each component

P ROBLEM 63 2.0 g of a crystal of CaCO3is dissolved in 50 mL water and then mixed with 50 mL of aHCl solution The resulting solution is boiled to remove all CO2and its 10 mL portion required 8.0 mL of

a NaOH solution to make the solution neutral Also 20 mL of original HCl solution is equivalent to 96

mL of NaOH solution Determine molarity of both NaOH and HCl solution

P ROBLEM 64 2.725 g of a mixture of K C O2 2 4, KHC O2 4 and H C O 2H O2 2 4⋅ 2 is dissolved in 100 mL

H O2 and its 10 mL portion is titrated with 0.1 N HCl solution

20 mL acid was required to reach the equivalence point In another experiment, 10 mL portion of thesame stock solution is titrated with 0.1 N KOH solution 20 mL of base was required to reach theequivalence point Determine mass percentage of each component in the mixture

P ROBLEM 65 A 1.0 g sample containing NH NO , (NH ) PO4 3 4 3 4 and some inert impurity wasdissolved in 100 mL water its 10 mL portion required 15 mL 0.1 M NaOH solution to reach theequivalence point In a separate experiment, 10 mL of the same stock solution was treated with excess ofBaCl2solution and 0.077 g of barium phosphate precipitate was obtained Determine mass percentage ofammonium nitrate in the original sample

P ROBLEM 66 10.38 mg of a diprotic acid (containing (C, H and O) is burned completely and all CO2was absorbed in 100 mL of alkali solution The resulting solution is separated into two-half and one-halfrequired 55 mL 0.005 M H SO2 4solution to reach the phenolphthalein end point Other half was titrated

in presence of methyl orange indicator and 80 mL H SO2 4 solution of same strength was required toreach the end point In a separate analysis, 0.168 g of the same acid required 16.18 mL 0.125 M NaOHsolution to reach the end point Deduce formula of the acid and determine molarity of alkali solution usedinitially

P ROBLEM 67 A 3.0 g sample containing Na CO , NaHCO , NaCl2 3 3 and some inert impurity wasdissolved in 100 mL of water and its 10 mL portion was titrated against 0.1 M HCl solution usingphenolphthalein indicator 11.32 mL of acid solution was required to reach the end point The resultingsolution was then mixed with excess of AgNO3 solution resulting in formation of 0.306 g of AgClprecipitate The solution was filtered-off and filtrate was again titrated, but now against 0.05 M NaOHsolution 42.64 mL of alkali was required to reach the end point Determine mass percentage of Na CO2 3,NaHCO3 and NaCl in the original sample

P ROBLEM 68 In neutralization titration of Na PO3 4, if phenolphthalein is used as indicator, end point isindicated only when Na PO3 4 is converted into Na HPO2 4 while, if methyl orange is used as indicator,end point appear only when Na PO3 4 is converted into H PO3 4 In an experiment a 4.0 g mixturecontaining Na PO , Na HPO3 4 2 4 and NaH PO2 4 is dissolved in 50 mL water and its 10 mL portionrequired 24.4 mL 0.1 M HCl solution to reach the end point using phenolphthalein indicator In aseparate analysis, 10 mL portion of the same stock solution required 23.572 mL 0.5 M HCl solution toreach the end point using methyl orange as indicator Determine mass percentage of all components inthe mixture

P ROBLEM 69 A mixture containing LiHCO , NaCl3 and Na CO2 3 on gentle heating loses 26.5% of itsweight 5.0 g of this mixture was heated gently and residue was dissolved in 100 mL water A 10 mLportion of this solution was then treated with 20 mL 0.2 M H SO2 4 solution A 10 mL portion of theresulting solution required 3.86 mL 0.1 M NaOH solution to reach the end point Determine masspercentage of each component in the mixture

P ROBLEM 70 A mixture containing LiHCO NaHCO3, 3 and CaCO3 on gentle heating loses 48.4% ofits weight In an experiment, 5.0 g of this mixture was dissolved in 100 mL water and its 10 mL portionwas treated with 10 mL 0.5 M NaOH solution The resulting solution was then treated with excess of

BaCl2 solution resulting in precipitation of all carbonates as BaCO3 Precipitate was separated out byfiltration and filtrate required 15.3 mL 0.1 N HCl solution to reach the end point Determine masspercentage of all components present in the mixture.

P ROBLEM 71 5.0 g of a mixture containing NaCl, NaHCO3, Na CO2 3 and CaCO3 on gentle heatingreduces to 4.25 g of solid residue In a separate experiment, 1.0 g of the same mixture required 10 mL 0.2

M NaOH to reach the end point In a 3rd experiment, 1.0 g of the same mixture was dissolved in 100 mLwater and required 10 mL 1.053 M HCl solution to reach the end point Determine mass percentage ofeach component in the mixture

P ROBLEM 72 2.0 g of a sample of CaCO3, NaHCO3 and some volatile, inert impurity, was heatedstrongly where CaCO3and NaHCO3, were decomposed into CaO and Na CO2 3respectively and all CO2gas produced in decomposition was absorbed in a 50 mL NaOH solution NaOH was little less than thestoichiometric requirement therefore, CO2 during reaction with NaOH, produced Na CO2 3 and someNaHCO3 The resulting solution was titrated first in presence of phenolphthalein indicator and 5.0 mL1.0 M HCl was required to reach the phenolphthalein end point Methyl orange was then added andtitration continued with HCl of same strength where 15 mL HCl was required to reach the final end point

On the other hand, the residue obtained after heating of the original sample was dissolved in waterand treated with excess of BaCl2, giving 0.985 g of BaCO3precipitate Determine mass percentage ofCaCO3and NaHCO3 in the original sample

P ROBLEM 73 A one gram sample containing NaOH as the only basic substance and some inertimpurity was left exposed to atmosphere for a very long time so that part of NaOH got converted into

Na CO2 3by absorbing CO2 from atmosphere The resulting sample was dissolved in water and volumemade upto 100 mL A 100 mL portion of this solution required 16 mL 0.25 M HCl solution to reach theequivalence point when methyl orange was used as indicator In a separate analysis, 20 mL portion of thesame solution was taken alongwith phenolphthalein indicator and mixed with 50 mL of 0.1 M HClsolution An additional 9.00 mL 0.1 M Ba(OH)2solution was required to just restore the pink colour ofsolution Determine mass percentage of NaOH in the original sample and mass percentage of Na CO2 3inthe sample after exposure to atmosphere

P ROBLEM 74 The monochloroacetic acid (ClCH COOH)2 preservative in a 100 mL of carbonatedbeverage was extracted by shaking with dimethyl ether and then returned to aqueous solution asClCH COO2 – by extraction with 1.0 M NaOH This solution was acidified and treated with 50 mL0.0452 M AgNO3 solution where the following reaction occurred:

ClCH COOH + AgNO2 3 +H O2 → HOCH COOH + H + NO + AgCl( )2 + 3– s

After filtering the AgCl, titration of filtrate required 10.43 mL of an NH SCN4 solution Titration of ablank taken through the entire procedure used 22.98 mL of same NH SCN4 solution Calculate weight in

mg, of ClCH COOH2 in the beverage sample

P ROBLEM 75 2.0 g of a sample containing sodium oxalate, oxalic acid dihydrate and some inertimpurity was dissolved in 100 mL water and its 20 mL portion required 23.34 mL 0.04 M acidifiedpermanganate solution to reach the equivalence point In a separate analysis, 20 mL portion of the samestock solution required 26.67 mL 0.1 N NaOH solution to reach the end point Determine masspercentage of Na C O2 2 4and H C O 2H O2 2 4⋅ 2 in the original sample

P ROBLEM 76 A 1.5 g sample containing (NH ) SO4 2 4, NH NO4 3 and some inert impurity wasdissolved in water and volume made upto 100 mL A 20 mL portion of this solution was mixed with 50

mL 0.1 M NaOH solution A 30 mL aliquot of this resulting solution required 9.00 mL 1/28 M H SO2 4solution for complete neutralization In a separate analysis, 32 mL of the original stock solution on

treatment with excess of BaCl2 solution produced 0.466 g BaSO4 precipitate Determine masspercentage of NH NO4 3and (NH ) SO4 2 4 in the original sample.

P ROBLEM 77 A 1.0 g impure sample containing [Zn(NH ) ]Cl4 4 2and some inert impurity was treatedwith 15 mL of 1 M NaOH solution where all complex is converted into Na [Zn(OH) ]2 4 The excess baserequired 10 mL1

6M HCl solution for back titration.

