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A distillation column with a total condenser and a partial reboiler is separating $250$ moles$/$hr of a feed that is $80$ mole$\%$ benzene and $20$ mole$\%$ ethanol. The feed enters the column as a two$-$phase mixture that is $30\%$ vapor.

A distillate composition of $40$ mole$\%$ ethanol is needed, and a bottom of $2\mathrm{.}5$ mole$\%$ ethanol. Reflux is returned as a saturated liquid, and CMO$($constant molar overflow$)$ can be assumed. An external reflux ratio of L$/$D $=1\mathrm{.}0$ is used. Pressure is $101\mathrm{.}3$kPa$/1$atm.

$1.$ The optimum feed location and the # of equilibrium stages needed?

$2.$ If the fourth stage below the condenser is used as the feed stage, # of equilibrium stages needed for the separation?

$3.$ Using the optimum feed location, what is the maximum distillate concentration that can be obtained?