Problem $5.[30$ points$]$

A distillation column with a total condenser and a partial reboiler is separating $250$mole$\frac{s}{h}r$ of a feed that is $80$

mole $\%$ benzene and $20$ mole$\%$ ethanol. The feed enters the column as a two$-$phase mixture that is $30\%$ vapor.

A distillate composition of $40$ mole$\%$ ethanol is desired, and a bottoms of $2\mathrm{.}5$ mole$\%$ ethanol. Reflux is returned

as a saturated liquid, and CMO can be assumed. An external reflux ratio of $\frac{L}{D}=1\mathrm{.}0$ is used. Pressure $=$

$101\mathrm{.}3$kPa.

$5\mathrm{.}1.$ What is the optimum feed location and how many equilibrium stages are needed?

$5\mathrm{.}2.$ If the fourth stage below the condenser is used as the feed stage, how many equilibrium stages are needed

for the separation?

$5\mathrm{.}3.$ If you use the optimum feed location, what is the maximum distillate concentration that can be obtained? please use a mcCabe Thiele Txy diagram graphed along with the equilibrium curve. needs to be hand drawn. thank you!