Chapter 9.8, Problem 12P

Interpretation Introduction

Interpretation:

To derive the expression for the molar Gibbs free energy of mixing for an ideal gas mixture

Concept Introduction:

Gibbs free energy:

The fundamental property relation for molar Gibbs free energy.

$\Delta {\underset{\_}{G}}^{ig}=\Delta {\underset{\_}{H}}^{ig}-T\Delta {\underset{\_}{S}}^{ig}$

Here, temperature is T, molar Gibbs free energy of mixing assumed as an ideal gas is $\Delta {\underset{\_}{G}}^{ig}$, molar enthalpy of mixing assumed  as an ideal gas is $\Delta {\underset{\_}{H}}^{ig}$ and molar entropy of mixing modeled as an ideal gas is $\Delta {\underset{\_}{S}}^{ig}$.

The molar entropy of mixing assumed as an ideal gas.

$\begin{array}{c}\Delta {\underset{\_}{S}}^{ig}=\underset{\_}{S}-{\underset{\_}{S}}^{ig}\\ =-R{y}_1\ln y_1-R{y}_2\ln y_2\end{array}$

Here, molar entropy of an ideal gas is ${\underset{\_}{S}}^{ig}$, molar entropy of the mixture is $\underset{\_}{S}$, gas constant is R, mole fraction of component 1$y_1$ and mole fraction of component 2 is $y_2$.