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MOLE CONCEPT

PROBLEM 1 A crystalline hydrated salt on being rendered anhydrous, loses 45.6% of its weight. The

percentage composition of anhydrous salt is: Al 10.5%= , K 15.1%= , S 24.8%= and O = 49.6%. Find

the empirical formula of the anhydrous and crystalline salt.

PROBLEM 2 How much quantity of zinc will have to be reacted with excess of dilute HCl solution to

produce sufficient hydrogen gas for completely reacting with the oxygen obtained by decomposing

5.104 g of potassium chlorate?

PROBLEM 3 A 1.85 g sample of mixture of CuCl2 and CuBr2 was dissolved in water and mixed

thoroughly with 1.8 g portion of AgCl. After reaction, the solid which now contain AgCl and AgBr was

filtered, dried and weighed to be 2.052 g. What was the % by weight of CuBr2 in the mixture?

PROBLEM 4 1.0 g of a sample containing NaCl, KCl and some inert impurity is dissolved in excess of

water and treated with excess of AgNO3 solution. 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.

PROBLEM 5 A one gram sample containing CaBr2 , NaCl and some inert impurity was dissolved in

enough water and treated with excess of aqueous silver nitrate solution where a mixed precipitate of

AgCl and AgBr weighing 1.94 g was obtained. Precipitate was washed, dried and shaken with an

aqueous solution of NaBr where all AgCl was converted into AgBr. The new precipitate which contain

only AgBr now weighed to be 2.4 g. Determine mass percentage of CaBr2 and NaCl in the original

sample.

PROBLEM 6 Sulphur combines with oxygen to form two oxide SO2 and SO3 . If 10 g of S is mixed with

12 g of O2 , what mass of SO2 and SO3 will be formed, so that neither S nor oxygen will be left at the end

of reaction?

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

molality m of this solution.

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

molarity (M).

PROBLEM 9 Octane is a component of gasoline. Incomplete combustion of octane produces some CO

along with CO2 and H O2 , which reduces efficiency of engine. In a certain test run, 1.0 gallon of octane is

burned and total mass of CO, CO2 and H O2 produced was found to be 11.53 kg. Calculate efficiency of

the engine, density of octane is 2.65 kg/gallon.

PROBLEM 10 The formula of a hydrated salt of barium is BaCl H O2 2⋅ x . If 1.936 g of this compound

gives 1.846 g of anhydrous BaSO4 upon treatment with H SO2 4 , calculate x.

PROBLEM 11 A mixture of CuSO H O24 5⋅ and MgSO 7H O4 2⋅ was heated until all the water was

driven-off. If 5.0 g of mixture gave 3 g of anhydrous salts, what was the percentage by mass of

CuSO 5H O4 2⋅ in the original mixture?

PROBLEM 12 A sample of clay contain 15% moisture, and rest are CaCO3 and non-volatile SiO2 . This

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

Problems 3

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

original sample.

PROBLEM 13 Chlorine dioxide (ClO )2 , has been used as a disinfectant in air conditioning systems. It

reacts with water according to the reaction:

ClO + H O HClO + HCl2 2 3→

In an experiment, a 10.0 L sealed flask containing ClO2 and some inert gas at 300 K and 1.0

atmosphere pressure is opened in a bath containing excess of water and all ClO2 is reacted quantitatively.

The resulting solution required 200 mL 0.9 M NaOH solution for neutralization. Determine mole

fraction of ClO2 in the flask.

PROBLEM 14 Potassium salt of benzoic acid (C H COOK)6 5 can be made by the action of potassium

permanganate on toluene as follows:

C H CH + KMnO C H COOK + MnO + KOH + H O6 5 3 4 6 5 2 2→

If the yield of potassium benzoate can’t realistically be expected to be more than 71%, what is the

minimum number of grams of toluene needed to achieve this yield while producing 11.5 g of

C H COOK6 5 ?

PROBLEM 15 Manganese trifluoride can be prepared by the following reaction:

MnI ( ) + F ( ) MnF IF2 2 5s g → +3

What is minimum number of grams of F2 that must be used to react with 12.0 g of MnI2 if overall

yield of MnF3 is no more than 75%.

