$11\mathrm{.}7-6.$

Distillation of Multicomponent Alcohol Mixture. A feed of $30$ mol $\%$ methanol $($A$),20\%$ ethanol $($B$),15\%$ n$-$propanol $($C$),$ and $35\%$ n$-$butanol $($D$)$ is distilled at $101\mathrm{.}32$kPa abs pressure to give a distillate composition containing $95\mathrm{.}0$mol$\%$ methanol and a residue composition containing $5\mathrm{.}0\%$ methanol and the other components as calculated. The feed is below the boiling point, so that $q=1\mathrm{.}1.$ The operating reflux ratio is $3\mathrm{.}0.$ Assume that Raoult's law applies and use vapor$-$pressure data from Problem $11\mathrm{.}7-3.$ Calculate the following:

a$.$ Composition and amounts of distillate and bottoms for a feed of $100mo\frac{l}{h}.$

b$.$ Top and bottom temperatures and number of stages at total reflux. $($Also$,$ calculate the distribution of the other components.$)$

c$.$ Minimum reflux ratio, number of stages at $R=3\mathrm{.}00,$ and feed$-$tray location.

$A32$: Ans. $(a)D=27\mathrm{.}778mo\frac{l}{h},x_{AD}=0\mathrm{.}95,x_{BD}=0\mathrm{.}05,x_{CD}=0,x_{DD}=0$;$W=72\mathrm{.}222mo\frac{l}{h},x_{AW}=$

$0\mathrm{.}0500,x_{BW}=0\mathrm{.}2577,x_{CW}=0\mathrm{.}2077,x_{DW}=0\mathrm{.}4846$;$(b)65\mathrm{.}5C$ top temperature $,94\mathrm{.}3C$

bottom, $N_m=9\mathrm{.}21$ stages, $x_{CD}=3\mathrm{.}0410-5,x_{DD}=8\mathrm{.}7910-7(trace$ compositions$)$; $(c)R_m=$