Chapter 20, Problem 20.68P

(a)

Interpretation Introduction

Interpretation:

For the given reaction entropy value ${\text{ΔG}}^{\text{o}}$ has to be calculated at $298K$

    $2H_{2}S\left(g\right)+2O_2\left(s\right)\underset{}{\rightleftharpoons }2H_{2}O\left(s\right)+S{O}_2\left(g\right);K=6.57\times {10}^{173}$

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

  $\begin{array}{l}{\text{ΔG}}^{\text{o}}\text{=}\text{-RTlnK}\\ \text{where,}\\ {\text{ΔG}}^{\text{o}}\text{-}\text{standard}\text{free}\text{energy}\text{change}\\ \text{R}\text{-}\text{gas}\text{constant}\text{8}\text{.314}\text{J/mol}\times \text{K}\\ \text{T}\text{-}\text{temperature}\text{298K}\\ \text{K}\text{-}\text{equilibrium}\text{constant}\text{.}\end{array}$

(b)

Interpretation Introduction

Interpretation:

For the given reaction entropy value ${\text{ΔG}}^{\text{o}}$ has to be calculated at $298K$

    $H_{2}S{O}_4\left(l\right)\underset{}{\rightleftharpoons }{H}_{2}O\left(l\right)+S{O}_3\left(g\right);K=4.46\times {10}^{-15}$

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

  $\begin{array}{l}{\text{ΔG}}^{\text{o}}\text{=}\text{-RTlnK}\\ \text{where,}\\ {\text{ΔG}}^{\text{o}}\text{-}\text{standard}\text{free}\text{energy}\text{change}\\ \text{R}\text{-}\text{gas}\text{constant}\text{8}\text{.314}\text{J/mol}\times \text{K}\\ \text{T}\text{-}\text{temperature}\text{298K}\\ \text{K}\text{-}\text{equilibrium}\text{constant}\text{.}\end{array}$