A distillation column uses the optimum feed stage. A liquid side stream is withdrawn on the third stage below the total condenser at a rate of \(15.0 \mathrm{kmol} / \mathrm{h}\). Feed rate is \(100.0 \mathrm{kmol} / \mathrm{h}\) of a \(60.0 \mathrm{~mol} \%\) acetone and \(40.0 \mathrm{~mol} \%\) ethanol twophase mixture that is \(20 \%\) vapor. Distillate is \(90.0 \mathrm{~mol} \%\) acetone, and bottoms is \(10.0 \mathrm{~mol} \%\) acetone. We operate with an external reflux ratio of \(\mathrm{L} / \mathrm{D}=3\). A partial reboiler is used. VLE data are in Problem 4.D7. Find mole fraction ethanol in the side stream \(\mathrm{x}_{\mathrm{S}}\), optimum feed location, and total number of equilibrium contacts needed.

Problem 4.D7

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D7.* A distillation column with a total condenser is separating a feed that is 30 mol% acetone from ethanol. Distillate xD = 0.90, and bottoms xp = 0.13, both mole fractions acetone. Assume CMO is valid. L/V = 0.8. Boilup ratio is /B = 1.0. . Find the composition of the liquid leaving the fifth stage below the total condenser. . The column has a partial reboiler that acts as an equilibrium contact. Find the vapor composition leaving the second stage above the partial reboiler. Find optimum feed plate location, total number of stages, and required q value of feed. Equilibrium data for acetone (A) and ethanol at 1 atm (Perry et al., 1963, pp. 13-4): XA O 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.50 0.60 0.70 0.80 0.90 1.0 YA O 0.262 0.348 0.417 0.478 0.524 0.566 0.605 0.674 0.739 0.802 0.865 0.929 1.0 TC 78.3 - 67.3 65.9 63.6 - 60.4 59.1 58.0 57.0 56.1