A distillation column with a partial reboiler and a total condenser operating at \(7.0 \mathrm{bar}\) is separating \(100.0 \mathrm{kmol} / \mathrm{h}\) of a saturated liquid feed that is \(25.0 \mathrm{~mol} \%\) ethane (C2), \(35.0 \mathrm{~mol} \%\) n-butane (C4), and \(40.0 \mathrm{~mol} \% \mathrm{n}\)-pentane (C5). CMO can be assumed valid, and assume that ethane does not distribute. We want \(99.2 \%\) recovery of n-butane in the distillate and \(98.3 \%\) recovery of n-pentane in the bottoms. The K values at the distillate are \(\mathrm{K}_{\mathrm{C} 2}=5.56, \mathrm{~K}_{\mathrm{C} 4}=0.655\), and \(\mathrm{K}_{\mathrm{C} 5}=0.234\). The \(\mathrm{K}\) values at the bottoms are \(\mathrm{K}_{\mathrm{C} 2}=10.67, \mathrm{~K}_{\mathrm{C} 4}=2.21\), and \(\mathrm{K}_{\mathrm{C} 5}=\) 0.993 . Use the correct average for relative volatilities based on the values of the relative volatilities calculated at distillate and bottoms.

a. Find the distillate mole fractions and the value of the distillate flow rate.

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

c. Find \((\mathrm{L} / \mathrm{D})_{\min }\).

d. Find \(\mathrm{N}\) from the Gilliland correlation for \(\mathrm{M}=1.2\).