Chapter 13, Problem 94IAE

Interpretation Introduction

Interpretation:

The equation $\frac{S^{\circ }}{\Delta H^{\circ }}=\frac{2}{298.15\text{}\text{K}}=0.00671{\text{K}}^{\text{-1}}$ should be proven; assuming that the constant pressure heat capacity, $C_p$ of a linear function of temperature of the form of $C_p\text{= a}T$, where, $\text{a}$ is a constant from the expression $S^{\circ }={\displaystyle \underset{0\text{}\text{K}}{\overset{298.15\text{K}}{\int }}\frac{C_p}{T}dT}\Delta H^{\circ }={\displaystyle \underset{0\text{}\text{K}}{\overset{298.15\text{K}}{\int }}{C}_{p}dT}$.

Concept introduction:

$C_p$ of a linear function of temperature of the form of $C_p\text{= a}T$, where, $\text{a}$ is a constant from the expression $S^{\circ }={\displaystyle \underset{0\text{}\text{K}}{\overset{298.15\text{K}}{\int }}\frac{C_p}{T}dT}\Delta H^{\circ }={\displaystyle \underset{0\text{}\text{K}}{\overset{298.15\text{K}}{\int }}{C}_{p}dT}$.

Integrating the above two separately, substitute $C_p\text{= a}T$ and find $\frac{S^{\circ }}{\Delta H^{\circ }}$ ratio will prove the above statement.