For Example 4-3 prove that:

Example 4-3

A distillation column with a total condenser and a partial reboiler is separating an ethanol-water mixture. Feed is 20 mol% ethanol, feed rate is 1000 kmol/h, and feed temperature is 80°F. Distillate is 80 mol% ethanol, and bottoms is 2 mol% ethanol. External reflux ratio is 5/3. Reflux is a saturated liquid, and CMO can be assumed. Pressure is 1 atm. Find optimum feed plate location as stages above the reboiler and total number of equilibrium stages.

a. The top operating line and the \(y=x\) line intersect at \(y=x=x_{D}\).

b. The bottom operating line and the \(\mathrm{y}=\mathrm{x}\) line intersect at \(\mathrm{y}=\mathrm{x}=\mathrm{x}_{\mathrm{B}}\).