We wish to separate ethanol from water from two different feed solutions in a distillation column with a total condenser and a partial reboiler, at a column pressure of \(1 \mathrm{~atm}\). One of the feed solutions, a saturated vapor, flows at the rate of \(200 \mathrm{kmol} / \mathrm{h}\) and contains \(30 \mathrm{~mol} \%\) ethanol. The other feed, a subcooled liquid, flows at the rate of \(300 \mathrm{kmol} / \mathrm{h}\) and contains \(40 \mathrm{~mol} \%\) ethanol. One mol of vapor must condense inside the column to heat up \(4 \mathrm{~mol}\) of the second feed to its boiling point. We desire a bottoms product that is \(2 \mathrm{~mol} \%\) ethanol and a distillate product that is \(72 \mathrm{~mol} \%\) ethanol. The reflux ratio is 1.0; VLE data are available in Table 6.2. The feeds are to be input at their optimum feed locations. Find the optimum feed locations and the total number of equilibrium stages required.

Data From Table 6.2:-

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Table 6.2 VLE for the System Ethanol-Water at 1 atm Ethanol mol fraction in liquid, x Ethanol mol fraction in gas, y* Temp. (K) 0.000 0.000 373.10 0.0721 0.3891 362.10 0.1238 0.4704 358.40 0.2377 0.5445 355.80 0.2608 0.5580 355.40 0.3965 0.6122 353.80 0.5198 0.6599 352.80 0.5732 0.6841 352.40 0.6763 0.7385 351.84 0.7472 0.7815 351.51 0.8943 0.8943 351.25 1.000 1.000 351.40 Source: Data from Wankat (1988).