We are separating a mixture of benzene, toluene, and xylene in a distillation rectifying column. The column has a total condenser and no reboiler. The feed is a saturated vapor that is fed into the bottom stage of the column, flow rate \(\mathrm{F}=150 \mathrm{kmol} / \mathrm{h}\), and feed is \(52.0 \mathrm{~mol} \%\) benzene, \(38.5 \mathrm{~mol} \%\) toluene, and remainder xylenes. Pressure is 1.0 atm, CMO is valid, and the relative volatilities are constant: \(\alpha_{\text {Ben-Tol }}=\) 2.22, \(\alpha_{\mathrm{Tol}-\mathrm{Xy}}=2.01\). The column is at \(1.0 \mathrm{~atm}\). The reflux ratio \(\mathrm{L} / \mathrm{D}=9\), and the distillate is 0.007 mole fraction toluene.

a. Based on the best assumption you can make, use mass balances and CMO to calculate: B, mole fractions in bottoms, D, and mole fractions in distillate.

b. Although the column has a feed and bottoms removal, we can still operate at total reflux ( \(\mathrm{D}=0\) so that \(\mathrm{L} / \mathrm{V}=1\) ). At total reflux, how many stages are required to obtain the separation achieved in part a?

c. Use the Fenske equation to estimate xylene mole fraction in the distillate.

d. What is the minimum reflux ratio for separation in part

a, but with xylene distillate mole fraction from part \(\mathrm{c}\) ?

e. Use the Gilliland correlation to estimate the actual number of stages if \(\mathrm{L} / \mathrm{D}=9\).