Binary Distillation$-$calculation of product compositions $(30$ points$)$

A mixture of $54\mathrm{.}5$mol$\%$ benzene in chlorobenzene at its bubble point is fed continuously to the

bottom stage of a column containing two equilibrium stages at a flowrate of $100$kmo$\frac{l}{h}r.$ The

column is equipped with a partial reboiler and a total condenser. Sufficient heat is supplied to the

reboiler to give $\frac{?}{\text{b}\text{a}\text{r}}\frac{V}{F}=0\mathrm{.}855,$ and the reflux ratio $LD=0\mathrm{.}50.$ The equilibrium data for the column

pressure is provided below.

Equilibrium data at column pressure $-$ liquid $($x$)$ and vapor $($y$)$ mole fractions of benzene

a$)$ What is the relative volatility associated with the column pressure for the provided

equilibrium data $($Hint: fit the data to the function $y=\frac{x}{x+1-x}$ to obtain the value of $-$

review HW$2$ problem $1$B solution$)$

b$)$ Evaluate the bottoms and distillate flowrates

c$)$ What are the compositions of the distillation and bottoms products?

Hint $1$: Draw out the diagram of the column, and figure out what flowrates you know based on

mass balances. You should be able to figure out all of the flowrates, $\frac{?}{\text{b}\text{a}\text{r}}(L)\frac{,}{b}ar(V),L,V,B,D,$ to

determine the slopes of you operating lines.

Hint $2$: Where do the rectifying section operating line $($ROL$),$ stripping section operating line

$($SOL$)$ and feed operating line $($q$-$line$)$ cross in this case? How can you use this information to

write an equation with $x_D$ and $x_B?$

Hint $3$: Don't forget your overall component balance!