A distillation column with a partial reboiler and a partial condenser is separating two feeds containing mixtures of ethanol and water. Operation is at \(1.0 \mathrm{~atm}\) and CMO is valid. Feed A is \(40 \mathrm{~mol} \%\) ethanol, is a saturated vapor, and flow rate is \(200 \mathrm{kmol} / \mathrm{h}\). Feed B is \(30 \mathrm{~mol} \%\) ethanol, is a saturated liquid, and flow rate is 250 \(\mathrm{kmol} / \mathrm{h}\). Distillate has a mole fraction \(\mathrm{y}_{\mathrm{E}, \mathrm{D}}=0.7\), and bottoms mole fraction is \(\mathrm{x}_{\mathrm{E}, \mathrm{B}}\) \(=0.02\). VLE data are in Table 2-1.

a. Find the values of the distillate and bottoms flow rates.

b. What is the minimum reflux ratio \((\mathrm{L} / \mathrm{D})_{\min }\) ?

c. Use an actual reflux ratio \(\mathrm{L} / \mathrm{D}=2(\mathrm{~L} / \mathrm{D})_{\min }\), plot the operating lines, use the optimum feed stages, and find the total number of stages needed. Count stages from the top down, and list the locations of the optimum feed stages.

d. What is the value of \((\mathrm{s} / \mathrm{B})_{\min }\) ?

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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 0.5732 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