PROBLEM 16 A compound containing Ca, C, N and S was subjected to quantitative analysis and

formula mass determination. A 0.25 g of this compound was mixed with Na CO2 3 to convert all Ca into

0.16 g CaCO3 . A 0.115 g sample of compound was carried through a series of reactions until all its S was

changed into SO4

2– and precipitated as 0.344 g of BaSO4 . A 0.712 g sample was processed to liberate all

of its N as NH3 and 0.155 g NH3 was obtained. The formula mass was found to be 156. Determine the

empirical and molecular formula of the compound.

PROBLEM 17 A 0.2 g sample, which is mixture of NaCl, NaBr and NaI was dissolved in water and

excess of AgNO3 was added. The precipitate containing AgCl, AgBr and AgI was filtered, dried and

weighed to be 0.412 g. The solid was placed in water and treated with excess of NaBr, which converted

all AgCl into AgBr. The precipitate was then weighed to be 0.4881 g. It was then placed into water and

treated with excess of NaI, which converted all AgBr into AgI. The precipitate was then weighed to be

0.5868 g. What was the percentage of NaCl, NaBr and NaI in the original mixture.

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

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

PROBLEM 19 Ammonia is manufactured by the reaction of N 2 and H2 . An equilibrium mixture

contains 5.0 g of each N 2 , H2 and NH3 . Calculate mass of N 2 and H2 present initially and maximum

amount of NH3 that can be produced.

PROBLEM 20 Consider the following reactions:

XeF + F XeF2 2 6→

and XeF + ( CH CH ) ( CF CF )6 2 2 2 2— — — — — —n n→ + HF + XeF4

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

4 Problems in Chemistry

Page 15

out initially was analyzed. The mole fraction of the O2 was found to be 0.60, determine the degree of

dissociation.

PROBLEM 111 Proportion of a lighter isotope in a gaseous mixture containing both heavier and lighter

isotopes is increased by successive effusion of the gas mixture. A sample of neon gas has

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

20 Ne would be achieved?

PROBLEM 112 The density of vapour of a substance at 1.0 atm and 500 K is 0.35 k/m 3 . The vapour

effuses 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 energy

possessed by a molecule.

PROBLEM 113 Using van der Waals’ equation of state, calculate the pressure correction factor for two

moles of a gas confined in a four litre flask that exert a pressure of 11 atmosphere at 300 K.

b = 0.05 L mol–1 .

PROBLEM 114 For a van der Waals’ gas Z (compressibility factor) was found to be 1.5 at 273 K and one

atmosphere and TB of the gas is 107 K. Determine value of a and b.

PROBLEM 115 A flask containing 2.0 moles of He gas at 1.0 atm and 300K is connected to another

flask containing N ( )2 g at the same temperature and pressure by a narrow tube of negligible volume.

Volume of the nitrogen flask is three times volume of He-flask. Now the He-flask is placed in a

thermostat at 200 K and N 2-flask in another thermostat at 400 K. Determine final pressure and final

number of moles in each flask.

PROBLEM 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.

PROBLEM 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 of

collected gaseous mixture was found to be 0.45 times rate of effusion of pure oxygen gas. Determine the

degree of dissociation of PCl ( )5 g in the original sample.

PROBLEM 118 One mole of a monoatomic gas confined in a 22.5 litre flask at 273 K exert a pressure of

0.98 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 (TB ).

PROBLEM 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.

PROBLEM 120 Calculate the van der Waal’s constants for ethylene. TC = 282 K,PC = 50 atm.

Problems 17

Page 16

PROBLEM 121 The second Virial coefficient of an imperfect gas is 2 10 2× – (L/mol)2 . Calculate the

volume of a gm mole of the gas at 27°C and 5 atmosphere pressure.

PROBLEM 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?

PROBLEM 123 For carbon dioxide, critical density is 0.45 g/cc and its TC = 300 K. Determine its van

der Waal’s constants.

PROBLEM 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’.

PROBLEM 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.

PROBLEM 126 Using van der Waals’ equation of state, calculate pressure developed by 100 g of CO2

contained 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 .

