Example $1$

A saturated vapor comprising of $35\%($mol$)$ ethanol $($the balance is water vapor$),$ is fed to a distillation column operated at $1$atm. The desired composition of the distillate is at least $70\%($mol$)$ ethanol, and the bottom is at most $2\%($mol$)$ ethanol. A total condenser is used to provide a saturated liquid distillate and reflux. A partial reboiler is used to provide boilup. The external reflux ratio is $2\mathrm{.}5$ and the overall tray efficiency is $55\%.$

a$.$ Determine the optimum number of physical trays.

b$.$ What is the feed location for the equilibrium stages?

c$.$ Determine the minimum reflux ratio.

d$.$ Determine the minimum number of equilibrium stages for the column.