Problem $4.[15$ points$]$

A distillation column is separating methanol and water. The column has a partial reboiler, a total condenser, and

a saturated liquid reflux. The feed rate is $152$kg$-$moles$/$hr$,$ and feed composition is $40$ mole$\%$ methanol. The feed

is a two$-$phase mixture that is $60\%$ liquid and $40\%$ vapor and will be put into the column at the optimum feed

plate. The distillate composition is $0\mathrm{.}92,$ and bottoms is $0\mathrm{.}08$ mole fraction methanol. CMO can be assumed. Use

an external reflux ratio of L$/$D $=0\mathrm{.}9.$

$4\mathrm{.}1.$ Find the value of q$,$ and plot the feed line.

$4\mathrm{.}2.$ Plot the top and bottom operating lines. do this on graphing paper and have labels and correct values. need a operating line and an equilibrium line.

$4\mathrm{.}3.$ Find the optimum feed plate location and total number of equilibrium stages.