Chapter 13, Problem 93IAE

Interpretation Introduction

Interpretation:

The temperature that dissociates ${\text{COCl}}_{\text{2}}\text{(g)}$ 15% according to the reaction ${\text{COCl}}_{\text{2}}\text{(g)}\rightleftharpoons {\text{Cl}}_{\text{2}}\text{(g)}+\text{CO(g)}$ should be determined.

Concept introduction:

The Gibbs energy, G, for a system is defined by the equation,

$G=H-TS$

The Gibbs energy change, ${\Delta }_{r}G$ for a process at constant T is

${\Delta }_r{G}^{\circ }={\Delta }_r{H}^{\circ }-T{\Delta }_r{S}^{\circ }$

Relationship of to the Equilibrium Constant K represents by following equation,

$\begin{array}{l}{\Delta }_r{G}^{\circ }=-\text{R}T\ln \text{K }\\ \text{From the above two equations,}\\ -\text{R}T\ln \text{K =}{\Delta }_r{H}^{\circ }-T{\Delta }_r{S}^{\circ }\\ \ln \text{K = }\frac{{\Delta }_r{H}^{\circ }-T{\Delta }_r{S}^{\circ }}{-\text{R}T}\\ \ln \text{K = }\frac{-{\Delta }_r{H}^{\circ }}{\text{R}T}+{\frac{{\Delta }_{r}S}{\text{R}}}^{\circ }\end{array}$

With the use of the above equation twice for two different temperatures, following equation can be derived,

$\ln \frac{{\text{K}}_{\text{2}}}{{\text{K}}_{\text{1}}}=-\frac{{\Delta }_r{H}^{\circ }}{\text{R}}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)$