(a) Determine percentage purity

(b) If the last solution obtained after neutralization was treated with excess of AgNO3, what weight

of AgCl would have been produced?

P ROBLEM 78 1.2 g of a salt with their empirical formula K H C O )x y( 2 4 z was dissolved in 50 mL ofwater and its 10 mL portion required 11.00 mL of a 0.1 M HCl solution to reach the equivalence point In

a separate analysis, 15 mL of the stock solution required 20 mL 0.2475 M KOH to reach the equivalencepoint Determine empirical formula of the salt

P ROBLEM 79 Impure phosphoric acid for use in the manufacture of fertilizer is produced by thereaction of sulphuric acid on phosphate rock of which a principal component is Ca (PO )3 4 2and rest aresilica and other inert impurity In an analysis, 2.0 g of a sample of rock salt was dissolved in 100 mL

H SO2 4 solution Excess sulphuric acid left in 20 mL of this solution required 40 mL 0.02 M NaOH forback titration In a separate analysis 20 mL of the above solution required 50 mL 0.04 M NaOH forcomplete neutralization Determine mass percentage of Ca (PO )3 4 2in rock-sample

P ROBLEM 80 A 10 g sample of ammonium perchlorate containing some inert impurity was mixedwith 3 g Al powder where all perchlorate reacted to produce Al O , N , HCl2 3 2 and H O2 All HCl wasabsorbed in 100 mL 1 M NaOH solution Determine percentage purity of perchlorate sample and volume

of 0.5 M HCl required to neutralize the above solution

P ROBLEM 81 Potassium superoxide (KO )2 is utilized in closed system breathing apparatus to remove

CO2and water from exhaled air The removal of H O2 generate oxygen gas and KOH and this KOH in thesubsequent step remove CO2as KHCO3 5.0 kg of an impure sample of KO2is just sufficient to removeall CO2 and H O2 from a closed room of dimension 10 m 5 m 3m× × Determine mass of this KO2required to neutralize a 100 mL 0.1 M H SO2 4solution in a separate analysis Assume room conditions to

be at 1.0 atmosphere and 300 K and mole fraction of CO2 in that room is 0.01

P ROBLEM 82 3.25 g of a saturated, tribasic carboxylic acid required 68.4 mL of a 0.750 M NaOHsolution to reach the equivalence point Determine molecular formula of acid

P ROBLEM 83 A sample of chrome-vanadium steel weighing 2.0 g was dissolved in a mixture ofsulphuric acid and just sufficient oxidant was added to raise the oxidation state of iron to Fe3+, thechromium to Cr O2 72–, vanadium to VO3– and Mn to MnO4– The solution was then treated with HCl andresulting solution still containing Fe3+, Cr O2 72– and VO3– then treated with 25 mL of 0.101 M FeSO4.This resulted in reduction of dichromate and VO3– to Cr3+and VO2+ in the solution respectively Fe2+and VO2+ in the solution was then titrated with 0.02236 M KMnO4 and required 12.6 mL to reach the

equivalence point A small amount of Fe2+ was then added to again reduce the VO3– produced byKMnO4 back to VO2+and this then titrated directly with 0.02236 M KMnO4, a process requiring 0.86

mL to reach the equivalence point Calculate the following quantities:

(a) Moles of Fe2+ in 25 mL sample of standard FeSO4 solution

(b) Moles of Fe2+ titrated with 12.6 mL of standard KMnO4

(c) Moles of Fe2+ consumed by Cr O2 72–

(d) Percentage of V and Cr in the steel [Atomic weight of V=51,Cr=52]

P ROBLEM 84 A sample of crude uranium oxide is known to be contaminated with iron To determinethe extent of contamination, the crude oxide were dissolved and reduced with Zn to yield a solutioncontaining U4+and Fe2+ A 20 mL aliquot of this solution was treated with cupferron which precipitatedall uranium and the resulting precipitate on ignition yielded 423.3 mg of U O3 8 A further 20 mL samplewas treated with 0.024 M KMnO4 solution and consumed 27.23 mL Calculate mass percentage ofcontamination if the iron were present as Fe O2 3in a sample of crude oxide containing 100 g of U O3 8.KMnO4 solution oxidised Fe2+ to Fe3+ and U4+ to UO22+ Atomic mass of U=238

P ROBLEM 85 A 5.0 g sample containing Pb O , PbO3 4 2and some inert impurity is dissolved in 250 mLdil HNO3 solution and 2.7 g of Na C O2 2 4 was added so that all lead converted into Pb2+ A 10 mLportion of this solution required 8.0 mL 0.02 M KMnO4for titration of excess of oxalate In an anotherexperiment, 25 mL of solution was taken and excess oxalate was removed by extraction, this required 10

mL of a permanganate solution for oxidation of Pb2+ to Pb4+ 10 mL this permanganate solution isequivalent to 4.48 mL 5 V H O2 2solution Calculate mass percentage of PbO2and Pb O3 4in the originalsample

[Atomic mass of Pb=207]

P ROBLEM 86 An unknown cupric salt with formula Cu (CO ) (OH)x 3 y z is analyzed to determine theexact formula A 1.7225 g sample of salt was dissolved in 100 mL of pure water A 50 mL portion of thissolution required 10 mL 1.0 N H SO2 4 solution to reach the equivalence point if phenolphthalein wasused as indicator Another 50 mL portion was titrated using methyl orange as indicator and 15 mL acid ofsame strength was required Deduce the formula of the salt

P ROBLEM 87 Both CaCl2 and NaCl are used to melt ice and snow on roads in winter A certaincompany was marketing a mixture of these two compounds for this purpose A chemist, wishing toanalyze the mixture, dissolved 1 g of it in water and precipitated the calcium by adding sodium oxalate.The calcium oxalate was then carefully filtered, dissolved in dilute sulphuric acid, and titrated with 0.1

M KMnO4solution The titration required 22 mL of the KMnO4 solution Calculate freezing point of an

aqueous solution which is 5% (w/V) of the above mixture K f of water is 1.86 K kg mol–1

P ROBLEM 88 A 4.25 g sample containing CaC O , Na C O2 4 2 2 4and some inert impurity is heated gently

so that CaC O2 4 decomposed as:

CaC O2 4 → CaO + CO( ) + CO ( )g 2 g

All gaseous products were passed through a NaOH solution where following reaction occurredquantitatively:

2NaOH + CO ( )2 g → Na CO2 3

The resulting solution is separated into two equal part (by volume) and one part required 30 mL0.5 M HCl to reach the phenolphthalein end point while the other half solution required 50 mL 0.5 MHCl solution to reach the methyl orange end point In a separate experiment same mass of the samesample is dissolved into 100 mL dilute HCl solution and its 10 mL portion required 10 mL 0.1 M

K Cr O2 2 7 solution Determine the mass percentage of Na C O2 2 4in the original sample

P ROBLEM 89 In acidic solution, 45 mL KMnO4 solution is required to react with 50 mL 0.25 N

Na C O2 2 4solution How many mL of this same KMnO4solution would be required to oxidise 25 mL 0.1

N K C O2 2 4solution in alkaline medium where KMnO4 is reduced to MnO2

P ROBLEM 90 A sample weighing 0.3 g containing K [Fe(C O ) ] 3H O,3 2 4 3 ⋅ 2 FeCl 6H O3⋅ 2 and inertimpurity is dissolved in dilute sulphuric acid and volume made up to 100 mL A 20 mL portion of thissolution required 3.75 mL of 0.005 M acidified KMnO4 solution to reach the equivalence point In ananother experiment, 50 mL sample of the same stock solution is treated with Zn-amalgum and theresulting solution required 17.5 mL of permanganate solution of same strength Determine masspercentage of FeCl 6H O3⋅ 2 in the original sample

P ROBLEM 91 A 6.1 g sample containing oxalic acid dihydrate, sodium oxalate and NaHC O2 4 and isdissolved in 100 mL of water and its 10.0 mL portion required 16 mL 0.25 M HCl to reach theequivalence point In another experiment 10.0 mL portion of the same stock solution required 24 mL0.25 M NaOH to reach the equivalence point Determine the mass percentage of all components in theoriginal mixture

P ROBLEM 92 A 0.127 g of an unsaturated oil was treated with 25 mL of 0.1 M ICl solution Theunreacted ICl was then treated with excess of KI Liberated iodine required 40 mL 0.1 M hypo solution.Determine mass of I2 that would have been required with 100.0 g oil if I2 were used in place of ICl

