Chapter 13, Problem 67E

Interpretation Introduction

Interpretation:

The temperature calculated in example 13-12 using the van’t Hoff equation needs to be compared with the temperature calculated from the data in Appendix D and following equation:

${\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}{\text{ = Δ}}_{\text{r}}{\text{H}}^{\text{o}}{\text{ - TΔ}}_{\text{r}}{\text{S}}^{\text{o}}$

And,

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

Concept introduction:

The Gibb’s equation of thermodynamics proposed 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 we can predict the change in $\text{ΔS}$, $\text{ΔH}$ and $\text{ΔG}$. The relation between enthalpy, equilibrium constant and temperature can be written as

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

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