A distillation column is fed with a liquid mixture of 25.0 mole % benzene, 30 %

Question

A distillation column is fed with a liquid mixture of 25.0 mole % benzene, 30 % toluene, and 45 % xylene. The bottom product from the distillation column contains 97 mole % xylene and no benzene. The other stream (upper one) contains 29 % benzene and it is fed to a second distillation column. The upper product of the second distillation column contains 95 % of the benzene entered into the first column and no xylene. The bottom product of the second column contains 4 mole % benzene. All the percentages are mole percents. Draw a flow chart and label Write the unknowns and equations, find degree of freedom Complete the material balance choosing a basis and calculate molar flow rates and molar compositions of all the streams.

Explanation / Answer

Feed to the distillation column = 100 mol/hr

There are 3 variables and 3 independent equation can be written for overall system.

Overall balance   B+T+X= 100, B= Benzene, T =toluene and X = xylene

There is no benzene in the bottom stream from the 1st distillation column. So all the benzene is carried along with the upperstream. Hence Benzene in the upper stream =100*0.25= 25 moles/hr

This correspond to 29 mole% Benzene, feed to second distillation column= 25/0.29=86 moles/hr

Rest of   X   and T in upper stream = 86-25= 61 moles/hr ( unknown)

The feed to 1st distillation column= 100 moles/hr. Hence F= D+W, D is top and W= bottoms

Bottom from 1st distillation column= 100-86= 14 moles/hr.It does not contain any benzene

There is 97% xylene in it . Xylene =14*0.97= 13.58 mole and toluene= 14-13.58= 0.42 moles

Composition : X= 97% and T= 3%

Feed to 1st distillation column, B= 25, T= 30 and X= 45

Top products now contains ( moles) X= 45-13.58= 31.42, T= 30-0.42= 29.58, B= 25 mole/hr

moles

Composition , X= 31.42/86=0.3653 , T= 29.58/86=0.3439 and B= 25/86=0.291

2nd distillation column

Feed = 86 moles/hr, X= 31.42, T= 29.58 and B= 25

The upper product contains 95% of benzene entering the 1st distillation column. This is equal to

B =25*0.95= 23.75, X in top = 31.42

Flow rate in the bottom =86-(23.75-31.42)= 30.83 moles/hr

B in the bottoms = 25-23.75= 1.25 moles/hr

Balance has to be T = 30.83-1.25= 29.58 moles/hr

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