Question $4$:

D$15.$ A partial condenser takes vapor leaving the top of a distillation column and condenses a portion of it$.$ The vapor portion of mole fraction $y_D$ is removed as the distillate product. The liquid portion of mole fraction $x_0$ is returned to the column as reflux. The liquid and vapor leaving partial condensers and partial reboilers can be assumed to be in equilibrium. A distillation column with a partial condenser and a partial reboiler is separating $300$kmol$/$h of a mixture that is $30$mol$\%$ ethanol and $70$mol$\%$ water and is a saturated liquid. We desire a $98\%$ recovery of the ethanol in the vapor distillate and an $8\mathrm{.}1\%$ recovery of ethanol in the bottoms. If $\frac{L_0}{D}=2\mathrm{.}0$ find the optimum feed location and the total number of equilibrium stages.