P ROBLEM 93 Alkali metal nitrate on heating decomposes to metal nitrite and oxygen whereas alkalineearth metal on heating decomposes into metal oxide, NO2and oxygen In an experiment 15 g mixture ofNaNO3 and Mg(NO )3 2 was heated until no more gas were evolved The water soluble part of residuewas used for analysis and dissolved in 1.0 litre water 10 mL portion of this solution was reacted with 20

mL 0.02 M acidified KMnO4 solution The excess reagent required 10.00 mL 0.05 M oxalic acidsolution Determine mass percentage of each nitrate in the mixture Also determine the molar ratio ofoxygen to NO2 in the gaseous products given off

P ROBLEM 94 The mass percentage of MnO2 in a sample of mineral is determined by reacting with

As O2 3in acid solution A 0.225 g sample of mineral is ground and boiled with 75 mL 0.0125 M As O2 3solution After the reaction is complete, the solution is cooled and titrated with 2.28×10 3 M acidifiedKMnO4 solution 16.34 mL of the oxidizing agent solution was required to reach the end point.Determine mass percentage of MnO2in the sample

P ROBLEM 95 A driver is arrested and asked to pass “breath analyzer” test A sample consisting 56.5

mL of exhaled air is then bubbled into a spectrometer cell containing 3 mL 0.025% (w/V) K Cr O2 2 7

solution The transmittance of the solution was 41.5% initially and 43.4% after bubbling the samplethrough the reaction cell It is known that the alcohol content in blood stream is 2300 times higher than inexhaled air and that the legal limit is 80 mg of alcohol per 100 mL of blood Determine the concentration

of alcohol in the blood and state whether or not the driver should be charged with drunk driving

P ROBLEM 96 A sample of 0.3657 g powder containing only Ba(NO3 2) and Ca(NO3 2) are dissolved in

50 mL water Ammonia is added to the solution to raise the pH than an excess of Na C O2 2 4 is added toprecipitate the metals The precipitate is then filtered, washed with 1.0 L of water and transferred to abeaker containing 50 mL H O2 The solution is acidified to solublise the precipitate and finally titratedwith 0.05 M KMnO4solution A total of 13.94 mL of oxidizing agent solution was required to reach the

end point Find the composition of the initial mixture K sp. of BaC O = 1.5 102 4 × –8 and ofCaC O = 2.34 102 4 × –9

P ROBLEM 97 1.0 g sample containing KO2 and some inert impurity is dissolved in excess of aqueous

HI solution and finally diluted to 100 mL The solution is filtered off and 20 mL of filtrate required 15

mL 0.4 M Na S O2 2 3 solution to reduce the liberated iodine Determine mass % of KO2 in the originalsample

P ROBLEM 98 Cuprous ion is known to disproportionate quantitatively in acid medium A 3.0 g sample

of Cu O2 is dissolved in dilute H SO2 4 solution The solution is filtered off and 8.3 g pure KI crystal isadded to filtrate This caused precipitation of CuI with evolution of I2 The solution is filtered off andfiltrate is boiled till all I2 is expelled off Now, excess of an oxidizing agent is added to filtrate andliberated iodine required 10 mL 1.0 N Na S O2 2 3 solution Calculate mass percentage of Cu O2 in theoriginal sample

P ROBLEM 99 To a 10 mL 1.0 M aqueous solution of Br2, excess of NaOH is added so that all Br2disproportionated to Br– and BrO3– The resulting solution is freed from bromide ion by extraction andexcess of OH– neutralized by acidifying the solution The resulting solution is just sufficient to reactwith 1.5 g of an impure CaC O2 4sample Calculate percentage purity of oxalate sample

P ROBLEM 100 One gram of an impure sample of NaCl was dissolved in water and treated with excess

of AgNO3solution The precipitate AgCl thus, formed undergo decomposition into Ag and Cl ( )2 g and

latter disproportionate into chlorate (V) and chloride ions and chloride is re-precipitated due to presence

of excess of AgNO3 If the original precipitate was 60% decomposed and final precipitate weigh 1.5gram, determine mass percentage of NaCl in original sample

P ROBLEM 101 0.4 g of a sample containing CuCO3 and some inert impurity was dissolved in diutesulphuric acid and volume made up to 50 mL To this solution was added 50 mL 0.04 M KI solutionwhere copper precipitate as CuI and iodide ion is oxidized into I3– A 10 mL portion of this solution istaken for analysis, filtered, made free from I3– and treated with excess of acidic permanganate solution.Liberated iodine required 20 mL 2.5 m M sodium thiosulphate solution to reach the end point Determinemass percentage of CuCO3 in the original sample

P ROBLEM 102 One gram of an unknown sample of NaCN is dissolved in 50 mL 0.33 M alkalinesolution of KMnO4 and refluxed so that all cyanide is converted into cyanate (OCN–) The reactionmixture was cooled and its 5.0 mL portion was acidified by adding excess of sulphuric acid solution andfinally titrated with 19.0 mL 0.1 M FeSO4solution Determine mass percentage of NaCN in the originalsample

P ROBLEM 103 5.0 mL of a pure liquid toluene is dissolved in 100 mL of dilute alkaline KMnO4solution and refluxed so that all toluene is oxidized into benzoic acid and a dark brown precipitate ofMnO2is formed Solution is filtered off and filtrate and precipitate were analyzed separately Precipitate

was re-dissolved into 100 mL 1.0 M acidified solution of Na C O2 2 4and excess of oxalate required 50.73

mL 0.1 M acidic dichromate solution for back titration On the other hand 10.5 mL of filtrate wasacidified by adding excess of sulphuric acid and titrated with 0.1 M acidified solution of Na C O 2 2 4 A 38

mL of oxalate solution was required to reach the end point Determine density of liquid toluene andmolarity of original permanganate solution

P ROBLEM 104 A 2.0 g sample containing CaOCl2 and NaOCl is dissolved in 100 mL water and its 10

mL portion was titrated against 0.15 M acidified solution of Na C O2 2 4 10 mL of oxalate solution wasrequired to reach the end point Titrated solution was then treated with excess of aqueous solution ofAgNO3where all chloride precipitates as AgCl and weighed to be 0.287 g Determine mass percentage

of CaOCl2 and NaOCl in original sample

P ROBLEM 107 Calculate pressure exerted by 22.0 g of CO2in 0.5 L bulb at 300 K assuming it to be real

gas with a=363 kPaL mol2 –2and b=42.67 cc/mol

P ROBLEM 108 Molar volume of He at 10.1325 Mpa and 273 K is 0.011075 times its molar volume at

101.325 kPa Calculate radius of He atom assuming negligible ‘a’.

P ROBLEM 109 A gas mixture containing 5% by mass of butane and 95% by mass of Ar (40) is to beprepared by allowing gaseous butane to fill an evacuated 40 L cylinder at 1.0 atm and 27°C Calculatemass of Ar that gives the desired composition and total pressure of the final mixture

P ROBLEM 110 Cl O2 7 gas decomposes as:

Cl O2 7 → Cl2+O2

A partially decomposed gaseous mixture is allowed to effuse through a pin-hole and the gas comingout initially was analyzed The mole fraction of the O2 was found to be 0.60, determine the degree ofdissociation

P ROBLEM 111 Proportion of a lighter isotope in a gaseous mixture containing both heavier and lighterisotopes is increased by successive effusion of the gas mixture A sample of neon gas has

22Ne=90% and 20Ne=10% by moles In how many stages of successive effusion, 25% enrichment of

20Ne would be achieved?

P ROBLEM 112 The density of vapour of a substance at 1.0 atm and 500 K is 0.35 k/m3 The vapoureffuses through a small hole at a rate of 1.33 times faster than oxygen under similar condition.

(a) Determine (i) Molecular weight (ii) Molar volume (iii) Compression factor (Z) of the

vapour (iv) Which forces among the gas molecules are dominating, the attractive or repulsive?(b) If the vapour behaves ideally at 1000 K, determine the average translational kinetic energypossessed by a molecule

P ROBLEM 113 Using van der Waals’ equation of state, calculate the pressure correction factor for twomoles of a gas confined in a four litre flask that exert a pressure of 11 atmosphere at 300 K

P ROBLEM 116 In a spherical glass flask A of radius 1.0 m, containing 300 g H ( )2 g , there was a rubber

balloon B containing some N ( )2 g Inside B, there was another rubber balloon C containing some oxygen

gas At 27°C, it was found that the balloon B had radius 60 cm and of C was 30 cm Calculate the total

weight of the gas inside the flask Now 50 g H ( )2 g is further added to A, what would be the volume of B

and C.

