We plan to distill \(1100 \mathrm{kmol} /\) hour of a saturated vapor stream that is \(16 \mathrm{~mol} \%\) ethanol and \(84 \mathrm{~mol} \%\) water. The column has another feed that is \(900 \mathrm{kmol} /\) hour of a saturated liquid stream that is also \(16 \mathrm{~mol} \%\) ethanol and \(84 \mathrm{~mol} \%\) water. Both feed streams are sent to their optimum feed locations in the column. The column has a partial condenser and a partial reboiler and operates at \(1.0 \mathrm{~atm}\). We desire a vapor distillate with \(\mathrm{y}_{\mathrm{D}}=0.60\) mole fraction ethanol and a liquid bottoms with \(\mathrm{x}_{\mathrm{B}}\) \(=0.01\) mole fraction ethanol. Assume that CMO is valid. VLE data are in Table 2-1.

a. Find distillate flow rate \(\mathrm{D}\) and bottoms flow rate \(\mathrm{B}\).

b. If the boilup ratio \(r / B=1 / 3\), find the two optimum feed locations and the total number of stages required (step off stages from the bottom up).

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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