A charge of 1,000 kmol of a mixture 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 the equivalent of six theoretical plates and the distillate composition is to be maintained at 80 mol% ethanol by varying the reflux ratio, determine:
(a) The time in hours for the residue to reach an ethanol mole fraction of 0.05,
(b) The kmol of distillate obtained when the condition of part (a) is achieved,
(c) The minimum- and maximum-reflux ratios during the rectification period, and
(d) The variation of the distillate rate in kmol/h during the rectification period. Assume constant molar overflow, neglect liquid holdup, and obtain vapor-liquid equilibrium data from Exercise 7.29.