A distillation column with a total condenser and a partial reboiler is separating ethanol and water at \(1 \mathrm{~kg} / \mathrm{cm}^{2}\) pressure. Feed is \(32 \mathrm{~mol} \%\) ethanol and is at \(30^{\circ} \mathrm{C}\). Feed flow rate is \(100 \mathrm{kmol} / \mathrm{h}\). The distillate product is a saturated liquid, and distillate is \(80 \mathrm{~mol} \%\) ethanol. The condenser removes \(2,065,113 \mathrm{kcal} / \mathrm{h}\). The bottoms is \(4 \mathrm{~mol} \%\) ethanol. Assume that CMO is valid. Find the number of stages and the optimum feed stage location. Data: \(\mathrm{C}_{\mathrm{PL}, \mathrm{EtOH}}=24.65 \mathrm{cal} /\left(\mathrm{mol}^{\circ} \mathrm{C}\right)\) at \(0^{\circ} \mathrm{C}\). The enthalpy-composition diagram is given in Figure 2-4, and VLE data are in Table 2-1. Note: Watch your units.

100 04 1630 500 500 100