Chapter 11.11, Problem 5E

Interpretation Introduction

Interpretation:

Estimate the system pressure, vapor phase composition and excess molar Gibbs free for this system.

Concept Introduction:

Write the expression to obtain the liquid mole fraction of component 2 $\left(x_2\right)$.

$x_2=1-x_1$

Here, liquid mole fraction of component 1 is $x_1$.

Write the expression to obtain the activity coefficient of component 1 $\left({\gamma }_1\right)$.

$\ln {\gamma }_1=A{x}_2^2$

Here, Margules equation parameter is $A$.

Write the expression to obtain the activity coefficient of component 2 $\left({\gamma }_2\right)$.

$\ln {\gamma }_2=A{x}_1^2$

Write the expression to obtain the system pressure $\left(P\right)$.

$P={\gamma }_1{x}_1{P}_1^{sat}+{\gamma }_2{x}_2{P}_2^{sat}$

Here, vapor pressure of component 1 is $P_1^{sat}$, and vapor pressure of component 2 is $P_2^{sat}$.

Write the expression to obtain the vapor mole fraction of component 1 $\left(y_1\right)$.

$y_1=\frac{{\gamma }_1{x}_1{P}_1^{sat}}{{\gamma }_1{x}_1{P}_1^{sat}+{\gamma }_2{x}_2{P}_2^{sat}}$

Write the expression to obtain the vapor mole fraction of component 2 $\left(y_2\right)$.

$y_2=1-y_1$

Write the expression to obtain the excess molar Gibbs free for the system $\left(G^E/RT\right)$.

$\frac{G^E}{RT}=A{x}_1{x}_2$