Column distillation:

a$)$ A distillation column, at $1$atm, with a total condenser and a partial re$-$boiler is used to separate an ethanol $($EtOH$)$water mixture. The feed is $25$mol$\%$EtOH with a feed rate of $).$ A distillate composition of $70$mol$\%$EtOH and a bottom composition of $5$mol$\%$EtOH are required. The external reflux ratio is $2\mathrm{.}0$ and the reflux is a saturated liquid. If the constant molar overflow is assumed, find the number of equilibrium stages and the optimal feed stage. $(8$ marks, S&E $1\mathrm{.}7)$