PROBLEM 127 An equation of state for a non-ideal gas can be written as: PV A BP CPm = + +

2 ; where

Vm is the molar volume and P is the gas pressure in atmosphere. B = ×–

–2.879 10 2 and C = ×14.98 10 5–

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

will attain minimum.

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

P

TV

V RT+

=

α

β

2

( – )

Deduce expression for the first Virial coefficient (B) and Boyle’s temperature in term of α and β if

Virial equation of state is:

PV

RT

B

V

C

V

= + + +…1

2

PROBLEM 129 Assuming that dry air contain 79% N 2 and 21% O2 by volume, calculate the density of

moist air at 25°C and 1.0 atmosphere when the relative humidity is 60%. The vapour pressure of water at

25°C is 23.76 mm of Hg.

PROBLEM 130 At what temperature, three moles of SO2 will 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 –2 and b = 56.4 cm mol3 –1 .

PROBLEM 131 Pressure of He gas confined in a steel chamber drops from 4.0 to 1.0 atmosphere in 4.0

hours due to diffusion through a pin-hole in the steel chamber. If an equimolar mixture of He and

methane gas at 20 atmosphere and the same temperature are confined in the same chamber, what will be

the partial pressure of He and methane after 1.0 hour. Assume rate of diffusion to be linear function of

gas pressure and inverse function of square root of molar masses.

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

18 Problems in Chemistry

Page 30

CaCO ( ) CaO( ) + CO ( )3 2s s g .

The equilibrium vapour pressure of CO2 at 700°C and 950°C are 22.6 and 1830 mm of Hg. Calculate

∆ ∆H S° °and for the reaction.

PROBLEM 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?

PROBLEM 241 The internal engine of a 1200 kg car is designed to run on octane whose enthalpy of

combustion is 5510 kJ/mol. If the car is moving up a slope, calculate the maximum height to which the

car can be driven on 2.0 gallon of the fuel. Assume the cylinder temperature is 2200°C and the exit

temperature is 760°C and ignore all form of friction. The mass of 1.0 gallon of fuel is 3.1 kg.

PROBLEM 242 One gram sample of oxygen undergoes free expansion from 0.75 L to 3.0 L at 298 K.

Calculate ∆ ∆S q W H, , , and ∆E.

PROBLEM 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 ∆ ∆S Eand and

∆H, C / Rvm = ( )5 2 .

PROBLEM 244 A sample of 0.0133 mole of an ideal gas, initially at 5.00 atm, expands isothermally and

reversibly from 3.00 L to 10 L. Calculate ∆ ∆S G, and ∆H.

PROBLEM 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 Rv =1.5 . Calculate values of ∆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.

PROBLEM 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 CP for each gas is ( )5 2/ R, determine

∆S (mixing).

PROBLEM 247 For chloroform gas CPM is expressed as:

CPM = + × − ×

− −24.9 14.8 T T JK mol2 –1 –110 9 102 5 .

Assuming this gas to be ideal, determine entropy change involved in heating 2.0 mole of gas from

volume 100 L at 500 K to a volume of 70 Lit. at 700 K.

PROBLEM 248 For N 2 ( )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.

PROBLEM 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 CV = +18.8 0.021T JK mol

–1 –1 ,

determine ∆ ∆ ∆E H S, and .

32 Problems in Chemistry

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PROBLEM 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.

PROBLEM 251 One mole of an ideal gas at 25°C is subjected to a reversible isoentropic expansion until

final temperature reached to 75°C. If the initial pressure was 1.0 atm, determine final pressure

C / RV = ( )3 2 .

PROBLEM 252 A flask containing 1.00 mol of N 2 at 4.00 atm and 298 K was connected to a flask

containing 1.00 mol of N 2 gas at 2.00 bar and 298 K. The gases were allowed to mix isothermally.

Determine the entropy change for the system.

PROBLEM 253 One mole of solid iron was vaporized in an oven at 3500 K. If iron boils at 3133 K and

enthalpy of vaporization is 349 JK mol–1 –1 , determine ∆S system , ∆ ∆S Ssurroundings universeand .

