# 7.41: Untitled Page 186

## Chapter 7

In this problem you are asked to derive an expression for the ratio of molar flow rates, M

/ M , in terms of  given

that pure A enters the system in stream #1.

5

1

Figure 7.27. Catalytic converter

7‐28. A simple chemical reactor in which a reaction, A  products, s i shown in

Figure 7.28. The reaction occurs in the liquid phase and

the feed stream is pure

species A. The overall extent of reaction is designated by  where  is defined by the relation

( )

1   ( )

A 4

A 2

Here we see that   0 when no reaction takes place, and when   1 the reaction is complete and no species A leaves the reactor. We require that the mass fraction of species A entering the reactor be constrained by ( )

  ( )

A 2

A 1

in which  is some number less than one and greater than zero. Since the products of the reaction are not specified, assume that they can be lumped into a single “species” B. Under these conditions the reaction can be expressed as A B and the

n

reactio rates for the two species system must conform to Material Balances for Complex Systems

349

r   r . The objective in this problem is to derive an expression for the ratio of A

B

mass flow rates m

/ m in terms of  and  .

5

4

ure

Fig

7.28. Chemical reactor with recycle stream

7‐29. Solve problem 7‐28 using an iterative procedure (see Appendix B) for

  0 5

. and   0 . 3 for a feed stream flow rate of m

 100 , 000 mol/h . Use a

1

convergence criteria of 0.1 kmol/h for Stream #5.

7 30.

u

Ass me that the system

described in Problem 7‐28 contains N

molecular

species, thus species A represents the single reactant and there are N  1 product species. The reaction rates for the products can be expressed as

r   r I ,

r

II

III

N 1

  r ,

r

  r , ......., r   r

B

A

C

A

D

A

N

A

where the overall mass rate of production for species A is given by

I

II

III

1

r

r

N

r r

...... r

A

A

A

A

A

Begin your analysis with the axioms for the mass of an N‐component system and identify the conditions required in order that N  1 product species can be represented as a single species.

7‐31. In the air dryer illustrated in Figure

7.31, part of the effluent air stream is to

be recycled in an effort to control the inlet humidity. The solids entering the dryer (Stream #3) contain 20 % water on a mass basis and the mass flow rate of the wet solids entering the dryer is 1000 lb / h . The dried solids (stream #4) are m

to contain a maximum of 5 % water on a mass basis. The partial pressure of water vapor in the fresh air entering the system (Stream #1) is equivalent to 10

mm Hg and the partial pressure in the air leaving the dryer (Stream #5) must not exceed 200 mm Hg. In this particular problem the flow rate of the recycle stream (stream #6) is to be regulated so that the partial pressure of water vapor in the air  350