A continuous, steady-state distillation column with a total condenser and a partial reboiler is separating \(100 \mathrm{kmol} / \mathrm{h}\) of a \(55 \mathrm{~mol} \%\) methanol, \(45 \mathrm{~mol} \%\) water feed at one atmosphere. We desire a distillate product that is \(90 \mathrm{~mol} \%\) methanol and a bottoms product that is \(5 \mathrm{~mol} \%\) methanol. VLE data are in Table 2-8 Assume CMO.

a. If the external reflux ratio \(\mathrm{L} / \mathrm{D}=1.25\), plot the top operating line.

b. If the boilup ratio \(v / B=2.0\), plot the bottom operating line.

c. Step off stages, starting at the bottom, with the partial reboiler. Use the optimum feed stage. Report the optimum feed stage and the total number of stages.

d. Plot the feed line. Calculate its slope. Calculate q. What type of feed is this?

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