Problems 33

MOLE CONCEPT

PROBLEM 1 A crystalline hydrated salt on being rendered anhydrous, loses 45.6% of its weight. The

percentage composition of anhydrous salt is: Al 10.5%= , K 15.1%= , S 24.8%= and O = 49.6%. Find

the empirical formula of the anhydrous and crystalline salt.

PROBLEM 2 How much quantity of zinc will have to be reacted with excess of dilute HCl solution to

produce sufficient hydrogen gas for completely reacting with the oxygen obtained by decomposing

5.104 g of potassium chlorate?

PROBLEM 3 A 1.85 g sample of mixture of CuCl2 and CuBr2 was dissolved in water and mixed

thoroughly with 1.8 g portion of AgCl. After reaction, the solid which now contain AgCl and AgBr was

filtered, dried and weighed to be 2.052 g. What was the % by weight of CuBr2 in the mixture?

PROBLEM 4 1.0 g of a sample containing NaCl, KCl and some inert impurity is dissolved in excess of

water and treated with excess of AgNO3 solution. 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.

PROBLEM 5 A one gram sample containing CaBr2 , NaCl and some inert impurity was dissolved in

enough water and treated with excess of aqueous silver nitrate solution where a mixed precipitate of

AgCl and AgBr weighing 1.94 g was obtained. Precipitate was washed, dried and shaken with an

aqueous solution of NaBr where all AgCl was converted into AgBr. The new precipitate which contain

only AgBr now weighed to be 2.4 g. Determine mass percentage of CaBr2 and NaCl in the original

sample.

PROBLEM 6 Sulphur combines with oxygen to form two oxide SO2 and SO3 . If 10 g of S is mixed with

12 g of O2 , what mass of SO2 and SO3 will be formed, so that neither S nor oxygen will be left at the end

of reaction?

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

molality m of this solution.

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

molarity (M).

PROBLEM 9 Octane is a component of gasoline. Incomplete combustion of octane produces some CO

along with CO2 and H O2 , which reduces efficiency of engine. In a certain test run, 1.0 gallon of octane is

burned and total mass of CO, CO2 and H O2 produced was found to be 11.53 kg. Calculate efficiency of

the engine, density of octane is 2.65 kg/gallon.

PROBLEM 10 The formula of a hydrated salt of barium is BaCl H O2 2⋅ x . If 1.936 g of this compound

gives 1.846 g of anhydrous BaSO4 upon treatment with H SO2 4 , calculate x.

PROBLEM 11 A mixture of CuSO H O24 5⋅ and MgSO 7H O4 2⋅ was heated until all the water was

driven-off. If 5.0 g of mixture gave 3 g of anhydrous salts, what was the percentage by mass of

CuSO 5H O4 2⋅ in the original mixture?

PROBLEM 12 A sample of clay contain 15% moisture, and rest are CaCO3 and non-volatile SiO2 . This

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

Problems 3

Page 2

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

original sample.

PROBLEM 13 Chlorine dioxide (ClO )2 , has been used as a disinfectant in air conditioning systems. It

reacts with water according to the reaction:

ClO + H O HClO + HCl2 2 3→

In an experiment, a 10.0 L sealed flask containing ClO2 and some inert gas at 300 K and 1.0

atmosphere pressure is opened in a bath containing excess of water and all ClO2 is reacted quantitatively.

The resulting solution required 200 mL 0.9 M NaOH solution for neutralization. Determine mole

fraction of ClO2 in the flask.

PROBLEM 14 Potassium salt of benzoic acid (C H COOK)6 5 can be made by the action of potassium

permanganate on toluene as follows:

C H CH + KMnO C H COOK + MnO + KOH + H O6 5 3 4 6 5 2 2→

If the yield of potassium benzoate can’t realistically be expected to be more than 71%, what is the

minimum number of grams of toluene needed to achieve this yield while producing 11.5 g of

C H COOK6 5 ?

PROBLEM 15 Manganese trifluoride can be prepared by the following reaction:

MnI ( ) + F ( ) MnF IF2 2 5s g → +3

What is minimum number of grams of F2 that must be used to react with 12.0 g of MnI2 if overall

yield of MnF3 is no more than 75%.

