A distillation column with open steam heating is separating a feed that is 80.0 \(\mathrm{mol} \%\) methanol and \(20.0 \mathrm{~mol} \%\) water in a steady-state operation. The column has 10 stages, a total condenser, and the feed is on stage 5 . Operation is at \(1.0 \mathrm{~atm}\). The steam is pure water and is a saturated vapor. CMO is assumed to be valid. At 2:16 a.m. 25 days ago the feed and distillate flows were shut off \((\mathrm{D}=\mathrm{F}=0)\), but the steam rate was unchanged and the total condenser is still condensing the vapor to a saturated liquid. The column has now reached a new steady-state operation. VLE data are in Table 2-8.

a. What is the current methanol mole fraction in the bottoms?

b. At the new steady state, estimate the methanol mole fraction in the reflux liquid leaving the total condenser.

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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