\(10.0 \mathrm{kmol}\) of a feed with \(\mathrm{x}_{\mathrm{F}}=0.4\) (mole fraction methanol) and the remainder water is sent to a batch distillation system with a large still pot that is an equilibrium contact, a distillation column that acts as two equilibrium contacts (total three equilibrium contacts), and a total condenser. \(\mathrm{p}=1.0 \mathrm{~atm}\). We operate with a constant \(\mathrm{x}_{\mathrm{D}}=0.8\) as we increase \(\mathrm{L} / \mathrm{D}\). The batch operation is continued until \(\mathrm{L} / \mathrm{D}=4.0\). CMO is valid. VLE data are in Table 2-8. Find:

a. \(\mathrm{x}_{\mathrm{w} \text {,final }}\).

b. \(\mathrm{W}_{\text {final }}\) and \(\mathrm{D}_{\text {total }}\).

c. Initial L/D.

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0 TABLE 2-8. Vapor-liquid equilibrium data for methanol water (p = 1 atm) (mol %) Methanol Liquid 0 Methanol Vapor Temp., C 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