A saturated liquid mixture containing 60 mole % benzene and 40 mole % toluene is to be distilled continuously into a distillate product containing 90 mole % benzene and the bottom product containing 5 mole % benzene. The fractional distillation column will operate at approximately constant pressure of 1 atm. The reflux ratio is 2. How many theoretical plates must the column have if the feed is introduced into the eighth plate? Equilibrium data are:
x 0 0.017 0.075 0.13 0.211 0.288 0.37 0.411 0.581 0.78 1
y 0 0.039 0.161 0.261 0.393 0.496 0.591 0.632 0.777 0.9 1