Chapter 18, Problem 141CP

Interpretation Introduction

Interpretation:

Two different equations showing the change in Gibbs free energy are given. The derivation of $E°$ as a function of temperature for the given equations, the graphical determination of $\Delta H°$ and $\Delta S°$ from measurements of $E°$ at different temperature and the property used for designing a reference half-cell that would produce a potential relatively stable with respect to temperature is to be stated.

Concept introduction:

Gibbs free energy is basically the maximum amount of non-expansion work done. Therefore, it is represented as,

$W_{\max }=\Delta G°$

The relationship between Gibbs free energy change and cell potential is given by the formula,

$\Delta G°=-nFE{°}_{\text{cell}}$

The relation between $\Delta G°$, $\Delta H°$ and $\Delta S°$ is given as,

$\Delta G°=\Delta H°-T\Delta S°$

To determine: The derivation of $E°$ as a function of temperature for the given equations, the graphical determination of $\Delta H°$ and $\Delta S°$ from measurements of $E°$ at different temperatures and the property used for designing a reference half-cell that would produce a potential relatively stable with respect to temperature.

The relation obtained from the given equations is,

$E{°}_{\text{cell}}=T\left(\frac{\Delta S°}{nF}\right)+\left(-\frac{\Delta H°}{nF}\right)$