A distillation column separates \(100.0 \mathrm{kmol} /\) day of a saturated liquid feed that is \(20.0 \mathrm{~mol} \%\) ethanol (E), \(35.0 \mathrm{~mol} \% \mathrm{n}\)-propanol (P), and \(45.0 \mathrm{~mol} \%\) n-butanol (But). Fractional recovery of butanol in bottoms \(=0.972\). Bottoms mole fraction butanol \(\mathrm{x}_{\mathrm{B}, \text { But }}=0.986\). Assume relative volatilities are constant: \(\alpha_{\mathrm{E}-\text { But }}=4.883, \alpha_{\mathrm{P}-\text { But }}=2.336\), and \(\alpha_{\text {But-But }}=\) 1.0 .

a. Determine the flow rates of bottoms, \(\mathrm{B}\), and of distillate, \(\mathrm{D}\), in \(\mathrm{kmol} /\) day; and determine the mole fractions of E, P, and But in the bottoms and in the distillate.

b. Find the minimum number of stages, \(\mathrm{N}_{\min }\), required for this separation.

c. List any assumption(s) you have made and justify why they are reasonable. Note that the strongest justification is a calculation, not just words.