A distillation column is separating \(100.0 \mathrm{kmol} / \mathrm{h}\) of a saturated vapor feed that is \(30.0 \mathrm{~mol} \%\) ethanol, \(25.0 \mathrm{~mol} \% \mathrm{i}\)-propanol, \(35.0 \mathrm{~mol} \% \mathrm{n}-\) propanol, and \(10.0 \mathrm{~mol} \% \mathrm{n}\)-butanol at a pressure of \(1.0 \mathrm{~atm}\). We want a \(98.6 \%\) recovery of i-propanol in the distillate and \(99.2 \%\) recovery of npropanol in the bottoms. The column has a total condenser and a partial reboiler. For parts \

(b, c\), and

d, use the FUG method. If we choose \(\mathrm{n}\)-propanol as the reference, the relative volatilities are ethanol \(=2.17\), i-propanol \(=1.86\), n-propanol \(=1.0\), and n-butanol \(=0.412\). These relative volatilities can be assumed to be constant.

a. Find \(D, B, x_{D, i}\), and \(x_{B, i}\).

b. Find \(\mathrm{N}_{\text {min }}\) and \(\mathrm{N}_{\mathrm{F}, \text { min }}\).

c. Find \((\mathrm{L} / \mathrm{D})_{\min }\). A spreadsheet is highly recommended to find \(\phi\).

d. If \(\mathrm{L} / \mathrm{D}=1.10(\mathrm{~L} / \mathrm{D})_{\min }\), find \(\mathrm{N}\) and the feed stage.