Chapter 12.6, Problem 1E

Interpretation Introduction

Interpretation:

The second-virial coefficient of the mixture

Concept Introduction:

Write the expression to calculate the reduced temperature $\left(T_r\right)$.

$T_r=\frac{T}{T_c}$

Here, critical temperature is $T_c$ and system temperature is T.

Write the expression to calculate the virial parameter $\left(B^0\right)$.

$B^0=0.083-\frac{0.422}{T_r^{1.6}}$

Write the expression to calculate the virial parameter.

$B^1=0.139-\frac{0.172}{T_r^{4.2}}$

Write the expression to calculate the second virial coefficient.

$B{\text{'}}_1=\frac{R{T}_c\left(B^0+\omega B^1\right)}{P_c}$

Write the expression to calculate the second-virial coefficient of the mixture $\left(B{\text{'}}_m\right)$.

$B{\text{'}}_m=y_1{y}_{1}B{\text{'}}_1+y_1{y}_{2}B{\text{'}}_{12}+y_2{y}_{1}B{\text{'}}_{21}+y_2{y}_{2}B{\text{'}}_2$

Here, mole fraction of $n\text{-butane}$ in vapor phase is $y_1$, mole fraction of 1-butanol in vapor phase is $y_2$, second virial coefficient of $n\text{-butane}$ is $B{\text{'}}_1$, second virial coefficient of 1-butanol is $B{\text{'}}_2$, and cross term viral coefficient of $n\text{-butane}$ and 1-butanol is $B{\text{'}}_{21}\text{and}B{\text{'}}_{12}$.