Vapor phase non$-$ideality.

For a binary mixture of $35\%($mol$)$ n$-$butane $(1)$ and $65\%$ n$-$hexane $(2)$ at $373K,$ determine

the fugacity coefficient of each component at $10$ bars. Use:

a$)$ Assuming ideal mixture, use the truncated form of the virial equation of state.

$Z=1+\frac{BP}{RT}$

b$)$ Using the truncated form of the virial equation of state for the gas mixture.

$Z_{\text{m}\text{i}\text{x}}=1+\frac{B_{\text{m}\text{i}\text{x}}P}{RT}$; where $B_{\text{m}\text{i}\text{x}}={\displaystyle \underset{i=1}{\overset{k}{}}}{\displaystyle \underset{j=1}{\overset{k}{}}}{y}_i{y}_j{B}_{ij}$

First derive expressions for tilde$({)}_i$ using the given EOS.

Data: At $373K,$ the second virial coefficients for this system are $B_{11}=-422c\frac{m^3}{m}ol,$

$B_{22}=-103\mathrm{.}1c\frac{m^3}{m}ol,B_{12}(B_{21})=-650c\frac{m^3}{m}ol.$