A company wishes to distill a 0.80 mole fraction ethanol (0.20 mole fraction wat

Question

A company wishes to distill a 0.80 mole fraction ethanol (0.20 mole fraction water) solution. To aid in the distillation process, a 0.95 mole fraction benzene (0.05 mole fraction water) mixture containing fresh benzene and a recovered benzene solution is added. The plant wishes to product 90.0 moles/hour of a 0.999 mole fraction ethanol (0.001 mole fraction benzene) mixture from a distillation column. The other product from the distillation is water and benzene mixture. This mixture is sent to a separator which produces a 14.1 mole/hour stream of water. The other stream from the separator contains 0.91 mole fraction of benzene (0.09 mole fraction of water) mixture, some of which is recycled back to the fresh benzene stream. Using balance equations, find the flowrate (mole/hour) of fresh benzene entering the system, the recycle line, and the water-benxene mixture entering the separator.

Explanation / Answer

All the ethanol entering the system is removed from the top of the distillation column.

Ethanol recovered from top = 90*0.999=89.91 moles/hr, amount of water = 90-89.91= 0.09 moles/hr

Feed mixture contains 89.91 moles/hr ethanol. Feed contains 0.8 mole fraction ethanol.

Hence feed to distillation column= 89.91/0.8=112.3875 moles/hr

Water in the feed = 112.3875*0.2= 22.4775 moles/hr

Water entering the system is removed from ethanol products, as water from separator and from the bottom from separator.

Water entering = water in ethanol product + water from top of separator+ water from bottom of separator

22.4775= 90*0.001+14.1+ water from bottom of separator

Water from bottom of separator= 22.4775-0.09-14.1 = 8.2875 moles/hr

The bottom from separator contains 0.09 mole fraction water.

Hence bottoms from separator flow rate= 8.2875/0.09=92.08 moles/hr

Benzene in the bottoms = 92.09*0.91 = 83.8 moles/hr

This is the only source from benzene is removed. Hence Benzene that needs to be added as fresh feed = 83.8 moles/hr

Let R= Recycle

Writing benzene balance across the reactor

R*0.91+83.8= (R+83.8)*0.95, = 0.95R+79.61

R*0.04 = 83.8-79.61=4.19, R = 104.75 moles/hr

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