One thousand kmol of 20 mol% ethanol in water is to undergo batch rectification at 101.3 kPa at a vapor boilup rate of 100 kmol/h. If the column has six theoretical stages and the distillate composition is to be maintained at 80 mol% ethanol by varying the reflux ratio, determine the: 

(a) Time in hours for the residue to reach an ethanol mole fraction of 0.05; 

(b) Kmol of distillate obtained when the condition of part (a) is achieved; 

(c) Minimum and maximum reflux ratios during the rectification period; and 

(d) Variation of the distillate rate in kmol/h during the rectification period. Assume constant molar overflow, neglect liquid holdup, and obtain equilibrium data from 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.