A distillation unit consists of a partial reboiler, a column with seven equilibrium plates, and a total

condenser. The feed is a $50$mol$\%$ mixture of benzene in toluene. It is desired to produce a distillate

containing $96$mol$\%$ benzene, when operating at $101$kPa.

$($a$)$ With saturated$-$liquid feed fed to the fifth plate from the top, calculate: $(1)$ minimum reflux ratio

$($LD$)$min; $(2)$ the bottoms composition, using a reflux ratio $(LD)$ of twice the minimum; and $(3)$ moles of

product per $100$ moles of feed.

$($b$)$ Repeat part $($a$)$ for a saturated vapor fed to the fifth plate from the top.