P ROBLEM 117 A partially decomposed PCl ( )5 g along with its dissociation product is subjected to

diffusion study and the gases coming out initially collected in an another flask The rate of effusion ofcollected gaseous mixture was found to be 0.45 times rate of effusion of pure oxygen gas Determine thedegree of dissociation of PCl ( )5 g in the original sample.

P ROBLEM 118 One mole of a monoatomic gas confined in a 22.5 litre flask at 273 K exert a pressure of0.98 atm, whereas expected pressure was 1.0 atm has the gas behaved ideally Determine the van der

Waal’s constants ‘a’ and ‘b’ and Boyle’s temperature (T B)

P ROBLEM 119 One litre of a gas at 300 atm and 473 K is compressed to a pressure of 600 atm and 273

K The compressibility factors found to be 1.072 and 1.375 respectively at the initial and final states.Calculate the final volume

P ROBLEM 120 Calculate the van der Waal’s constants for ethylene T C =282 K,P C =50 atm

P ROBLEM 121 The second Virial coefficient of an imperfect gas is 2 10× –2 (L/mol)2 Calculate thevolume of a gm mole of the gas at 27°C and 5 atmosphere pressure

P ROBLEM 122 The van der Waal’s constant ‘b’ of a gas is 4.42 centilitre/mol How near can the centres

of the two molecules approach each other?

P ROBLEM 123 For carbon dioxide, critical density is 0.45 g/cc and its T C =300 K Determine its vander Waal’s constants

P ROBLEM 124 The Virial equation for ethane gas is given by PV =RT +BP At 0°C,

B=– 0.1814 L/mol Calculate volume of one mole of ethane at 10 atm, and ‘a’.

P ROBLEM 125 An unknown gas (X) at 2.0 atmosphere and Ar (40) at 1.0 atmosphere were injected simultaneously from the two ends of a 1.0 metre long glass tube and the first collision between X and Ar occurred at a distance of 38 cm from Ar-end.Determine the molar mass of X assuming that gases were

injected at same temperature and through the pin-hole of identical geometry

P ROBLEM 126 Using van der Waals’ equation of state, calculate pressure developed by 100 g of CO2contained in a volume of 5.0 litre at 40°C Also compare this value with that calculated using ideal gas

law and determine the percentage deviation from ideality a=3.6 atm L mol2 –2, b=44 cm mol3 –1

P ROBLEM 127 An equation of state for a non-ideal gas can be written as: PV m= +A BP+CP2; where

V m is the molar volume and P is the gas pressure in atmosphere B=–2.879 10× –2and C=14.98 10× 5

in litre atmosphere unit Under the experimental condition, determine the pressure at which PV-P curve

will attain minimum

P ROBLEM 128 A modified form of van der Waal’s equation of state for 1.0 mole of gas is given as:

B V

C V

P ROBLEM 129 Assuming that dry air contain 79% N2and 21% O2by volume, calculate the density ofmoist air at 25°C and 1.0 atmosphere when the relative humidity is 60% The vapour pressure of water at25°C is 23.76 mm of Hg

P ROBLEM 130 At what temperature, three moles of SO2will occupy 10 litre at a pressure of 15.0 atm if

it is a van der Waal’s gas with a=6.71 atm L mol2 –2and b=56.4 cm mol3 –1

P ROBLEM 131 Pressure of He gas confined in a steel chamber drops from 4.0 to 1.0 atmosphere in 4.0hours due to diffusion through a pin-hole in the steel chamber If an equimolar mixture of He andmethane gas at 20 atmosphere and the same temperature are confined in the same chamber, what will bethe partial pressure of He and methane after 1.0 hour Assume rate of diffusion to be linear function ofgas pressure and inverse function of square root of molar masses

P ROBLEM 132 One mole of a van der Waal’s gas at 0°C and 600 atmosphere occupies 0.075 L If

b=0.024 L mol–1, determine compressibility factor (Z) and predict the type of force dominating among

the gas molecule

P ROBLEM 133 A one litre flask containing NH ( )3 g at 2.0 atmosphere and 300 K is connected to

another 800 mL flask containing HCl(g) at 8.0 atmosphere and 300 K by means of a narrow tube of

negligible volume and gases were allowed to react quantitatively as:

NH ( ) + HCl( )3 g g → NH Cl( );4 s ∆H = – 43kJ/mol

If heat capacity of HCl(g) C V is 20JK mol–1 –1, determine final pressure inside the flask assumingnegligible heat capacity of flask and negligible volume of solid NH Cl4

P ROBLEM 134 A long cylindrical glass tube, equipped with a porous disc at the centre, containmethane gas at 5.0 atmosphere on one side and He gas at 2.0 atmosphere on the other side of the disc asshown in the diagram below:

Disc is permeable to both gases and rate of diffusion is directly proportional to the gas pressure andinversely proportional to square root of molar masses as:

–dp

dt k

P M

= where, k is a constant.

If k for the diffusion of methane gas is 2.5×10–2second–1, determine time after which pressure ofmethane chamber will drop to 4.0 atmospheres

P ROBLEM 135 At a given condition of temperature, rate of change of r.m.s of He gas is twice the rate

of change of absolute temperature Determine rms of He in the given condition

P ROBLEM 136 1.6 moles of ammonia gas at 300 K is taken in a 2.0 litre flask, sealed and heated to 500

K At this temperature, ammonia is partially decomposed into N2and H2and a pressure measurement atthis point gave 48.5 atmosphere Determine number of moles of each component present at 500 K

P ROBLEM 137 Decomposition of KClO3produces oxygen gas and KCl solid In a typical experiment,some KClO3 was decomposed and 36.00 mL oxygen gas was collected over water at 23°C Thelaboratory barometer reads 751 mm and vapour pressure of water at 23°C is 21.1 mm of Hg Find thevolume of the dry oxygen at 0°C and 1.0 atmosphere

P ROBLEM 138 A narrow tube of negligible volume connects two evacuated bulb of 1.0 litre capacityeach One bulb is placed in a 200 K thermostat bath and other in a 300 K thermostat bath and then 1.0mole of an ideal gas is injected into the system Find the pressure in the two flasks

P ROBLEM 139 Isothermal compressibility ( )κ of a gas is defined as:

Determine isothermal compressibility for an ideal gas at 1.0 atmosphere

P ROBLEM 140 What will be the temperature difference needed in a hot air balloon to lift 1.0 kg weight.Assume that the volume of balloon is100m , the temperature of atmosphere is 25°C and pressure is 1.03atmosphere Average molar mass of air is 29 amu

P ROBLEM 141 Using van der Waals’ equation of state, find pressure at which the PV vs P curve acquires minima for 1.0 mole of oxygen gas at 0°C a=1.36 L2 atm mol–2, and b=32 cm mol3 –1

P ROBLEM 142 The van der Waals’ constant ‘a’ is a correction factor to the ideal gas law for intermolecular force of attractions within the substance Match the following values of ‘a’ (

L atm mol2 –1): 0.2107, 5.464, 18.00 and 24.06 with gases benzene, toluene, Ne and steam

CH5.0 atm.4

He2.0 atm

P ROBLEM 143 The van der Waals’ constant ‘b’ is a correction factor to the ideal gas law for the intrinsic volume of the molecule Match the following values of ‘b’(L mol–1): 0.017, 0.0305, 0.1154 and0.1463, with the gases: toluene, benzene, Ne and steam.

P ROBLEM 144 The specific heat capacity of water is 4.18 J( C)° –1g–1 and that of copper is0.38 J( C)° –1g–1 Calculate the heat that must be supplied to a 500 g copper kettel containing 450 g ofwater to raise its temperature from 25°C to the boiling point of water What percentage of heat is used toraise the temperature of the water?

