We have a column separating benzene, toluene, and cumene. The column has a total condenser, a total reboiler, and nine equilibrium stages. The feed is \(25.0 \mathrm{~mol} \%\) benzene, \(30.0 \mathrm{~mol} \%\) toluene, and 45.0 \(\mathrm{mol} \%\) cumene. Feed rate is \(100 \mathrm{~mol} / \mathrm{h}\), and the feed is a saturated liquid at \(1.0 \mathrm{~atm}\). The column pressure is \(1.0 \mathrm{~atm}\). The equilibrium data can be represented as constant relative volatilities: \(\alpha_{\mathrm{BT}}=2.5, \alpha_{\mathrm{TT}}=\) 1.0 , and \(\alpha_{\mathrm{CT}}=0.21\). We desire \(99.0 \%\) recovery of toluene in the distillate and \(98.0 \%\) recovery of cumene in the bottoms.

a. Determine the required external reflux ratio.

b. If \(\alpha_{\mathrm{BT}}=2.25\) instead of 2.5 , what is the value of \(L / D\) ?