\(200.0 \mathrm{kmol} / \mathrm{h}\) of saturated vapor feed, \(80.0 \mathrm{~mol} \%\) water and \(20.0 \mathrm{~mol} \%\) n-butanol, is condensed and sent to a decanter. The water layer is the distillate product \(\mathrm{D}\), and the butanol (top) layer is sent to a stripping column that has a partial reboiler. The bottoms from the stripping column (B, the butanol product) is \(4.0 \mathrm{~mol} \%\) water. Vapor leaving the stripping column is condensed and sent to the decanter. Equilibrium data are in Table 8-5. Find:

a. Flow rates \(\mathrm{D}\) and \(\mathrm{B}\).
b. If \(v / B=4.0\), find the number of equilibrium stages (step off from the bottom up).
c. Determine \((\mathrm{z} / \mathrm{B})_{\min }\) for this separation.

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TABLE 8-5. VLE data for water and n-butanol at 1.0 atm mol% water Liquid Vapor TC Liquid Vapor TC 0.0 0.0 117.0 57.3 75.0 92.8 3.9 26.7 111.5 97.5 75.2 92.7 4.7 29.9 110.6 98.0 75.6 93.0 5.5 32.3 109.6 98.2 75.8 92.8 7.0 35.2 108.8 98.5 77.5 93.4 25.7 62.9 97.9 98.6 78.4 93.4 27.5 64.1 97.2 98.8 80.8 93.7 29.2 65.5 96.7 99.2 84.3 95.4 30.5 66.2 96.3 99.4 88.4 96.8 49.6 73.6 93.5 99.7 92.9 98.3 50.6 74.0 93.4 99.8 95.1 98.4 55.2 75.0 92.9 99.9 98.1 99.4 56.4 75.2 92.9 100.0 100.0 100.0 57.1 74.8 92.9