$(15\%)$ Answer the problems on the following information.

Consider a binary A$+$B mixture at vapor$-$liquid equilibrium at $300K$ and $15\mathrm{.}0$ bar. The mole fraction of component $A$ in the liquid phase is $0\mathrm{.}06.$ The mole fraction of component $B$ in the vapor phase is negligible. A series of experimental data on the compressibility factor of pure component A gas at $300K$ are curve fitted to give.

$z=1-ap+b{p}^2,P=[\frac{?}{\text{b}\text{a}\text{r}}],a=2\mathrm{.}00{10}^{-3},b=3\mathrm{.}50{10}^{-6}$

$($a$)$ Calculate the fugacity of component $A$ in the liquid phase.

$($b$)$ Calculate the Henry's constant of component A dissolved by component B liquid. That is$,$ fugacity of pure liquid component A with the properties equal to those in an infinitely dilute solution of component $B.$

$($c$)$ The vapor phase is mixed with a dissimilar gas which is insoluble in the liquid component $B.$ The mole fraction of component $A$ in the vapor phase is now $0\mathrm{.}5$ and the temperature and pressure are unchanged $(300K$ and $\frac{1\mathrm{.}5}{b}ar).$ The activity coefficient of component $A$ in the vapor phase $($relative to pure component A gas at $300K$ and $\frac{1\mathrm{.}5}{b}ar)$ was calculated as $1\mathrm{.}12.$ What is the equilibrium solubility of component $A$ in the component $B$ liquid in contact with this mixed vapor?