An equimolar liquid mixture of benzene and toluene is separated into two product streams by distillation. A process flowchart and a somewhat oversimplified description of what happens in the process follow: Vapor-97% mole benzene Reflux fB""' Overhead product, nj(mol) nj(mol) CONDENSER Feed 100 mol 0.500 mol B/mol 0.500 mol T/mol DISTILLATION COLUMN Boilup ys[mol B(v)/moIJ Bottoms product REBOILER xs[mol B(ll/mol] Student Workbook Inside the column a liquid stream flows downward and a vapor stream rises. At each point in the column some of the liquid vaporizes and some of the vapor condenses. The vapor leaving the top of the column, which contains 97 mole% benzene, is completely condensed and split into two equal fractions: one is taken off as the overhead product stream, and the other (the reflux) is recycled to the top of the column. The overhead product stream contains 89.2% of the benzene fed to the column. The liquid leaving the bottom of the column is fed to a partial reboiler in which 45 % of it is vaporized. The vapor generated in the reboiler (the boilup) is recycled to become the rising vapor stream in the column, and the residual reboiler liquid is taken off as the bottom product stream. The compositions of the streams leaving the reboiler are governed by the relation YB/ (1 - YB) = 225 xB/(l- XB) . where YB and XB are the mole fractions of benzene in the vapor and liquid streams, respectively. (a) Take a basis of 100 mol fed to the column. Draw and completely label a flowchart, and for each of four systems (overall process, column, condenser, and reboiler), do the degree-of-freedom analysis and identify a system with which the process analysis might appropriately begin (one with zero degrees of freedom). (b) Write in order the equations you would solve to determine all unknown variables on the flowchart, circling the variable for which you would solve in each equation. Do not do the calculations in this part. (c) Calculate the molar amounts of the overhead and bottoms products, the mole fraction of benzene in the bottoms product, and the percentage recovery of toluene in the bottoms product (100 X moles toluene in bottoms/mole toluene in feed).

Problem 4.31

An equimolar liquid mixture of benzene and toluene is separated into two product streams by distillation. A process flowchart and a somewhat oversimplified description of what happens in the process follow: Vapor-97% mole benzene Reflux fB""' Overhead product, nj(mol) nj(mol) CONDENSER Feed 100 mol 0.500 mol B/mol 0.500 mol T/mol DISTILLATION COLUMN Boilup ys[mol B(v)/moIJ Bottoms product REBOILER xs[mol B(ll/mol] Student Workbook Inside the column a liquid stream flows downward and a vapor stream rises. At each point in the column some of the liquid vaporizes and some of the vapor condenses. The vapor leaving the top of the column, which contains 97 mole% benzene, is completely condensed and split into two equal fractions: one is taken off as the overhead product stream, and the other (the reflux) is recycled to the top of the column. The overhead product stream contains 89.2% of the benzene fed to the column. The liquid leaving the bottom of the column is fed to a partial reboiler in which 45 % of it is vaporized. The vapor generated in the reboiler (the boil up) is recycled to become the rising vapor stream in the column, and the residual reboiler liquid is taken off as the bottom product stream. The compositions of the streams leaving the reboiler are governed by the relation YB/ (1 - YB) = 225 xB/(l- XB) . where YB and XB are the mole fractions of benzene in the vapor and liquid streams, respectively. (a) Take a basis of 100 mol fed to the column. Draw and completely label a flowchart, and for each of four systems (overall process, column, condenser, and reboiler), do the degree-of-freedom analysis and identify a system with which the process analysis might appropriately begin (one with zero degrees of freedom). (b) Write in order the equations you would solve to determine all unknown variables on the flowchart, circling the variable for which you would solve in each equation. Do not do the calculations in this part. (c) Calculate the molar amounts of the overhead and bottoms products, the mole fraction of benzene in the bottoms product, and the percentage recovery of toluene in the bottoms product (100 X moles toluene in bottoms/mole toluene in feed).

Step by step solution

Step 1 of 3

a)

For basis of 100 moles, the amount of benzene and toluene fed into the distillation column are

0.5 mol/mol of feed each.

The flowchart representing the whole process is as follows:

Overall Balance:

The unknowns in overall balance are and .

The overall mole balance in overall process is as follows:

Here, , is moles of overhead product, is moles of bottom product.

Two balance equations can be written one for benzene and the other for toluene. The

relationship present here is 89.2% recovery of benzene in the feed.

Now, obtain the degrees of freedom for the overall process in the following manner.

Number of degrees of Freedom = (number of unknowns)-(number of equations)-(number of relations)

= 3-2-1 = 0

Still Balance:

The unknowns in still balance are

The mole balance in still process is as follows:

Here, are moles of boil up. is mole fraction Benzene at the exit of the still.

Two balance equations can be written one for benzene and the other for toluene.

Now, obtain the degrees of freedom for still process in following manner:

Degrees of Freedom = (number of unknowns)-(number of equations)-(number of relations)

= 5-2-0 = 3

Condenser Balance:

The unknowns in condenser balance are .

Here, the available balances and relations are zero. Now, obtain the degrees of freedom for still

process in following manner:

Degrees of Freedom =(number of unknowns)-(number of equations)-(number of relations)

= 1-0- 0 = 1

Reboiler Balance:

The unknowns in reboiler balance are

The mole balance in still process is as follows:

Here, is mole fraction at the boil up, is mole fraction of Benzene at the exit of the still.

Two balance equations can be written one for benzene and the other for toluene.

The relationship for and in terms of relative volatility equal to 2.25 and also 45% of the liquid is vaporized in the reboiler.

Now, obtain the degrees of freedom to still process in the following manner.

Degrees of Freedom =(number of unknowns)-(number of equations)-(number of relations)

= 6-2-2 = 2

Since the overall process has zero degrees of freedom, it is appropriate to begin process

analysis with overall process.

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