# An equimolar liquid mixture of benzene and toluene is separated

An equimolar liquid mixture of benzene and toluene is separated into two product streams by distillation. A process flowchart and a somewhat oversimplified description of what happens in the process follow:

Inside the column a liquid stream flows downward and a vapor stream rises. At each point in the column some of the liquid vaporizes and some of the vapor condenses. The vapor leaving the top of the column, which contains 97mole% benzene, is completely condensed and split into two equal fractions: one is taken off as the overhead product stream, and the other (the reflux) is recycled to the top of the column. The overhead product stream contains 89.2% of the benzene fed to the column. The liquid leaving the bottom of the column is fed to a partial re-boiler in which 45% of it is vaporized. The vapor generated in the re-boiler (the boil up) is recycled to become the rising vapor stream in the column, and the residual re-boiler liquid is taken off as the bottom product stream. The compositions of the streams leaving the re-boiler are governed by the relation yB/(1 – yB) xB/ (1 – xB) = 2.25 where yB and xB are the mole fractions of benzene in the vapor and liquid streams, respectively.

(a) Take a basis of 100 mol fed to the column. Draw and completely label a flowchart, and for each of four systems (overall process. column, condenser, and re-boiler), do the degree-of-freedom analysis and identify a system with which the process analysis might appropriately begin (one with zero degrees of freedom).

(b) Write in order the equations you would solve to determine all unknown variables on the flowchart, circling the variable for which you would solve in each equation. Do not do the calculations in this part.

(c) Calculate the molar amounts of the overhead and bottoms products, the mole fraction of benzene in the bottoms product, and the percentage recovery of toluene in the bottoms product (100 x moles toluene in bottoms/mole toluene in feed).