You have been asked to separate a feed with $0\mathrm{.}25$ mole fraction $n-$butane, $0\mathrm{.}40$ mole

fraction n$-$pentane, and the rest $n-$hexane. The fractional recovery of $n-$butane in the

distillate is $98\%.$ The fraction recovery of $n-$pentane in the bottoms is $95\%.$ The feed is a

saturated vapor. You are given that: ${}_{butane-pentane}=2\mathrm{.}71$ and ${}_{\text{h}\text{e}\text{x}\text{a}\text{n}\text{e}-pentane}=0\mathrm{.}46.$

a$.$ Use the Fenske method to estimate the minimum number of stages and the

recovery of $n-$hexane in the distillate.

b$.$ Use the Underwood equations to determine the minimum reflux ratio.

c$.$ Use the Gilliland correlation to determine the number of stages $(N)$ for $\frac{L}{D}=$

$1\mathrm{.}5(\frac{L}{D}{)}_{\text{m}\text{i}\text{n}\text{.}}.($Ans$.N=12)$