A distillation column with a total condenser (TC) and a partial reboiler (PR) is separating a feed that is \(45.0 \mathrm{~mol} \%\) methanol and \(55.0 \mathrm{~mol} \%\) water. Feed flow rate is \(300.0 \mathrm{kmol} / \mathrm{h}\) and is a two-phase feed that is \(20 \%\) liquid. The bottoms product is \(5.0 \mathrm{~mol} \%\) methanol, and the average distillate composition is \(90.0 \mathrm{~mol} \%\) methanol. \(75.0 \%\) of the distillate product is a liquid from the TC and the other \(25.0 \%\) of the distillate product is vapor that is withdrawn from the top of the column \(\left(\mathrm{D}_{\mathrm{V}}=\mathrm{D}_{\mathrm{L}} / 3\right)\). Reflux is the same composition as the liquid distillate product. The boilup ratio \((\mathrm{v} / \mathrm{B})=2.0\). Pressure \(=1.0 \mathrm{~atm}\). CMO is valid. Use the optimum feed stage. Equilibrium data are in Table 2-8.

a. What are the mole fractions of liquid distillate \(\mathrm{x}_{\mathrm{D}}\), vapor distillate \(\mathrm{y}_{\mathrm{D}}\), and liquid reflux \(\mathrm{x}_{0}\) ?

b. Find values of \(\mathrm{B}, \mathrm{D}_{\mathrm{V}}\), and \(\mathrm{D}_{\mathrm{L}}\) in \(\mathrm{kmol} / \mathrm{h}\).

c. Determine the number of stages and the optimum feed location (stages above the PR).

d. Determine \(\mathrm{L}\) in \(\mathrm{kmol} / \mathrm{h}\).

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TABLE 2-8. Vapor-liquid equilibrium data for methanol water (p = 1 atm) (mol %) Methanol Liquid Methanol Vapor Temp., C 0 0 100 2.0 13.4 96.4 4.0 23.0 93.5 6.0 30.4 91.2 8.0 36.5 89.3 10.0 41.8 87.7 15.0 51.7 84.4 20.0 57.9 81.7 30.0 66.5 78.0 40.0 72.9 75.3 50.0 77.9 73.1 60.0 82.5 71.2 70.0 87.0 69.3 80.0 91.5 67.6 90.0 95.8 66.0 95.0 97.9 65.0 100.0 100.0 64.5