QUESTION $3$

The excess Gibbs energy for the system chloroform $(1)+$ ethanol $(2)$ at $55C$ is well represented by the Margules

equation written as:

$\frac{g^E}{RT}=(1\mathrm{.}42x_1+0\mathrm{.}59x_2)x_1{x}_2$

$ln{}_1=x_2^2(0\mathrm{.}59+1\mathrm{.}66x_1),ln{}_2=x_1^2(1\mathrm{.}42+1\mathrm{.}66x_2)$

The vapour pressure of chloroform and ethanol at $55C$ are $82\mathrm{.}37$ and $37\mathrm{.}31$kPa respectively.

a$)$ Calculate the system pressure at a liquid phase composition of $x_1=0\mathrm{.}5$

b$)$ Calculate the system pressure at the liquid phase composition of $x_1=0\mathrm{.}5$ if one assumes the vapour phase to

be non$-$ideal and describes by the Virial EoS with virial coefficients: $B_{11}=-963c\frac{m^3}{m}ol,B_{22}=-1523$

$c\frac{m^3}{m}ol$ and $B_{12}=52c\frac{m^3}{m}ol.$