Chapter 13.12, Problem 12E

Interpretation Introduction

Interpretation:

Stability criterion equation in 13.16 has to be proved.

Concept introduction:

Stability criterion equation in 13.16 has to be proved using the expression for the binary mixture excess Gibbs energy and the relationship of Gibbs-Duhem.

The expression for the binary mixture excess Gibbs energy is given as follows:

$\frac{G^E}{RT}=x_1\ln {\gamma }_1+x_2\ln {\gamma }_2$

Here, gas constant is R, temperature is T, activity coefficients of binary mixture are ${\gamma }_1\text{and}{\gamma }_2$, and liquid phase mole fraction of binary mixture is $x_1\text{and}{x}_2$ respectively.

The relationship of Gibbs-Duhem is given as follows.

$x_1\frac{d\ln {\gamma }_1}{d{x}_1}+x_2\frac{d\ln {\gamma }_2}{d{x}_1}=0$