Chapter 4, Problem 4.2P

Interpretation Introduction

Interpretation:

The standard molar entropies of water ice, liquid, and vapour at 298 K are 37.99, 69.91 and $188.83J{K}^{-1}mo{l}^{-1}$ respectively. On a single graph, it has to be shown that how the Gibbs energies of each of these phases vary with temperature.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by $\Delta G$.

Molal Gibbs free energy can be determined using the following formulas as show below,

$\Delta G=RT\ln \frac{V_1}{V_2}\boxed{\begin{array}{l}Where,\\ \Delta G:ChangeinGibbsfreeenergy\\ R:Gascons\tan t\\ T:Temperature\\ V_1:Initialvolume\\ V_2:Finalvolume\end{array}}$

$\Delta G=\Delta H-T\Delta S\boxed{\begin{array}{l}where,\\ \Delta H:Enthalpychange\\ T:Temperature\\ \Delta S:Changeinentropy\end{array}}$

For an isomermal reaction enthalpy change is zero, thus this equation can be written as,

$\begin{array}{c}\Delta G=-T\Delta S\\ =-T\left(C_P\ln \frac{T_2}{T_1}-R\ln \frac{P_2}{P_1}\right)\\ =-T\left(0-R\ln \frac{P_2}{P_1}\right)\end{array}$