\(150 \mathrm{~mol} / \mathrm{h}\) of a saturated liquid that is \(25 \mathrm{~mol} \%\) ethanol and \(75 \mathrm{~mol} \%\) water is fed to a distillation column with a total condenser and a partial reboiler. Reflux is a saturated liquid, and CMO is valid. The column has three equilibrium stages (i.e., four equilibrium contacts), and the feed stage is second below the condenser.

Bottoms is \(5 \mathrm{~mol} \%\) ethanol, and distillate is \(63 \mathrm{~mol} \%\) ethanol. VLE data are in Table 2-1. Find the required external reflux ratio.

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TABLE 2-1. Vapor-liquid equilibrium data for ethanol and water at 1 atm y and x in mole fractions XEtoh Xw YEtoh Yw T, C 0 1.0 0 1.0 100 0.019 0.981 0.170 0.830 95.5 0.0721 0.9279 0.3891 0.6109 89.0 0.0966 0.9034 0.4375 0.5625 86.7 0.1238 0.8762 0.4704 0.5296 85.3 0.1661 0.8339 0.5089 0.4911 84.1 0.2337 0.7663 0.5445 0.4555 82.7 0.2608 0.7392 0.5580 0.4420 82.3 0.3273 0.6727 0.5826 0.4174 81.5 0.3965 0.6035 0.6122 0.3878 80.7 0.5079 0.4921 0.6564 0.3436 79.8 0.5198 0.4802 0.6599 0.3401 79.7 0.5732 0.4268 0.6841 0.3159 79.3 0.6763 0.3237 0.7385 0.2615 78.74 0.7472 0.2528 0.7815 0.2185 78.41 0.8943 0.1057 0.8943 0.1057 78.15 1.00 0 1.00 0 78.30