Chapter 13, Problem 70E

Interpretation Introduction

Interpretation:

The value of K at $100{}^{\circ }\text{C}$ needs to be determined.

Concept introduction:

The Gibb’s equation of thermodynamic purposed a relation between $\text{ΔS}$, $\text{ΔH}$ and $\text{ΔG}$ with Temperature. The mathematical expression of Gibb’s equation can be written as

$\text{ΔrG}°\text{ = ΔrH}°\text{ - TΔrS}°$

With the help of this equation, one can predict the change in $\text{ΔS}$, $\text{ΔH}$ and $\text{ΔG}$.

$\begin{array}{l}\text{ΔrH° = ΔrH°(product) - ΔrH°(reactant) }\\ \text{ΔrG° = ΔrG°(product) - ΔrG°(reactant) }\end{array}$

The relation between equilibrium constant and $\Delta \text{rG}°$ can be written as

$\text{ΔrG° = - 2}\text{.303 RT log K}$

The Van’t Hoff equation can be show as:

$\text{ln}\left(\frac{\text{K1}}{\text{K2}}\right)\text{ = }\frac{\text{ΔrH°}}{\text{R}}\left(\frac{\text{1}}{\text{T2}}\text{-}\frac{\text{1}}{\text{T1}}\right)$

With the help of equation, one can calculate the equilibrium constant at different temperature values.