PROBLEM 16 A compound containing Ca, C, N and S was subjected to quantitative analysis and

formula mass determination. A 0.25 g of this compound was mixed with Na CO2 3 to convert all Ca into

0.16 g CaCO3 . A 0.115 g sample of compound was carried through a series of reactions until all its S was

changed into SO4

2– and precipitated as 0.344 g of BaSO4 . A 0.712 g sample was processed to liberate all

of its N as NH3 and 0.155 g NH3 was obtained. The formula mass was found to be 156. Determine the

empirical and molecular formula of the compound.

PROBLEM 17 A 0.2 g sample, which is mixture of NaCl, NaBr and NaI was dissolved in water and

excess of AgNO3 was added. The precipitate containing AgCl, AgBr and AgI was filtered, dried and

weighed to be 0.412 g. The solid was placed in water and treated with excess of NaBr, which converted

all AgCl into AgBr. The precipitate was then weighed to be 0.4881 g. It was then placed into water and

treated with excess of NaI, which converted all AgBr into AgI. The precipitate was then weighed to be

0.5868 g. What was the percentage of NaCl, NaBr and NaI in the original mixture.

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

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

PROBLEM 19 Ammonia is manufactured by the reaction of N 2 and H2 . An equilibrium mixture

contains 5.0 g of each N 2 , H2 and NH3 . Calculate mass of N 2 and H2 present initially and maximum

amount of NH3 that can be produced.

PROBLEM 20 Consider the following reactions:

XeF + F XeF2 2 6→

and XeF + ( CH CH ) ( CF CF )6 2 2 2 2— — — — — —n n→ + HF + XeF4

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

4 Problems in Chemistry

Page 15

out initially was analyzed. The mole fraction of the O2 was found to be 0.60, determine the degree of

dissociation.

PROBLEM 111 Proportion of a lighter isotope in a gaseous mixture containing both heavier and lighter

isotopes is increased by successive effusion of the gas mixture. A sample of neon gas has

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

20 Ne would be achieved?

PROBLEM 112 The density of vapour of a substance at 1.0 atm and 500 K is 0.35 k/m 3 . The vapour

effuses 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 energy

possessed by a molecule.

PROBLEM 113 Using van der Waals’ equation of state, calculate the pressure correction factor for two

moles of a gas confined in a four litre flask that exert a pressure of 11 atmosphere at 300 K.

b = 0.05 L mol–1 .

PROBLEM 114 For a van der Waals’ gas Z (compressibility factor) was found to be 1.5 at 273 K and one

atmosphere and TB of the gas is 107 K. Determine value of a and b.

PROBLEM 115 A flask containing 2.0 moles of He gas at 1.0 atm and 300K is connected to another

flask containing N ( )2 g at the same temperature and pressure by a narrow tube of negligible volume.

Volume of the nitrogen flask is three times volume of He-flask. Now the He-flask is placed in a

thermostat at 200 K and N 2-flask in another thermostat at 400 K. Determine final pressure and final

number of moles in each flask.

PROBLEM 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.

PROBLEM 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 of

collected gaseous mixture was found to be 0.45 times rate of effusion of pure oxygen gas. Determine the

degree of dissociation of PCl ( )5 g in the original sample.

PROBLEM 118 One mole of a monoatomic gas confined in a 22.5 litre flask at 273 K exert a pressure of

0.98 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 (TB ).

PROBLEM 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.

PROBLEM 120 Calculate the van der Waal’s constants for ethylene. TC = 282 K,PC = 50 atm.

Problems 17

Page 16

PROBLEM 121 The second Virial coefficient of an imperfect gas is 2 10 2× – (L/mol)2 . Calculate the

volume of a gm mole of the gas at 27°C and 5 atmosphere pressure.

PROBLEM 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?

PROBLEM 123 For carbon dioxide, critical density is 0.45 g/cc and its TC = 300 K. Determine its van

der Waal’s constants.

PROBLEM 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’.

PROBLEM 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.

