Chapter 13.13, Problem 19P

Interpretation Introduction

Interpretation:

The values for the double tangency.

Concept Introduction:

The Gibbs free energy of the system as a result of the mixing process is,

$\begin{array}{l}\Delta {\underset{\_}{G}}_{mix}={\underset{\_}{G}}^E+RT{x}_1\ln \left(x_1\right)+RT{x}_2\ln \left(x_2\right)\\ \frac{\Delta {\underset{\_}{G}}_{mix}}{RT}=\frac{{\underset{\_}{G}}^E}{RT}+x_1\ln \left(x_1\right)+RT{x}_2\ln \left(x_2\right)\end{array}$

Here, Gibbs free energy of the system as a result of the mixing process is $\Delta {\underset{\_}{G}}_{mix}$, excess molar Gibbs free energy of the mixture is ${\underset{\_}{G}}^E$, gas constant is $R$, temperature is $T$, Margules parameters are $A_{21}\text{and}{A}_{12}$ respectively, liquid mole fraction of component 1 is $x_1$, and liquid mole fraction of component 2 is $x_2$.