A mixture containing 60 mol% benzene and 40 mol% toluene is subjected to batch, differential distillation at 1 atm, under three different conditions:

1. Until the distillate contains 70 mol% benzene

2. Until 40 mol% of the feed is evaporated

3. Until 60 mol% of the original benzene leaves in the vapor phase Using α = 2.43, determine for each of the three cases:

(a) The number of moles in the distillate for 100 mol of feed.

(b) The compositions of distillate and residue.