P ROBLEM 145 How much heat can be produced from a reaction mixture of 50 g of iron (III) oxide and

25 g of aluminium in the thermite reaction:

Fe O ( ) + 2Al( )2 3 s s → Al O ( ) + 2Fe( );2 3 s s ∆H = – 851.5 kJ/mol

P ROBLEM 146 Calculate the reaction enthalpy for the hydrogenation of ethyne to ethane, givenstandard enthalpy of combustion of ethyne, ethane and hydrogen; – 1300, – 1560 and – 286 kJ/molrespectively

P ROBLEM 147 Calculate the reaction enthalpy for the synthesis of HCl(g) from the following data:

P ROBLEM 149 Using reaction a, b and c determine the enthalpy change of this reaction:

CH ( ) +3

2O ( ) CO( ) + 2H O( )

(a) CH ( ) + 2O ( )4 g 2 g → CO ( ) + 2H O( )2 g 2 g ∆H° =– 802 kJ/mol(b) CH ( ) + CO ( )4 g 2 g → 2CO( ) + 2H ( )g 2 g ∆H°= + 206 kJ/mol(c) CH ( ) + H O( )4 g 2 g → CO( ) + 3H ( )g 2 g ∆H°= + 247 kJ/mol

P ROBLEM 150 The bond energy of H2( )g is 436 kJ/mol and that of N2( )g is 941.3 kJ/mol Calculate

the average bond energy of an N—H bond in ammonia if∆H° of ammonia is – 46 kJ/mol

P ROBLEM 151 The heat of formation of PCl3 and PH3 are 306 kJ/mol and 8 kJ/mol respectively, andthe heats of atomization of phosphorus, chlorine and hydrogen are 314, 121 and 216.5 kJ/molrespectively Calculate P-Cl and P-H bond energy.

P ROBLEM 152 At 25°C, the molar heat of formation of SO2 and H O2 are – 296.81 and – 285.83 kJrespectively Using the information from the following reactions,

2H S( ) + Fe( )2 g s → FeS + 2H ( )2 2 g ∆H° =– 137 kJ/mol

H S( ) + O ( )2 g 3 2 g H O( ) + SO ( )2 l 2 g

Calculate heat of formation of H S( )2 g and FeS2( )s at 25°C.

P ROBLEM 153 The standard molar enthalpy of formation of cyclohexane (l) and benzene (l) at 25°C

are – 156 and+49 kJ/mol respectively The standard enthalpy of hydrogenation of cyclohexene (l) at

25°C is – 119 kJ/mol Use this data to estimate the magnitude of the resonance energy of benzene

P ROBLEM 154 For the reaction cis-2-butene → trans-2-butene and cis-2-butene → 1-butene,

∆H =– 950 and+1771cal/mol respectively The heat of combustion of 1-butene is – 649.8 kcal/mol

Determine the heat of combustion of trans-2-butene Also calculate the bond energy of C==C bond in

trans-2-butene Given B.E ofC==O=196, O—H=110, O==O = 118, C—C=80 and C—H=98 kcal/molrespectively.∆H v(H O) 11 kcal / mol2 =

P ROBLEM 155 Using the data (all values are in kJ/mol at 25°C) given below:

(i) Enthalpy of polymerization of ethylene=– 72

(ii) Enthalpy of formation of benzene(l)=49

(iii) Enthalpy of vaporization of benzene(l)=30

(iv) Resonance energy of benzene(l)=– 152

(v) Heat of formation of gaseous atoms from the elements in their standard states H=218,C=715.Average bond energy of C—H=415 Calculate the B.E of C—C and C==C [ : A 331 and 590 kJ/mol]

P ROBLEM 156 Calculate energy of aromatization of cyclohexane according to the following reaction,both cyclohexane and benzene are in liquid state:

Given, bond energies: C—C =348, C—H =415, C==C=600, H—H=436 kJ/mol respectively,sublimation energy of C(gr) is 717 kJ/mol, resonance energy of C H ( ) = – 152 kJ/mol6 6 l , ∆H v° ofbenzene=30.8 and of cyclohexane is 33 kJ/mol

P ROBLEM 157 Enthalpy of polymerization of ethylene and acetylene into corresponding polymers are– 86 kJ/mol and – 148 kJ/mol respectively Enthalpy of hydrogenation of ethylene is – 132 kJ/mol,

determine C==C bond energy B.E of H2( )g is 436 kJ/mol and of C—H=415 kJ/mol

P ROBLEM 158 ∆HComb of methane and ethane are – 210 kcal/mol and – 368 kcal/mol respectively.Determine∆HComb of decane

P ROBLEM 159 Determine resonance energy of benzene [C H6 6( )l ] from the following information :

∆H°f of C H ( ) = + 49 kJ6 6 l ;

∆H°f of C H ( ) = + 75 kJ2 2 g ∆ °H v of C H ( ) = + 45 kJ6 6 l B.E. C≡≡ =C 930 kJ/mol; C==C 615 kJ/mol; C=  =C 348 kJ/mol

+ 3H ( )2g

P ROBLEM 160 Consider the following thermodynamic data:

Enthalpy of formation of CaC ( ) = – 60 kJ/mol2 s ;

Enthalpy of sublimation of Ca( ) = 179 kJ/mols ;

Enthalpy of sublimation of C( ) = 718 kJ/mols ;

First ionization energy of Ca(g) = 590 kJ/mol;

Second ionization energy of Ca(g) 1143 kJ/mol;

Bond energy of C ( ) = 614 kJ/mol2 g ;

First electron affinity of C ( ) = – 315 kJ/mol2 g ;

Second electron affinity of C ( ) = + 410 kJ/mol2 g

Draw a clear Born-Haber cycle and determine lattice energy of CaC2( )s

P ROBLEM 161 Normal L.P.G contains 90% propane and 10% methane by weight If combustion of

L.P.G produces acetylene, CO(g) and H O2 ( )l , calculate the heat evolved by combustion of 100 g of

L.P.G

Given: enthalpy of combustion of methane =– 890 kJ/mol, C H = – 2220 kJ/mol3 8 ,

C H = –2 2 1300kJ/moland CO( ) = – 285 kJ/molg

P ROBLEM 162 A swimmer breaths 20 times in one minute when swimming and inhale 200 mL of air inone breath Inhaled air contain 20% O2 by volume and exhaled air contain 10% O2 by volume If alloxygen are consumed in combustion of glucose in the body and 25% of energy obtained fromcombustion is available for muscular work Determine the maximum distance this swimmer can swim inone hour if 100 kJ energy is required for 1.0 km swimming Standard molar enthalpy of combustion ofglucose is – 2880 kJ/mol and body temperature is 37°C

P ROBLEM 163 Standard molar enthalpies of formation of H O2 ( )l and H O2 2( )l are – 285 and – 200

kJ/mol respectively and their molar enthalpies of vaporization are 41 and 60 kJ respectively If enthalpy

of atomization of O2( )g is 298 kJ/mol, determine bond energy of O—O bond.

P ROBLEM 164 Determine resonance energy of 1,3-butadiene using the following information:Enthalpy of combustion : 1,3-butadiene =– 2841 kJ/mol, C gr( ) –= 394kJ/mol,

H2( ) –g = 285kJ/mol

Bond enthalpy : C—C=348 kJ/mol, C==C=615kJ/mol Also standard enthalpy of formation ofcyclobutene=130 kJ/mol,

P ROBLEM 165 Standard molar enthalpy of formation of hydrazine liquid (N H2 4) is 50 kJ/mol,

NH ( ) = – 46 kJ/mol.3 g Average N—H and H—H bond energies are 393 and 436 kJ/mol respectively Ifenthalpy of vaporization of N H2 4 is 18 kJ/mol, determine N—N bond energy in N H2 4

P ROBLEM 166 Using following standard enthalpies:

∆H°fHF(aq) –= 329kJ/mol ∆H°fH O2 ( ) –l = 285kJ/mol,

∆H°fF–(aq) – 320= kJ /mol and

H+(aq)+OH–(aq) → H O2 ( ),l ∆H =–56kJ/mol

Determine enthalpy of neutralization of HF against a strong base

P ROBLEM 167 From the following reactions and thermal information at 25°C:

2Fe( ) +3

2O2 Fe O ( )2 3

FeO( ) + 2H (s + aq) → H O( ) + Fe2 l 2+(aq)

P ROBLEM 168 A 150 cc portion of 0.4 N HCl is neutralized with excess of NH OH4 in a bombcalorimeter which results in a temperature rise of 2.36°C If the heat capacity of calorimeter content is1316.7 J/°C, calculate heat of neutralization of HCl Vs NH OH4

P ROBLEM 169 Determine S—S bond energy;

Given∆H°f of (C H ) S( ) = – 147 kJ/mol2 5 2 g ,

∆H°f of (C H ) S ( ) = – 202 kJ/mol2 5 2 2 g and ∆H°Sublimation of S( ) = 223 kJ/mol.s

P ROBLEM 170 Given the following standard molar enthalpies:

