Chapter 18, Problem 18.107QP

(a)

Interpretation Introduction

Interpretation:

For the given reaction the value of ${\text{ΔG}}^{\text{o}}\text{and}{\text{ΔS}}^{\text{o}}$ has to be calculated at $\text{458}{}^{\text{o}}\text{C}$.

Concept introduction:

Standard free energy change:

Standard free energy change is measured by subtracting the product of temperature and standard entropy change from the standard enthalpy change of a system.

$\begin{array}{l}{\text{ΔG}}^{\text{o}}\text{=}{\text{ΔH}}^{\text{o}}\text{-}{\text{TΔS}}^{\text{o}}\\ \text{where,}\\ {\text{ΔG}}^{\text{o}}\text{-}\text{standard}\text{free}\text{energy change}\\ {\text{ΔH}}^{\text{o}}\text{-}\text{standard}\text{enthalpy}\text{change}\\ {\text{ΔS}}^{\text{o}}\text{-}\text{standard}\text{entropy change}\text{and T}\text{-}\text{temperature}\text{.}\end{array}$

Relationship between $\Delta G^{o}andK$:

The relationship between free energy change and equilibrium constant is given by

$\begin{array}{l}{\text{ΔG}}^{\text{o}}\text{=}\text{-RTlnK}\\ \text{where,}\\ {\text{ΔG}}^{\text{o}}\text{-}\text{standard}\text{free}\text{energy}\text{change}\\ \text{R}\text{-}\text{gas}\text{constant}\\ \text{T}\text{-}\text{temperature}\text{and}\text{K}\text{-}\text{equilibrium}\text{constant}\text{.}\end{array}$

(b)

Interpretation Introduction

Interpretation:

For the given reaction the value of ${\text{ΔG}}^{\text{o}}\text{and}{\text{ΔS}}^{\text{o}}$ has to be calculated at $\text{458}{}^{\text{o}}\text{C}$.

Concept introduction:

Standard free energy change:

Standard free energy change is measured by subtracting the product of temperature and standard entropy change from the standard enthalpy change of a system.

$\begin{array}{l}{\text{ΔG}}^{\text{o}}\text{=}{\text{ΔH}}^{\text{o}}\text{-}{\text{TΔS}}^{\text{o}}\\ \text{where,}\\ {\text{ΔG}}^{\text{o}}\text{-}\text{standard}\text{free}\text{energy change}\\ {\text{ΔH}}^{\text{o}}\text{-}\text{standard}\text{enthalpy}\text{change}\\ {\text{ΔS}}^{\text{o}}\text{-}\text{standard}\text{entropy change}\text{and T}\text{-}\text{temperature}\text{.}\end{array}$

Relationship between $\Delta G^{o}andK$:

The relationship between free energy change and equilibrium constant is given by

$\begin{array}{l}{\text{ΔG}}^{\text{o}}\text{=}\text{-RTlnK}\\ \text{where,}\\ {\text{ΔG}}^{\text{o}}\text{-}\text{standard}\text{free}\text{energy}\text{change}\\ \text{R}\text{-}\text{gas}\text{constant}\\ \text{T}\text{-}\text{temperature}\text{and}\text{K}\text{-}\text{equilibrium}\text{constant}\text{.}\end{array}$