Chapter 14.6, Problem 4E

(A)

Interpretation Introduction

Interpretation:

The equilibrium constant.

Concept Introduction:

Write the expression to obtain the equilibrium constant.

$K_T=\exp \left(-\frac{\Delta {\underset{\_}{G}}_T^0}{RT}\right)$

Here, standard change in Gibbs free energy is $\Delta {\underset{\_}{G}}_T^0$, gas constant is $R$, and temperature is $T$.

Write the expression of short-cut van’t Hoff equation.

$\frac{\Delta {\underset{\_}{G}}_T^0}{RT}=\frac{\Delta {\underset{\_}{G}}_R^0}{R{T}_R}+\left(\frac{\Delta {\underset{\_}{H}}_R^0}{R}\right)\left(\frac{1}{T}-\frac{1}{T_R}\right)$

Here, standard change in Gibbs free energy at reference temperature is $\Delta {\underset{\_}{G}}_R^0$, standard enthalpy of a reaction at reference temperature is $\Delta {\underset{\_}{H}}_R^0$, and reference temperature is $T_R$.

Write the expression of standard change in Gibbs free energy at reference temperature.

$\Delta {\underset{\_}{G}}_R^0=\Delta {\underset{\_}{G}}_{f,{\text{N}}_{\text{2}}{\text{O}}_4}^0-2\Delta {\underset{\_}{G}}_{f,\text{NO}}^0-\Delta {\underset{\_}{G}}_{f,{\text{O}}_2}^0$

Here, standard Gibbs free energy of ${\text{N}}_{\text{2}}{\text{O}}_4$ is $\Delta {\underset{\_}{G}}_{f,{\text{N}}_{\text{2}}{\text{O}}_4}^0$, standard Gibbs free energy of $\text{NO}$ is $\Delta {\underset{\_}{G}}_{f,\text{NO}}^0$, and standard Gibbs free energy of ${\text{O}}_2$ is $\Delta {\underset{\_}{G}}_{f,{\text{O}}_2}^0$.

Write the expression of standard enthalpy of reaction at reference temperature.

$\Delta {\underset{\_}{H}}_T^0=\Delta {\underset{\_}{H}}_{f,{\text{N}}_{\text{2}}{\text{O}}_4}^0-2\Delta {\underset{\_}{H}}_{f,\text{NO}}^0-\Delta {\underset{\_}{H}}_{f,{\text{O}}_2}^0$

Here, the standard enthalpy of reaction of ${\text{N}}_{\text{2}}{\text{O}}_4$ is $\Delta {\underset{\_}{H}}_{f,{\text{N}}_{\text{2}}{\text{O}}_4}^0$, the standard enthalpy of reaction of $\text{NO}$ is $\Delta {\underset{\_}{H}}_{f,\text{NO}}^0$, and the standard enthalpy of reaction of ${\text{O}}_2$ is $\Delta {\underset{\_}{H}}_{f,{\text{O}}_2}^0$.

(B)

Interpretation Introduction

Interpretation:

The equilibrium constant.

Concept Introduction:

Write the expression of standard change in Gibbs free energy at reference temperature.

$\Delta {\underset{\_}{G}}_T^0=2\Delta {\underset{\_}{G}}_{f,{\text{O}}_3}^0-3\Delta {\underset{\_}{G}}_{f,{\text{O}}_2}^0$

Here, standard Gibbs free energy of ${\text{O}}_3$ is $\Delta {\underset{\_}{G}}_{f,{\text{O}}_3}^0$.

Write the expression of standard enthalpy of reaction at reference temperature.

$\Delta {\underset{\_}{H}}_T^0=2\Delta {\underset{\_}{H}}_{f,{\text{O}}_3}^0-3\Delta {\underset{\_}{H}}_{f,{\text{O}}_2}^0$

Here, standard enthalpy of reaction of ${\text{O}}_3$ is $\Delta {\underset{\_}{H}}_{f,{\text{O}}_3}^0$.

(C)

Interpretation Introduction

Interpretation:

The equilibrium constant.

Concept Introduction:

Write the expression of standard change in Gibbs free energy at reference temperature.

$\Delta {\underset{\_}{G}}_R^0=2\Delta {\underset{\_}{G}}_{f,S{\text{O}}_3}^0-2\Delta {\underset{\_}{G}}_{f,{\text{SO}}_3}^0-\Delta {\underset{\_}{G}}_{f,{\text{O}}_2}^0$

Here, standard Gibbs free energy of ${\text{SO}}_3$ is $\Delta {\underset{\_}{G}}_{f,S{\text{O}}_3}^0$, and standard Gibbs free energy of ${\text{SO}}_2$ is $\Delta {\underset{\_}{G}}_{f,S{\text{O}}_2}^0$.

Write the expression of standard enthalpy of reaction at reference temperature.

$\Delta {\underset{\_}{H}}_R^0=2\Delta {\underset{\_}{H}}_{f,S{\text{O}}_3}^0-2\Delta {\underset{\_}{H}}_{f,{\text{SO}}_3}^0-\Delta {\underset{\_}{H}}_{f,{\text{O}}_2}^0$

Here, standard enthalpy of reaction of ${\text{SO}}_3$ is $\Delta {\underset{\_}{H}}_{f,S{\text{O}}_3}^0$, and standard enthalpy of reaction of ${\text{SO}}_2$ is $\Delta {\underset{\_}{H}}_{f,{\text{SO}}_3}^0$.