Question

Asked Mar 4, 2019

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 *ṅ _{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 *ṅ _{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

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

Step 2

From this flowchart, the unknown variables associated with distillation column are four, *ṅ _{2}*,

*n*_{unknown} = 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,

*n*_{in.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.

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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