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Chemical Thermodynamics and Electrochemistry: Homework Problems and Solutions - Prof. S. K, Assignments of Physical Chemistry

A comprehensive set of homework problems and solutions covering key concepts in chemical thermodynamics and electrochemistry. It delves into topics such as equilibrium constants, gibbs free energy, standard potentials, and the debye-huckel limiting law. The problems provide practical applications of these principles, enhancing understanding and problem-solving skills in these areas.

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2023/2024

Uploaded on 12/07/2024

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Chem 113A Homework #6
Solutions
1. If the reaction ๐น๐‘’๐‘(๐‘ )+3 2๐ป2(๐‘”)โ‡Œ๐น๐‘’(๐‘ )+๐‘๐ป3(๐‘”)
โ„ comes to equilibrium at
a total pressure of 1 atm, analysis of the gas shows that at 700 K and 800 K,
๐‘ƒ๐‘๐ป3
๐‘ƒ๐ป2=2.165 and 1.083, respectively, if only ๐ป2(๐‘”) was initially present in the
gas phase and ๐น๐‘’๐‘(๐‘ ) was in excess.
a) Calculate ๐พ๐‘ƒ at 700 K and 800 K.
b) Calculate โˆ†๐ป๐‘…
ยฐ and โˆ†๐‘†๐‘…
ยฐ at 700 K and 800 K (assuming they are both
independent of temperature).
c) Calculate โˆ†๐บ๐‘…
ยฐ for this reaction at 298 K.
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Chem 113A Homework # 6

Solutions

  1. If the reaction ๐น๐‘’๐‘

2

3

comes to equilibrium at

a total pressure of 1 atm, analysis of the gas shows that at 700 K and 800 K,

๐‘ƒ

๐‘๐ป 3

๐‘ƒ

๐ป 2

= 2. 165 and 1. 083 , respectively, if only ๐ป

2

(๐‘”) was initially present in the

gas phase and ๐น๐‘’๐‘(๐‘ ) was in excess.

a) Calculate ๐พ

๐‘ƒ

at 700 K and 800 K.

b) Calculate โˆ†๐ป

๐‘…

ยฐ

and โˆ†๐‘†

๐‘…

ยฐ

at 700 K and 800 K (assuming they are both

independent of temperature).

c) Calculate โˆ†๐บ

๐‘…

ยฐ

for this reaction at 298 K.

  1. Consider the Daniell cell, for which the overall cell reaction is ๐‘๐‘›(๐‘ ) +

2 +

2 +

. The concentrations of CuSO 4

and ZnSO 4

are

2.50 and 1.10 ร— 10

  • 3

m, respectively.

a) Calculate E setting the activities of the ionic species equal to their molalities

b) Calculate ๐›พ

ยฑ

for each of the halfโ€“cell solutions using the Debyeโ€“Huckel

limiting law.

c) Calculate E using the mean ionic activity coefficients determined in part (b).

  1. Consider the gas phase reaction H 2

+ I

2

= 2HI at equilibrium at T= 870 K and p =

1 bar. If ๏„Gหš (870K, 1 bar) = - 48.96 kJ, determine K, ฮพ and the equilibrium

amounts of H 2

, I

2

and HI (in mol) if the intial composition was nหš(H 2

mol, nหš(I 2

) = 0.400 mol, and nหš(HI) = 0.200 mol.

ln ๐พ

๐‘

ยฐ

48. 96 ร— 10

3

J/mol

๐‘

  1. 768

This equilibrium constant was calculated in the pressure standard state (since we

use the table value for ๏„ Gยฐ). We convert to the mole fraction standard state to

calculate the equilibrium composition.

