A distillation column with a total condenser and a partial reboiler is separating acetone from ethanol. A desired distillate and bottom composition are $x_D=0\mathrm{.}9$ and $x_B=0\mathrm{.}13,$ respectively. Under constant overflow assumptions, operating conditions are $\frac{L}{V}=0\mathrm{.}8,$ and $V_B=1.$ The feed composition is $Z_F=0\mathrm{.}3($all concentrations are mole

fraction of more volatile component$).$

Phase equilibrium data for acetone and ethanol at $1$atm are given below.

Determine:

$2\mathrm{.}1.$ The total number of stages.

$2\mathrm{.}2.$ The optimum feed plate location.

$2\mathrm{.}3.$ Required q$-$value of the feed.

$2\mathrm{.}4.$ The composition of the liquid leaving the $5^{th}$stage.