Chapter 15, Problem 99A

Interpretation Introduction

Interpretation:

Free energy change, ${\text{ΔG}}_{\text{system}}$ for each process is to be calculated and to state the process is spontaneous or nonspontaneous.

Concept introduction:

Free energy change, ${\text{ΔG}}_{\text{system}}$ is the difference between the system’s change in enthalpy ( ${\text{ΔH}}_{\text{system}}$ ) and the product of the kelvin temperature and the change in entropy ( ${\text{TΔS}}_{\text{system}}$ ). That is,

${\text{ΔG}}_{\text{system}}\text{=}{\text{ΔH}}_{\text{system}}-{\text{TΔS}}_{\text{system}}$

Answer to Problem 99A

a. ${\text{ΔG}}_{\text{system}}$ is positive, therefore the reaction is non-spontaneous.

b. ${\text{ΔG}}_{\text{system}}$ is negative, therefore the reaction is spontaneous.

c. ${\text{ΔG}}_{\text{system}}$ is positive, therefore the reaction is non-spontaneous.

Explanation of Solution

a. Given information:

$\begin{array}{c}{\text{ΔH}}_{\text{system}}=\text{145kJ,}\text{T}=\text{293K,}\\ {\text{ΔS}}_{\text{system}}\text{=195J/K}\\ {\text{ΔS}}_{\text{system}}=\text{0}\text{.195kJ/K}\end{array}$

As already stated,

$\begin{array}{c}{\text{ΔG}}_{\text{system}}={\text{ΔH}}_{\text{system}}-{\text{TΔS}}_{\text{system}}\\ {\text{ΔG}}_{\text{system}}=\text{145kJ}-\text{293K×0}\text{.195kJ/K}\\ {\text{ΔG}}_{\text{system}}=\text{87}\text{.865kJ}\end{array}$

Since, ${\text{ΔG}}_{\text{system}}$ is positive, therefore the reaction will be non-spontaneous.

b. Given information:

$\begin{array}{c}{\text{ΔH}}_{\text{system}}=-\text{232kJ,}\text{T}=\text{273K,}\\ {\text{ΔS}}_{\text{system}}=\text{138J/K}\\ {\text{ΔS}}_{\text{system}}=\text{0}\text{.138kJ/K}\end{array}$

As already stated,

$\begin{array}{c}{\text{ΔG}}_{\text{system}}={\text{ΔH}}_{\text{system}}-{\text{TΔS}}_{\text{system}}\\ {\text{ΔG}}_{\text{system}}=-\text{232kJ}-\text{273K×0}\text{.138kJ/K}\\ {\text{ΔG}}_{\text{system}}=-\text{269}\text{.674kJ}\end{array}$

Since, ${\text{ΔG}}_{\text{system}}$ is negative, therefore the reaction will be spontaneous.

c. Given information:

$\begin{array}{c}{\text{ΔH}}_{\text{system}}=-\text{15}\text{.9kJ,}\text{T}=\text{373K,}\\ {\text{ΔS}}_{\text{system}}=\text{-268J/K}\\ {\text{ΔS}}_{\text{system}}=\text{-0}\text{.268kJ/K}\end{array}$

As already stated,

$\begin{array}{c}{\text{ΔG}}_{\text{system}}={\text{ΔH}}_{\text{system}}-{\text{TΔS}}_{\text{system}}\\ {\text{ΔG}}_{\text{system}}=-\text{15}\text{.9kJ}-\text{373K×(}-\text{0}\text{.268kJ/K)}\\ {\text{ΔG}}_{\text{system}}=8\text{4}\text{.064kJ}\end{array}$

Since, ${\text{ΔG}}_{\text{system}}$ is positive, therefore the reaction will be non-spontaneous.

Conclusion

Because ${\text{ΔG}}_{\text{system}}$ is a measure of how favorable a reaction is, it also relates to the equilibrium constant.