Two thousand gallons of 70 wt% ethanol in water having a specific gravity of 0.871 is to be separated at 1 atm in a batch rectifier operating at a constant distillate composition of 85 mol% ethanol with a constant molar vapor boilup rate to obtain a residual wastewater containing 3 wt% ethanol. If the task is to be completed in 24 h, allowing 4 h for charging, start-up, shutdown, and cleaning, determine: 

(a) The number of theoretical stages; 

(b) The reflux ratio when the ethanol in the still-pot is 25 mol%; 

(c) The instantaneous distillate rate in lbmol/h when the concentration of ethanol in the still-pot is 15 mol%; 

(d) The lbmol of distillate product; and 

(e) The lbmol of residual wastewater. Vapor–liquid 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.