PROBLEM 126 Using van der Waals’ equation of state, calculate pressure developed by 100 g of CO2

contained 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 .

PROBLEM 127 An equation of state for a non-ideal gas can be written as: PV A BP CPm = + +

2 ; where

Vm is the molar volume and P is the gas pressure in atmosphere. B = ×–

–2.879 10 2 and C = ×14.98 10 5–

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

will attain minimum.

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

P

TV

V RT+

=

α

β

2

( – )

Deduce expression for the first Virial coefficient (B) and Boyle’s temperature in term of α and β if

Virial equation of state is:

PV

RT

B

V

C

V

= + + +…1

2

PROBLEM 129 Assuming that dry air contain 79% N 2 and 21% O2 by volume, calculate the density of

moist air at 25°C and 1.0 atmosphere when the relative humidity is 60%. The vapour pressure of water at

25°C is 23.76 mm of Hg.

PROBLEM 130 At what temperature, three moles of SO2 will 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 –2 and b = 56.4 cm mol3 –1 .

PROBLEM 131 Pressure of He gas confined in a steel chamber drops from 4.0 to 1.0 atmosphere in 4.0

hours due to diffusion through a pin-hole in the steel chamber. If an equimolar mixture of He and

methane gas at 20 atmosphere and the same temperature are confined in the same chamber, what will be

the partial pressure of He and methane after 1.0 hour. Assume rate of diffusion to be linear function of

gas pressure and inverse function of square root of molar masses.

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

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CaCO ( ) CaO( ) + CO ( )3 2s s g .

The equilibrium vapour pressure of CO2 at 700°C and 950°C are 22.6 and 1830 mm of Hg. Calculate

∆ ∆H S° °and for the reaction.

PROBLEM 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?

PROBLEM 241 The internal engine of a 1200 kg car is designed to run on octane whose enthalpy of

combustion is 5510 kJ/mol. If the car is moving up a slope, calculate the maximum height to which the

car can be driven on 2.0 gallon of the fuel. Assume the cylinder temperature is 2200°C and the exit

temperature is 760°C and ignore all form of friction. The mass of 1.0 gallon of fuel is 3.1 kg.

PROBLEM 242 One gram sample of oxygen undergoes free expansion from 0.75 L to 3.0 L at 298 K.

Calculate ∆ ∆S q W H, , , and ∆E.

PROBLEM 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 ∆ ∆S Eand and

∆H, C / Rvm = ( )5 2 .

PROBLEM 244 A sample of 0.0133 mole of an ideal gas, initially at 5.00 atm, expands isothermally and

reversibly from 3.00 L to 10 L. Calculate ∆ ∆S G, and ∆H.

PROBLEM 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 Rv =1.5 . Calculate values of ∆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.

PROBLEM 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 CP for each gas is ( )5 2/ R, determine

∆S (mixing).

PROBLEM 247 For chloroform gas CPM is expressed as:

CPM = + × − ×

− −24.9 14.8 T T JK mol2 –1 –110 9 102 5 .

Assuming this gas to be ideal, determine entropy change involved in heating 2.0 mole of gas from

volume 100 L at 500 K to a volume of 70 Lit. at 700 K.

PROBLEM 248 For N 2 ( )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.

PROBLEM 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 CV = +18.8 0.021T JK mol

–1 –1 ,

determine ∆ ∆ ∆E H S, and .

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PROBLEM 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.

PROBLEM 251 One mole of an ideal gas at 25°C is subjected to a reversible isoentropic expansion until

final temperature reached to 75°C. If the initial pressure was 1.0 atm, determine final pressure

C / RV = ( )3 2 .

PROBLEM 252 A flask containing 1.00 mol of N 2 at 4.00 atm and 298 K was connected to a flask

containing 1.00 mol of N 2 gas at 2.00 bar and 298 K. The gases were allowed to mix isothermally.

Determine the entropy change for the system.

PROBLEM 253 One mole of solid iron was vaporized in an oven at 3500 K. If iron boils at 3133 K and

enthalpy of vaporization is 349 JK mol–1 –1 , determine ∆S system , ∆ ∆S Ssurroundings universeand .

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