๐‘ฅ

๐‘

ยฐ

โˆ†๐œˆ

๐‘

ยฐ

Let the extent of reaction at equilibrium be denoted ๐œ‰. The number of moles at

equilibrium and the mole fractions for each reactant and product are:

๐ป

2

๐ป 2

ยฐ

๐ผ

2

๐ผ 2

ยฐ

๐ป๐ผ

๐ป๐ผ

ยฐ

๐ป

2

๐‘› ๐ป

2

๐‘›

  1. 3 โˆ’๐œ‰

  2. 9

๐ผ

2

๐‘› ๐ผ

2

๐‘›

  1. 4 โˆ’๐œ‰

  2. 9

๐ป๐ผ

๐‘›

๐ป๐ผ

๐‘›

  1. 2 + 2 ๐œ‰

  2. 9

๐‘ฅ

๐ป๐ผ

2

๐ป

2

๐ผ

2

2

2

2

2

The roots of the equation are ๐œ‰ = 0. 411 ๐‘š๐‘œ๐‘™ and ๐œ‰ = 0. 293 ๐‘š๐‘œ๐‘™. Since a value

for the extent of reaction at equilibrium ๐œ‰ = 0. 411 ๐‘š๐‘œ๐‘™ is unphysical (it leads to

negative moles for H 2

and I 2

at equilibrium), the extent of reaction at equilibrium

is:

Finally, the equilibrium compositions are:

๐ป

2

๐ผ

2

๐ป๐ผ

  1. Calculate the equilibrium constant of the reaction ๐ถ๐‘‚(๐‘”) + ๐ป

2

2

Given that, for the production of liquid formaldehyde from the same reactants,

๐‘Ÿ

0

๐พ๐ฝ

๐‘š๐‘œ๐‘™

at 298 K and that the vapor pressure of formaldehyde is

1500 Torr at that temperature.

  1. The principal ions of human blood plasma and their molar concentrations are

mNa

= 0.14 m, mCl

= 0.10 m, mHCO 3

โˆ’ = 0.025 m. Calculate the ionic strength

of blood plasma.

[

2

2

2

)] = 0. 1325

  1. Consider the water gas shift equilibrium ๐ถ๐‘‚(๐‘”) + ๐ป

2

2

2

At 1000 K, the equilibrium composition of the reaction mixture is

Substance ๐ถ๐‘‚

2

2

2

Mole % 27.1 27.1 22.9 22.

Calculate ๐พ

๐‘ƒ

and โˆ†๐บ

๐‘…

ยฐ

at 1000 K.

๐‘ฅ

๐‘Ÿ

ยฐ

) ( 1000 ๐พ) ln( 0. 714 ) = 2. 80 ร— 10

3

  1. Consider the Daniell cell, for which the overall cell reaction is ๐‘๐‘›

2 +

2 +

. The concentrations of CuSO 4

and ZnSO 4

are 2.50 and 1.10 ร— 1 0

3

m, respectively.

a) Calculate E setting the activities of the ionic species equal to their molalities.

b) Calculate ๐›พ

ยฑ

for each of the halfโ€“cell solutions using the Debyeโ€“Huckel

limiting law.

c) Calculate E using the mean ionic activity coefficients determined in part (b).

  1. In this problem, you calculate the error in assuming that โˆ†๐ป ๐‘…

ยฐ

is independent of T for a

specific reaction. The following data are given at 25ยบC:

a) From Equation 6.64, โˆซ

๐‘‘ ln ๐พ

๐‘ƒ

๐พ ๐‘ƒ

(๐‘‡

๐‘“

)

๐พ

๐‘ƒ

(๐‘‡

0

)

1

๐‘…

โˆ†๐ป

๐‘…

ยฐ

๐‘‡

2

๐‘‡

๐‘“

๐‘‡

0

๐‘‘๐‘‡. To a good

approximation we can assume that the heat capacities are independent of

๐‘ƒ

๐‘‚

2

ยฐ

= 9. 48 ร— 10

โˆ’ 4

๐‘‚

2

= 9. 48 ร— 10

โˆ’ 4

c) What value would you obtain if you assume that โˆ†๐ป ๐‘…

ยฐ

is independent of temperature

in the range 298.15 K to 1350 K?

๐‘ƒ

ln ๐พ

๐‘ƒ

๐‘‚ 2

= 1. 66 ร— 10

โˆ’ 3