A distillation column is separating \(1000 \mathrm{~mol} / \mathrm{h}\) of a \(32 \mathrm{~mol} \%\) ethanol, \(68 \mathrm{~mol} \%\) water mixture at atmospheric pressure. The feed enters as a subcooled liquid that will condense \(1 \mathrm{~mol}\) of vapor in the feed plate for every \(4 \mathrm{~mol}\) of feed. The column has a total condenser and uses open steam heating. We desire a distillate with an ethanol content of \(75 \mathrm{~mol} \%\), and a bottoms product with \(10 \mathrm{~mol} \%\) ethanol. The steam used is saturated at \(1 \mathrm{~atm}\). Table 6.2 gives VLE data for this system.

(a) Find the minimum reflux ratio.

(b) Find the number of real stages and the optimum feed location for \(R=1.5 R_{\min }\) if the Murphree vapor efficiency is 0.7 for all stages.

(c) Find the steam flow rate used.

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).