40. A liquid mixture containing 30.0 mole% benzene (B), 25.0% toluene (T), and the balance xylene (X) isfed to a distillation column. The bottoms product contains 98.0 mole% X and no B, and 96.0% of the Xin the feed is recovered in this stream. The overhead product is fed to a second column. The overheadproduct from the second column contains 97.0% of the B in the feed to this column. The composition ofthis stream is 94.0 mole% B and the balance T.(a) Draw and label a flowchart of this process and do the degree-of-freedom analysis to prove that foran assumed basis of calculation, molar flow rates and compositions of all process streams can becalculated from the given information. Write in order the equations you would solve to calculateunknown process variables. In each equation (or pair of simultaneous equations), circle thevariable(s) for which you would solve. Do not do the calculations.(b) Calculate (i) the percentage of the benzene in the process feed (i.e., the feed to the first column) thatemerges in the overhead product from the second column and (ii) the percentage of toluene in theprocess feed that emerges in the bottom product from the second column.

Question
Asked Mar 4, 2019
40. A liquid mixture containing 30.0 mole% benzene (B), 25.0% toluene (T), and the balance xylene (X) is
fed to a distillation column. The bottoms product contains 98.0 mole% X and no B, and 96.0% of the X
in the feed is recovered in this stream. The overhead product is fed to a second column. The overhead
product from the second column contains 97.0% of the B in the feed to this column. The composition of
this stream is 94.0 mole% B and the balance T.
(a) Draw and label a flowchart of this process and do the degree-of-freedom analysis to prove that for
an assumed basis of calculation, molar flow rates and compositions of all process streams can be
calculated from the given information. Write in order the equations you would solve to calculate
unknown process variables. In each equation (or pair of simultaneous equations), circle the
variable(s) for which you would solve. Do not do the calculations.
(b) Calculate (i) the percentage of the benzene in the process feed (i.e., the feed to the first column) that
emerges in the overhead product from the second column and (ii) the percentage of toluene in the
process feed that emerges in the bottom product from the second column.
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40. A liquid mixture containing 30.0 mole% benzene (B), 25.0% toluene (T), and the balance xylene (X) is fed to a distillation column. The bottoms product contains 98.0 mole% X and no B, and 96.0% of the X in the feed is recovered in this stream. The overhead product is fed to a second column. The overhead product from the second column contains 97.0% of the B in the feed to this column. The composition of this stream is 94.0 mole% B and the balance T. (a) Draw and label a flowchart of this process and do the degree-of-freedom analysis to prove that for an assumed basis of calculation, molar flow rates and compositions of all process streams can be calculated from the given information. Write in order the equations you would solve to calculate unknown process variables. In each equation (or pair of simultaneous equations), circle the variable(s) for which you would solve. Do not do the calculations. (b) Calculate (i) the percentage of the benzene in the process feed (i.e., the feed to the first column) that emerges in the overhead product from the second column and (ii) the percentage of toluene in the process feed that emerges in the bottom product from the second column.

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Expert Answer

Step 1

Part (a)

The basis of the given process is taken as 100 mol/h of feed mixture.

The process involves distillation of benzene-toluene-xylene mixture, so ‘distillation column’ is one of the process unit. 100 mol/h mixture is fed to the distillation column; thus, it is the ‘input stream’. Benzene (B) is 30.0% by mol, toluene (T) is 25.0% by mol and rest of the mixture is xylene (X). Thus, benzene per  is 0.300, toluene per  is 0.250 and xylene per  is 0.450.

The bottom stream from distillation column flows at 3 mol/h and contains 0.980 mol X/mol and 0.020 mol T/mol.

The top stream from the distillation column flowing at the rate of 2 mol/h is now fed to second column which is the other process unit of the system. From the second column, the resulting top feed contains 0.940 mol B/mol and 0.060 mol T/mol and flows at the rate of 4 mol/h. The bottom stream from the second column flows at 5 mol/h

Therefore, the complete labelled flowchart of the given process is:

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Step 2

From this flowchart, the unknown variables associated with distillation column are four, 2, 3, xB2, and xT2, and those associated with second column are also four, 4, 5, xB5, and xT5. Thus,

nunknown = 8

About the distillation column, there are total three independent equations formed from total molar flow rate balance and mole balance of benzene and toluene present . One equation is formed from the xylene recovery in the bottom stream.

About the second column, there are total three independent equations formed from total molar flow rate balance and mole balance of benzene and toluene present . One equation is formed from the benzene recovery in the top stream.

Thus, total independent equations are,

nin.equations = 8

Now, apply the formula for degree of freedom as shown below.

Therefore, the degree of freedom analysis results in the zero degree of freedom for the given process. Hence, all the unknown variables corresponding to the molar flowrates of the process streams and its compositions can be calculated.

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Step 3

The variables being evaluated is encircled in each equation step wise.

For distillation column, the equation for 96.0% xylene recovered from feed stream to bottom is written as equation (1).

...

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