Open$-$Ended Problem $(30$ points$)$

The bubble pressure for a non$-$ideal binary mixture is $1\mathrm{.}479$ bar at $42C.$ The mole fraction of component $1$ in the liquid and vapor is $x_1=0\mathrm{.}35$ and $y_1=0\mathrm{.}578,$ respectively. The saturate pressures are $P_1^{\text{s}\text{a}\text{t}}=1\mathrm{.}3$ bar and $P_2^{\text{s}\text{a}\text{t}}=0\mathrm{.}8$ bar. The liquid can be modeled by the one parameter Margules equation:

$\frac{G^E}{RT}=A{x}_1{x}_2=x_{1}ln{}_1+x_{2}ln{}_2$

$7\mathrm{.}1$ Using the given information, find the Margules parameter A$.(10$ points$)$

$7\mathrm{.}2$ Find the bubble pressure at $42C$ and $x_1=0\mathrm{.}85,$ and the mole fraction $y_1$ of the gas phase in equilibrium with the liquid. $($If you did not find an $A,$ use $A=1\mathrm{.}6$ points$)$