A distillation column is separating phenol from p-cresol at \(1 \mathrm{~atm}\) pressure. Distillate is \(96 \mathrm{~mol} \%\) phenol. An external reflux ratio of \(\mathrm{L} / \mathrm{D}=4\) is used, and reflux is returned to the column as a saturated liquid. The equilibrium data can be represented by a constant relative volatility, \(\alpha_{\text {phenol-cresol }}=1.76\) (Perry et al., 1963, pp. 13-3). CMO can be assumed.

a. What is the vapor mole fraction leaving the third equilibrium stage below the total condenser? Solve this problem using an analytical, stage-by-stage calculation alternating between the operating equation and the equilibrium equation.

b. What is the liquid mole fraction leaving the sixth equilibrium stage below the total condenser? Solve this problem graphically using a McCabe-Thiele diagram plotted for \(\alpha_{p-c}=1.76\).