The fermentation of corn produces a mixture of 3.3 mol% ethyl alcohol in water. If this mixture is distilled at 1 atm by a differential distillation, calculate and plot the instantaneous-vapor composition as a function of mol% of batch distilled. If reflux with three theoretical stages (including the boiler) is used, what is the maximum purity of ethyl alcohol that can be produced by batch rectification?
Equilibrium data are given in Exercise 7.29.

Data From Exercise 7.29.

One hundred kmol of 30 mol% methanol, 30 mol% ethanol, and 40 mol% n-propanol is charged at 120 kPa to a batch rectifier consisting of a still-pot, a column with the equivalent of 10 equilibrium stages, and a total condenser. After establishing a total-reflux condition, the column begins a sequence of two operating steps, each for a duration of 15 h at a distillate flow rate of 2 kmol/h and a reflux ratio of 10. Thus, the two accumulated distillates are equal in moles to the methanol and ethanol in the feed. Neglect the liquid holdup in the condenser and column. The column pressure drop is 8 kPa, with a pressure drop of 2 kPa through the condenser. Using a simulation program with UNIFAC (§2.6.9) for liquid-phase activity coefficients, determine the composition and amount in kmol for the three cuts.