A batch distillation column with six theoretical stages (first stage is the still pot) is charged with \(100 \mathrm{kmol}\) of a \(20 \mathrm{~mol} \%\) ethanol in water mixture at atmospheric pressure. The boil-up rate is constant at \(10 \mathrm{kmol} / \mathrm{h}\). If the distillate composition is to be maintained constant at \(80 \mathrm{~mol} \%\) ethanol by varying the reflux ratio, calculate the distillation time required to reduce the still composition to \(5 \mathrm{~mol} \%\) ethanol. Calculate the fractional recovery of ethanol in the distillate. The equilibrium distribution curve is given in 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).