We are separating 100 moles of a feed that is \(60.0 \mathrm{~mol} \%\) methanol and \(40.0 \mathrm{~mol} \%\) water by batch distillation in a system with a still pot and a column that has one equilibrium contact (two equilibrium contacts total). Start the operation with a constant reflux ratio of \(\mathrm{L} / \mathrm{D}=2 / 3\). Operate with \(\mathrm{L} / \mathrm{D}=2 / 3\) until \(\mathrm{x}_{\text {dist }}=0.70\). Then keep the distillate mole fraction constant by varying \(\mathrm{L} / \mathrm{D}\). When \(\mathrm{L} / \mathrm{D}=4.0\), stop the batch distillation.

a. Find \(\mathrm{x}_{\mathrm{W}, \text { final }}\).

b. Find \(\mathrm{W}_{\text {final }}\) and \(\mathrm{D}_{\text {total }}\).

c. Find \(\mathrm{x}_{\mathrm{D}, \text { avg }}\).