A distillation column is being designed to process a feed that is 10.0 \(\mathrm{mol} \%\) ethanol and \(90.0 \mathrm{~mol} \%\) water. The feed rate is \(100.0 \mathrm{kmol} / \mathrm{h}\), and the feed is a saturated liquid at a pressure of \(5.0 \mathrm{~atm}\). The column has a partial reboiler, a total condenser, \(\mathrm{N}=10\) in Aspen notation, \(\mathrm{D}=10.0\), and \(\mathrm{L} / \mathrm{D}=2.0\). Do tray sizing for a sieve try with one pass, \(0.4572-\mathrm{m}\) tray spacing, \(85.0 \%\) approach to flood (use Jim Fair's flooding calculation method), and default values for other design variables.

a. Operate the column at \(1.0 \mathrm{~atm}\). Find and report the optimum feed stage (based on maximum separation). For the optimum feed stage, report \(\mathrm{Q}_{\text {reboiler }}, \mathrm{Q}_{\text {condenser }}\), the distillate and bottoms mole fractions ethanol, and the maximum tray diameter.
b. Operate the column at \(3.0 \mathrm{~atm}\). Find and report the optimum feed stage (based on maximum separation). For the optimum feed stage, report \(\mathrm{Q}_{\text {reboiler }}, \mathrm{Q}_{\text {condenser }}\), the distillate and bottoms mole fractions ethanol, and the maximum tray diameter.
c. Operate the column at \(5.0 \mathrm{~atm}\). Find and report the optimum feed stage (based on maximum separation). For the optimum feed stage, report \(\mathrm{Q}_{\text {reboiler }}, \mathrm{Q}_{\text {condenser }}\), the distillate and bottoms mole fractions ethanol, and the maximum tray diameter.
d. Compare your results.
D1. Which pressure gives the best separation? Why?
D2. Which pressure has the lowest \(\mathrm{Q}_{\text {reboiler }}\) ? Why?
D3. Which pressure has the lowest absolute value of \(\mathrm{Q}_{\text {condenser }}\) ? Why?
D4. Which pressure has the smallest diameter column? Why?
e. When operating and capital costs are considered, the optimum pressure to obtain the same purity is usually between 1.0 and 6.8 atm. Speculate on the reasons for this.