One thousand kilograms per hour of a mixture of benzene and toluene that contain

Question

One thousand kilograms per hour of a mixture of benzene and toluene that contains 50% by mass are seperated by distallation into two fractions.

The mass flow of benzene in the top stream is 450kg benzne/hour, and toluene in the bottom stream is 475 kg toulene/hour.

Write the material balance on benzene and toluene to calculate the unknown components in the output stream.

I am not very familiar with this type of process, so any qualitative explanations for the methodology of solving this problem would be greatly appreciated!

Explanation / Answer

For Benzene:

The initial flow rate is 1000kg/hr = F (say)

the distillate flow rate is 450kg.hr = D (say)

The mass flow rate balance for Benzene would be

F = D + W

where,

W is the flow rate of Benzene in the bottom.

thus W = 550kg/hr

now using the component mass balance:

FXf = DXd + WXw

where, X is the mole fraction in the subscripted stream.

Similarly For Toluene:

D = 525kg/hr

FXf' = DXd' + WXw'

Xd + Xd' = 1 and similarly,

Xw + Xw' = 1

Now we have three equations and three unknowns. Solve and get the answer.

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