∆H°f of CH CN( ) = 88 kJ/mol3 g , ∆H°f of C H = – 84 kJ/mol2 6 , ∆H°Sublimation ofC(gr) = 717 kJ/mol, bond dissociation energy of N2( )g and H2( )g are 946 and 436 kJ/mol respectively, B.E (C—H)=410 kJ/mol Determine C—C and C N≡≡ bond energies

P ROBLEM 171 Determine standard state enthalpy of the following reaction:

CH COOH( )3 l → CH ( ) + CO ( )4 g 2 g

Given∆H°Combustion CH = – 860 kJ/mol4 Bond energies in kJ/mol C—H=410, C—C=348, C==O

=728, C—O =352, O—H=463, O==O=498 ∆H°Vaporization of acetic acid and water are 52 and 41kJ/mol respectively

P ROBLEM 172 ∆H°f of C H OH( ) = – 66 kcal/mol,2 5 l enthalpy of combustion of

CH OCH ( ) = – 348 kcal/mol3 3 g ,∆H°f of water is – 68 kcal/mol and∆H°f of CO ( ) = – 94 kcal/mol.2 g

Determine enthalpy of the following isomerization reaction:

C H OH( )2 5 l → CH OCH ( )3 3 g

P ROBLEM 173 The standard enthalpies of formation of BH ( )3 g and B H ( )2 6 g are 100 kJ and 36 kJ per

mol respectively and the enthalpies of formation of B( )g and H( ) g are 563 kJ mol–1 and 218 kJ mol–1respectively Determine mean BHbond enthalpies in each case Assume terminal B—H bonds havesame strengths, estimate enthalpies of the three centre B H Bbonds in B H2 6 Which bonds wouldyou expect to be longer-terminal or bridged one?

P ROBLEM 174 Enthalpy of combustion of C H6 6( )l , C H6 12( )l (cyclohexane) H2( )g are –3268, –3920

and –289 kJ/mol respectively If enthalpy of hydrogenation of cyclohexane is –120 kJ/mol, determineresonance energy of benzene( )l

P ROBLEM 175 Assuming that mileage of an automobile gets is directly proportional to the heat ofcombustion of fuel, calculate how many times farther an automobile could be expected to go on one litregasoline than on 1.0 litre ethanol

Assume gasoline to be pure n-octane (ρ =0.7025 gmL–1) Density of ethanol is 0.7893 gmL–1.∆H f°

of ethanol and octane are −278 kJ mol–1 and –208.4 kJ mol–1 ∆H f° of CO2( )g and H O2 ( )l are

−394 kJ mol–1and –286 kJ mol–1respectively

P ROBLEM 176 10 g of propane was burnt in air at 30°C and 1.0 atm pressure Assume air to be 21.00%

O2, determine volume of air required for combustion process If all the heat produced from combustion

of 10 g of propane was transferred to 8.00 kg of water at 30°C, determine final temperature of water C P

of water is 418 Jg K–1 –1 Also,∆H f°of propane, CO2and H O2 are: −104 kJ mol , 394 kJ mol–1 – –1and–286 kJ mol–1respectively

P ROBLEM 177 With the following informations, determine standard state Gibb’s free energy offormation of N O2 4( )g

difference in calculate and observed value of enthalpies

P ROBLEM 179 One mole of N2( )g and 3.0 mole of H2( )g taken in a flask at 25°C and heated to 450°C.

Now pressure was applied on the gaseous mixture which results in conversion of 0.1 mole of N2 into

NH3 The gases are then cooled rapidly back to 25°C Determine the net heat change in this processgiven the following bond enthalpies:

N2( )g =944kJ mol–1; H2 =436kJ mol–1and average NHbond energy=388 kJ mol–1

P ROBLEM 180 A 150 cc portion of 0.4 NHCl is neutralized with an excess of NH OH4 in a Dewarvessel with a resulting rise in temperature of 2.36°C If the heat capacity of Dewar and its contents afterthe reaction is 1316.7 J C/° , calculate heat of neutralization

P ROBLEM 181 At 25°C, the heat of solution of anhydrous CuSO4in a large volume of water is−66.044

kJ mol–1, while that of CuSO 5H O4⋅ 2 is –11.495 kJ Determine heat of reaction:

Determine enthalpies of the following hydration reactions:

(a) CaCl (s) + 2H O2 2 → CaCl 2H O2⋅ 2

(b) CaCl 2H O + 2H O2⋅ 2 2 → CaCl 4H O2⋅ 2

(c) CaCl ( ) + 6H O2 s 2 → CaCl 6H O2⋅ 2

P ROBLEM 183 The enthalpy of following reactions at 25°C are:

(i) Na( ) + Cls 12 2( )g → NaCl( )s ∆H° = −410.6 kJ

H ( ) + Cl ( )2 g 2 g → HCl( )g ∆H° = −92.21 kJ

(iv) H ( ) + O ( )2 g 12 2 g → H O( )2 l ∆H° = −394 kJ

P ROBLEM 185 Draw Lewis structures of hypothetical molecule N6( )g consisting of a six membered

ring of nitrogen atom If its standard enthalpy of formation is 1072 kJ mol–1, predict the most likelystructure Given:

B.E N2 =944kJ mol–1, NN = 163 kJ mol–1and N == N = 409 kJ mol–1

P ROBLEM 186 A male burns 2000 kJ of energy while jogging for 1.0 hour If the standard heat ofcombustion of a typical fat is 38 kJ g–1and only 70% energy is available for muscular activity Whatminimum hours would he need to jog if he wished to lose 0.5 g fat?

P ROBLEM 187 Strong sunshine bombards the Earth with about 1 kJ m s–2 –1 If a beaker containingethanol, is placed in sunlight for 10 minutes, 3.24 g of liquid was vaporized Assuming that all the heat isused for vaporization, not to increase temperature, determine surface area of beaker Enthalpy ofvaporization is 42.6 kJ mol–1

P ROBLEM 188 From the following enthalpies values, determine resonance energy of C H6 6( )l

“Benzene”

Also, given the resonance energy of 1,3-cyclohexadiene is 70 kJ mol–1

(i) + H2 ∆H° = – 38 kJ

(ii) + 2H2 ∆H° = – 170 kJ

T HERMODYNAMICS

P ROBLEM 189 Suppose that a gas obeys the modified van der Waals’ equation P ×(V m – )b =RTand

b=0.02 L mol–1 If 0.5 mol of the gas is reversibly compressed from an initial volume of 2dm to a final3volume of 0.5 dm3, how much work is done on the system at 27°C

P ROBLEM 190 One mole of a monoatomic, ideal gas confined in a 5 L piston fitted cylinder at 300 K isheated such that its temperature increased to 400 K but at the same time gas also expanded to a volume of

8 L Calculate change in enthalpy of the system

P ROBLEM 191 One mole of a monoatomic ideal gas confined in a 5 L, piston fitted cylinder at 300 K isheated to 800 K as well as allowed to expand to a volume of 8 L simultaneously Calculate change inenthalpy of the system

P ROBLEM 192 100 g of nitrogen gas at 300 K are held by a piston under 30 atmosphere The pressure is

suddenly released to 10 atmosphere and gas is allowed to expand adiabatically If C V =20.8 JK mol–1 –1,calculate∆SSystem

P ROBLEM 193 Calculate entropy change when 0.5 L of an ideal gas (C V =12.6 JK mol–1 –1)at 300 Kand one atmosphere is allowed to expand to double its volume and simultaneously heated to 373 K

P ROBLEM 194 10 g of ice at 0°C are added to 20 g water at 90°C in a thermally insulated flask ofnegligible heat capacity The heat of fusion of ice is 6 kJ/mol What is the final temperature,∆SSystem?

C p=75.42 JK mol–1 –1

P ROBLEM 195 One mole of a supercooled liquid water at – 10°C and one atmosphere turns into ice at

– 10°C Calculate entropy change for the system C p for liquid water and ice are 75.42 and37.2 JK mol–1 –1 respectively

P ROBLEM 196 In an open beaker at 27°C and one atm pressure, 100 g of zinc are caused to react withdilute sulphuric acid Calculate the work done by the liberated hydrogen gas assuming it to behaveideally What would be the work done if the reaction took place in a sealed vessel?

