A distillation column with two feeds is separating ethanol and water at a pressure of 1.0 atm. The column has a total condenser with saturated liquid reflux and a partial reboiler. Feed (1) is a saturated liquid and is 42 mol% ethanol. Feed (2) flow rate is F2=100 kmol/hF_2 = 100 \text{ kmol/h}F2=100 kmol/h, contains 18 mol% ethanol and is a two-phase mixture that is 30% vapor. The external reflux ratio is 1/2, and the distillate flow rate is D=80 kmol/hD A distillate mole fraction of xD=0.66 mole fraction ethanol and a bottoms xW=0.04 mole fraction ethanol. Assume that constant molar flow rate is valid.
Determine:
i) The flow rates of Feed (1) and Bottoms (F1 and W).
ii) The liquid and vapor flow rates in the middle section.
iii) The operating lines for the three sections.
iv) Find both optimum feed locations.
v) Total number of equilibrium stages needed.