Let's assume that a mixture of benzene $(1)$ and toluene $(2)$ at $T=105C$ and $P=120$

kPa obeys Raoult's law:

$y_{1}P=x_1{P}_1$ sat

$y_{2}P=x_2{P}_2$ sat

a$)$ Adding eqns. $1$ and $2,$ calculate $x_1$ for this mixture at the given $T$ and $P.$ Once you

solve for $x_1,$ evaluate $x_2.$

b$)$ Next, calculate $y_1$ and $y_2.$

c$)$ What is the value of the fugacity of component $1$ in the vapor mixture $((hat(f_1^v)))?$

d$)$ What is the value of the fugacity of component $1$ in the liquid mixture $(hat(f{)}_1^l)?$

e$)$ The following is a "flash" equipment that operates at constant T and P$.$ At T and P$,$ a

mixture of liquid and vapor separates into a pure vapor mixture $(V)$ and a pure liquid

mixture $(L).$ One mole of a mixture $F$ of liquid and vapor enters the flash tank at a mole

fraction $z_1=0\mathrm{.}33.V$ and $L$ are the number of moles of the vapor and liquid mixtures

leaving the flash.

Write a total mole balance for the flash tank.

Write a mole balance for component $1.$

Using these two mole balance equations, solve for $V$ and $L$ as functions of $z_1,x_1,$

and $y_1$

Using your values of $y_1,y_2,x_1,x_2,$ calculated in $($a$)$ and $($b$),$ what are $V$ and $L?$