P ROBLEM 197 A balloon is 0.5 m in diameter and contains air at 25°C and 1 bar pressure It is thenfilled with air isothermally and reversibly until the pressure reaches to 5 bar Assume that pressure isproportional to the diameter of the balloon, calculate (a) final diameter and (b) work done in the process

P ROBLEM 198 One mole of an ideal gas initially at 10 bar and 300 K is allowed to expand against aconstant external pressure of 2.00 bar to a final pressure of 2 bar During this process, the temperature ofthis gas falls to 250 K Construct a reversible path connecting this initial and final state as a combination

of reversible isothermal expansion followed by reversible adiabatic expansion so that the final state is

attained and calculate work done by the system in attaining the final state C vm =3 2/ R

P ROBLEM 199 With the temperature maintained at 0°C, 2 mole of an ideal gas are allowed to expandagainst a piston that supports 2.0 bar pressure The initial pressure of the gas is 10 bar and the finalpressure 2 bar

(a) How much energy is transferred to the surrounding during the expansion?

(b) What is the change in internal energy and enthalpy of the gas?

(c) How much heat the gas has absorbed?

P ROBLEM 200 A gas behaving ideally was allowed to expand reversibly and adiabatically to twice its

volume Its initial temperature was 25°C and C vm=( / )5 2 R, calculate∆E mand∆H m

P ROBLEM 201 One mole of a gas at 300 K is compressed isothermally and reversibly from an initialvolume of10 dm3 to a final volume of 0.2 dm mol3 –1 Calculate work done on the system if the equation

of state of the gas is (V m – )b P=RT with b=0.03 dm mol3 –3

P ROBLEM 202 One mole of a gas at 100 K is compressed isothermally from an initial volume of

20dm to a final volume of 53 dm Calculate the work done on the system if the equation state is:3

P ROBLEM 203 Find q,W,∆U and∆H if 2.0 g of He undergoes a reversible isobaric expansion from 20

to 40 L at 0.8 atm pressure followed by reversible isochoric heating till pressure reaches to 1.0 atm

Depict the change of state on a P-V diagram.

P ROBLEM 204 One mole of liquid water at 30°C is adiabatically compressed, pressure increasing from1.0 atm to 10.0 atm Since, liquids and solids are rather incompressible, it is a fairly approximastion to

take V constant Calculate q,∆U and∆H for the process C p of H O( ) = 75.42 JK mol2 l –1 –1

P ROBLEM 205 For a perfect gas, C v =2.5 2.0 moles of this gas undergoes following change of state:R

(a) A reversible isobaric expansion from 1.0 atm, 20 L to 1.0 atm, 40 L

(b) A reversible isochoric change from 1.0 atm, 40 L to 0.5 atm, 40 L

(c) A reversible isothermal compression from 0.5 atm, 40 L to 1.0 atm, 20 L Sketch each process on

the P-V diagram and calculate : q, W,∆U and∆H.

P ROBLEM 206 A sample of an ideal gas underwent an adiabatic expansion from 298 K, 15 bar to 2.5bar against a constant external pressure of 1.0 bar What is the final temperature of the system and work

done by the system, assume C vm =2.5 R?

P ROBLEM 207 A gas behaves ideally and its C v is given by: C v =21.52 8.2 10+ × 3T(all parameters

in SI unit) A sample of this gas is initially at T1 =300K, P1 =10bar andV1 =1L It is allowed to expand

until P2 =1atm and V2 =10L What are∆U and∆H for this process? Could the process be carried out

C p =28.58 1.76 10+ × 2T

Calculate∆U ,∆H, and∆S.

P ROBLEM 210 An ideal gas expand against a constant external pressure of 2.0 atmosphere from 20 L to

50 L and absorb 20 kJ of energy from surrounding What is the change in internal energy of the system?

P ROBLEM 211 A gas expands against a variable pressure given by P

V

=10atm, where V is volume of

gas at each stage of expansion Further during expansion from volume 10 L to 100 L, the gas undergoes achange in internal energy of 420 J How much heat is absorbed by the gas during expansion?

P ROBLEM 212 Three moles of an ideal gas is heated at constant pressure of one atmosphere from 27°C

to 127°C If C v is expressed as: C v =30 14 10+ × 3TJK–1 mol–1, determine W,∆E and q.

P ROBLEM 213 One mole of an ideal gas at state A (500 K, 5.0 atm) is cooled at constant volume to

B (300 K) and then expanded isothermally and reversibly to C and finally compressed adiabatically to A.

Sketch the change on a P-V diagram and determine the net work done in this cyclic process.γ =5

P ROBLEM 215 One mole of an ideal gas initially at A (300 K and 5.0 bar) is heated at constant pressure

to double its volume (B) The gas is then expanded isothermally and reversibly to a new state C The gas

is then cooled at constant pressure to another new state D (200 K) and finally compressed adiabatically and reversibly to A Depicting on a P-V diagram, determine the net work done in the above cyclic process C v =1.5 R

P ROBLEM 216 One mole of an ideal gas at A (500 K, 5.0 bar) is expanded isothermally and reversibly

to a new state B and then cooled at constant pressure to C (250 K) and finally compressed adiabatically and reversibly to A Depicting on a P-V diagram, determine the net work done in the cyclic process.

C v =1.5 R

P ROBLEM 217 One mole of an ideal gas at 500 K and 10 bar, defined by state A is allowed to expand

isothermally and does a work equal to 4200 J Construct a combination of initial irreversible expansionupto 2.0 bar followed by reversible expansion so that final state is reached and determine final pressure

of the gas

P ROBLEM 218 One mole of an ideal gas at 500 K and 10 bar is allowed to expand till the final pressurefalls to 1.0 atmosphere and final temperature falls to 250 K Construct a combination of reversible pathof:

(a) initial adiabatic expansion followed by isothermal expansion so that final state is reached and

determine the total work done C v =1.5 R

(b) Determine the work by reversing the order of combination in (a) and compare the two workdone

P ROBLEM 219 One mole of an ideal gas at 300 K and 1.0 atmosphere is heated to 500 K and expandedsimultaneously to 36 litre Determine∆H assuming heat capacity to be independent of temperature and

P ROBLEM 222 One mole of an ideal gas is taken in a one litre sealed flask at 300 K and heated till the

pressure becomes equal to 40 atmosphere If C v =12 28 10+ × 3T(in SI unit), determine∆S.

P ROBLEM 223 A gaseous reactant A forms two different product in a parallel reaction B and C as

follows:

A → B; ∆H° =–3kJ,∆S° =20JK–1

A → C; ∆H° =–3.6 kJ,∆S° =10JK–1

Discuss the relative stability of B and C on the basis of Gibb’s free energy change at 27°C.

P ROBLEM 224 One mole of an ideal gas contained in a sealed flask at 1.0 bar is heated from 27°C to127°C Determine∆G if: S(JK ) = 10 +12 10–1 × –3T

P ROBLEM 225 Two moles of NO2 is heated at constant volume from 27°C to 127°C and

C p (JK mol ) = 28 + 31 10–1 –1 × –3T

Determine∆S.

P ROBLEM 226 Two moles of an ideal gas is expanded isothermally and irreversibly at 27°C from

volumeV1to 2.5V and 4.17 kJ heat is absorbed from surroundines Determine1 ∆Ssys,∆Ssurrand∆Suniv

P ROBLEM 227 One mole of He(g) is mixed isothermally and reversibly with 2.0 mole of Ne(g).

Determine∆S.

P ROBLEM 228 C vm for an ideal gas is 2.5 R and it is independent of temperature If 2.0 moles of this gas

is subjected to the following change of state :

P ROBLEM 229 An ideal gas has

C vm = +a bT

where a=25 JK–1mol–1 and b=0.03 JK–2 mol–1 If 3.0 moles of this gas is subjected to a

thermodynamic change of state from A (300 K, 2.0 bar) to B (500 K, 3.0 bar), determine q, W,∆E,∆H

and∆S.

P ROBLEM 230 One mole of an ideal gas defined by state A (400 K, 5.0 bar) is heated at constant pressure to B (500 K) and then cooled at constant volume to C The gas is then expanded isothermally and reversibly to a new state D (1.0 bar) and finally compressed adibatically to A Depicting on a P-V diagram, determine the net work done in this cyclic process C v =1.5 R

P ROBLEM 231 One mole of an ideal gas is subjected to the following change of state:

Depicting the above change on a P-V diagram, determine the net work done.

