\(10.0 \mathrm{kmol}\) of a \(40.0 \mathrm{~mol} \%\) methanol and \(60.0 \mathrm{~mol} \%\) water mixture is processed in a normal batch distillation system with a still pot that acts as an equilibrium stage and a column with two equilibrium stages (total of three equilibrium contacts). The column has a total condenser, and reflux is a saturated liquid. The column is operated with a varying reflux ratio so that \(\mathrm{x}_{\mathrm{D}}\) is held constant. We desire a final still pot concentration of 8.0 \(\mathrm{mol} \%\) methanol, and distillate should be \(84.0 \mathrm{~mol} \%\) methanol. Pressure is \(1 \mathrm{~atm}\), and \(\mathrm{CMO}\) is valid.

a. What initial external reflux ratio, \(\mathrm{L}_{0} / \mathrm{D}\), must be used?

b. What final external reflux ratio must be used?

c. How much distillate product is withdrawn, and what is the value of \(\mathrm{W}_{\text {final }} ?\)