A distillation column with a total condenser is separating a feed that is \(30 \mathrm{~mol} \%\) acetone from ethanol. Distillate \(\mathrm{x}_{\mathrm{D}}=0.90\), and bottoms \(\mathrm{x}_{\mathrm{B}}=0.13\), both mole fractions acetone. Assume \(\mathrm{CMO}\) is valid. \(\mathrm{L} / \mathrm{V}=0.8\). Boilup ratio is \(v / \mathrm{B}=1.0\).

a. Find the composition of the liquid leaving the fifth stage below the total condenser.

b. The column has a partial reboiler that acts as an equilibrium contact. Find the vapor composition leaving the second stage above the partial reboiler.

c. Find optimum feed plate location, total number of stages, and required \(\mathrm{q}\) value of feed.
Equilibrium data for acetone (A) and ethanol at 1 atm (Perry et al., 1963, pp. 13\(4)\):

0 YA O TC 78.3- 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.50 0.60 0.70 0.80 0.90 1.0 0.262 0.348 0.417 0.478 0.524 0.566 0.605 0.674 0.739 0.802 0.865 0.929 1.0 63.6 - 60.4 59.1 58.0 57.0 56.1 67.3 65.9 -