P ROBLEM 232 The entropy of vaporization of benzene is 85 JK mol–1 –1

(a) Estimate the enthalpy of vaporization of benzene at its normal boiling point of 80°C

(b) Determine the entropy change of surroundings when 100 g benzene vaporizes at its normalboiling point

P ROBLEM 233 The entropy of vaporization of acetone is 85 JK mol–1 –1

(a) Estimate enthalpy of vaporization of acetone at its normal boiling point 56°C

(b) Determine entropy change of surrounding if 100 g of acetone condenses at its boiling point

P ROBLEM 234 With the help of following reduction reactions:

TiO ( ) + 2C( )2 s s → Ti( ) + 2CO( )s g …(i)TiO ( ) + C( )2 s s → Ti( ) + CO ( )s 2 g …(ii)

at 1000 K, given ∆G f°(CO)= −200kJ mol–1, ∆G f° (CO2)= −396 kJ mol–1 and

∆G f° TiO2( )s = −762kJ mol–1, determine which will be the predominant mode of reduction of TiO2( )s

at 1000 K

P ROBLEM 235 The reaction for the production of synthetic fuel ‘water gas’ from coal is:

C( ) + H O( )gr 2 g → CO( ) + H ( )g 2 g

Standard molar entropies of C( ),gr H O2 ( ),g CO( )g and H2( )g are 5.7, 70, 190 and 131 JK mol–1 –1

respectively Also, standard enthalpy of formations of H O and CO2 are –242 and –111 kJ mol–1respectively Determine the standard reaction free energy of reaction at 27°C Also, predict about thespontaneity and effect of temperature on direction of reaction

P ROBLEM 236 The thermodynamic informations for isomerization of alkene (C H )4 8 at 300 K are asfollows:

H CHC==C

CHH3

–1

kJ mol -2-butene

H f

HCH3

3 –1

kJ mol -2-butene

11.

∆

∆

G f trans

H f

° =

° = − 2 kJ mol–1H

HC==C

CH

CH2-methylpropene

= +58 kJ mol

3

3

∆G f°

If the temperature of the above system is increased to 400 K and equilibrium was allowed to

re-establish, mole percentage of trans-2-butene at new equilibrium was 18 Determine∆H°and∆S°forthe isomerization reactions below:

cis-2-butene 2-methylpropene

trans-2-butene 2-methylpropene

P ROBLEM 237 At a temperature above 65 K, decarboxylation of acetic acid, (i.e., loss of CO2)becomes spontaneous If ∆H f° of CH COOH3 , CO2( )g and CH4 are −484.5,−394and−74.8kJ/molrespectively, determine standard state entropy change (∆S°)for the decarboxylation reaction What isthe driving force for getting this reaction to proceed?

P ROBLEM 238 For the reaction:

The equilibrium vapour pressure of CO2at 700°C and 950°C are 22.6 and 1830 mm of Hg Calculate

∆H°and∆S°for the reaction

P ROBLEM 240 A certain reaction is spontaneous at 72°C If the enthalpy change for the reaction is

19 kJ, what is the minimum value of∆S for the reaction?

P ROBLEM 241 The internal engine of a 1200 kg car is designed to run on octane whose enthalpy ofcombustion is 5510 kJ/mol If the car is moving up a slope, calculate the maximum height to which thecar can be driven on 2.0 gallon of the fuel Assume the cylinder temperature is 2200°C and the exittemperature is 760°C and ignore all form of friction The mass of 1.0 gallon of fuel is 3.1 kg

P ROBLEM 242 One gram sample of oxygen undergoes free expansion from 0.75 L to 3.0 L at 298 K.Calculate∆S q W, , ,∆Hand∆E.

P ROBLEM 243 A 550 ml sample of an ideal gas at 300 K exerts 3 atm The thermodynamic state of the

system changes in a process In the final state, P=3.5 atm and V =730 mL Calculate∆Sand∆Eand

∆H, C vm =(5 2 / )R

P ROBLEM 244 A sample of 0.0133 mole of an ideal gas, initially at 5.00 atm, expands isothermally andreversibly from 3.00 L to 10 L Calculate∆ ∆S, Gand∆H.

P ROBLEM 245 One mole of an ideal gas originally at a volume of 8.00 Lit at 1000 K, is allowed to

expand adiabatically until final volume is 16.00 Lit For the gas C v =1.5 Calculate values ofR ∆S for

the process when:

(a) The expansion takes place reversibly

(b) The expansion takes place against a constant pressure of 3.00 atm

(c) The change in volume involves a free expansion

P ROBLEM 246 One mole of an ideal gas at 0°C and 1.0 atm pressure is mixed adiabatically with one

mole of a different gas at 100°C and 1.0 atm to yield a mixture If C Pfor each gas is (5 2/ )R, determine

∆S (mixing).

P ROBLEM 247 For chloroform gas C PM is expressed as:

C PM =24.9 14.8+ ×10−2T− ×9 10−5T JK mol2 –1 –1.Assuming this gas to be ideal, determine entropy change involved in heating 2.0 mole of gas fromvolume 100 L at 500 K to a volume of 70 Lit at 700 K

P ROBLEM 248 For N2( )g , entropy function as a function of temperature is expressed as:

S = 25.1 + 29.3 ln T

Determine Gibb’s free energy change∆G of one mole of nitrogen if it is heated from 298 K to 348 K

at 2.0 atm pressure

P ROBLEM 249 One mole of an ideal gas initially at 400 K and 10 atm, is adiabatically expanded

against a constant pressure of 5.0 atm until equilibrium is attained If C V =18.8 0.021T JK mol+ –1 –1,determine∆ ∆E, H and∆S

P ROBLEM 250 Molar volume of C H ( )6 6 l is 89 c.c at 27°C and 1.0 atm pressure Assuming the volume

to be constant, determine∆G for compression of 5.00 moles of liquid benzene from 1.0 atm to 100 atm.

P ROBLEM 251 One mole of an ideal gas at 25°C is subjected to a reversible isoentropic expansion untilfinal temperature reached to 75°C If the initial pressure was 1.0 atm, determine final pressure

C V =(3 2/ )R

P ROBLEM 252 A flask containing 1.00 mol of N2 at 4.00 atm and 298 K was connected to a flaskcontaining 1.00 mol of N2 gas at 2.00 bar and 298 K The gases were allowed to mix isothermally.Determine the entropy change for the system

P ROBLEM 253 One mole of solid iron was vaporized in an oven at 3500 K If iron boils at 3133 K andenthalpy of vaporization is 349 JK mol–1 –1, determine∆Ssystem,∆Ssurroundingsand∆Suniverse

and 1.0 bar is to be excited to their 2nd excited state, what will be the total energy consumption?

P ROBLEM 257 A H-like species is in their excited state (A) and absorb a photon of 3.868 eV and get excited into a new state B The electron from B in returning back to lower energy orbit, can give a

maximum of 10 emission lines with different wavelengths, some lines having energy greater than 3.868

eV, some lines with energy equal to 3.868 eV but two lines with energy less than 3.868 eV Determine

the orbit number of states A and B and ionization energy of the species.

P ROBLEM 258 What is the speed of an electron whose de Broglie wavelength is 0.1 nm By whatpotential difference, must have such an electron be accelerated from an initial speed zero

P ROBLEM 259 Consider a colloidal particle of mass 6 10× –16kg Suppose that its position is measured

to 1 nm accuracy, calculate the uncertainty in its velocity

P ROBLEM 260 The wavelength of a photoelectric threshold of a metal is 230 nm Determine the kineticenergy of photoelectron ejected from the surface by UV radiation emitted from the second largestwavelength of transition of electron in Lyman series of atomic spectrum of H-atom

P ROBLEM 261 A hydrogen like species with atomic number Z is in higher excited state ‘n’ and emits

photons of energy 25.7 and 8.7 eV when makes a transitions to 1st and 2nd excited state respectively

Determine ‘n’ and ionization energy of the species.

P ROBLEM 262 Light from a discharge tube containing H-atoms in some excited state, falls on thesurface of sodium metal The kinetic energy of the fastest photoelectron was found to be 10.93 eV If

He+ ions were present in the same excited state, the kinetic energy of the fastest photoelectron wouldhave been 49.18 eV Determine the excited state orbit number and work function of Na

P ROBLEM 263 Certain sun glasses have small crystals of AgCl incorporated in the lenses When thelenses are exposed to light of appropriate wavelength, the following reaction occurs:

AgCl → Ag + ClThe Ag atoms formed produce a uniform gray colour that reduces the glare If∆H for the reacton is

248 kJ, what maximum wavelength would be required to induce this process?

P ROBLEM 264 Ozone in the stratosphere absorbs the harmful radiation from the sun by undergoingdecomposition:

O3 → O + O2