# 7.2: Untitled Page 148

## Chapter 7

 Total molar rate of

consumption of species A

Conversion of reactant A

(7‐8)

 Molar flow rate of 

species

A in the feed 

Since A

R represents the net molar rate of production of species A, we can express the conversion as

Conversion of reactant

A

A

R

( M

(7‐9)

)

A 1

An experimental determination of the conversion of reactant A requires the measurement of the molar flow rate of species A into and out of the reactor illustrated in Figure 7‐2. If the reaction of benzene and propylene does not go to completion, one might obtain a result given by

 R

( M

)  ( M

)

C H

C H

1

C H

2

6

6

6

6

6

6

Conversion of C H

 0 . 68

6

6

( M

)

( M

(7‐10)

)

C6H6 1

C6H6 1

This indicates that 68% of the incoming benzene is consumed in the reaction, but it does not indicate how much of this benzene reacts to form the desired product, cumene, and how much reacts to form the undesired product, p‐diisopropyl benzene. In an efficient reactor, the conversion would be close to one and the amount of undesired product would be small.

A second defined quantity, the selectivity, indicates how one product (cumene for example) is favored over another product (p‐diisopropyl benzene for example), and this quantity is defined by

Selectivity of D/U

(7‐11)

Total molar rate of production of Desire

d product

RD

Total molar rate of production of Undesire

d product

RU

For the system illustrated in Figure 7‐2, the desired product is cumene ( C H ) , 9

12

and the undesired product is p‐diisopropyl benzene ( C H ) . If the selectivity 12

18

for this pair of molecules is 0.85 we have

RC H

Selectivity of C H

C H

 0 . 85

(7‐12)

9

12

12

18 

9 12

RC12H18

Material Balances for Complex Systems

273

and this suggests rather poor performance of the reactor since the rate of production of the undesirable product is greater than the rate of production of the desired product. In an efficient reactor, the selectivity would be large compared to one.

A third defined quantity is the yield of a reactor which is the ratio of the rate of production of a product to the rate of consumption of a reactant. We express the yield for a general case as

A

R A

A B

Total rate of production of species

Yield of

(7‐13)

Total rate of consumption of species B

 R B

If we choose the product to be p‐diisopropyl benzene and the reactant to be propylene, the yield takes the form

Yield of C H

C H

12

18

3

6 

Total rate of production of p‐diisopropyl benzene

(7‐14)

Total rate of consumption of propylene

R 12

C H18

 RC3H6

If the yield of p‐diisopropyl benzene is 0.15 we have the result given by R

Yield of C H

C H

12

18

3

6 

12

C H18

 RC H

3 6

(7‐15)

RC12H18

 0 . 15

( M

)  ( M

)

C3H6 1

C3H6 2

In an efficient reactor, the yield of an undesirable product would be small compared to one, while the yield of a desirable product would be close to one.

The conversion, selectivity and yield of a reactor must be determined experimentally and these quantities will depend on the operating conditions of the reactor (i.e., temperature, pressure, type of catalyst, etc.). In addition, the value of these quantities will depend on their definitions, and within the chemical engineering literature one encounters a variety of definitions. To avoid errors, the definitions of conversion, selectivity and yield must be given in precise form and we have done this in the preceding paragraphs. 274