# 8.18: Untitled Page 207

- Page ID
- 18340

## Chapter 8

*Figure 8.8*. Accidental overflow from a stirred tank reactor *Section* 8.2

8‐9. Show how Eq. 8‐27 can be used to derive Eq. 8‐28.

8‐10. A perfectly mixed batch reactor is used to carry out the reversible reaction described by

*k* 1

Chemical kinetic schema:

*A * *E *

*B *

(1)

*k * 2

and the use of mass action kinetics provides a chemical reaction rate equation given by

Chemical reaction rate equation:

*R*

*k c c*

*k c*

(2)

*A*

1 *A E*

2

*B*

*second order*

*first order*

* reaction*

*decomposition*

If species *E* is present in great excess, the concentration *c * will undergo *E*

negligible changes during the course of the process and we can define a pseudo first order rate coefficient by

*k*

*k c *

(3)

1

1 *E*

Given initial conditions of the form

I.C.

o

o

*c*

*c , *

*c*

*c , *

*t * 0

(4)

*A*

*A*

*B*

*B*

use the pseudo first order rate coefficient to determine the concentration of species *A* and *B* as a function of time.

387

8‐11. When molecular species *A* and *B* combine to form a product, one often adopts the chemical kinetic schema given by

*k*

*A * *B *

products

(1)

Use of mass action kinetics then leads to a chemical kinetic rate equation of the form

*R*

*k c c *

(2)

*A*

*A B*

One must always look upon such rate expressions as hypotheses to be tested by experimental studies. For a homogeneous, liquid‐phase reaction, this test can be carried out in a batch reactor which is subject to the initial conditions I.C.1

o

*c*

*c , t * 0

(3)

*A*

*A*

I.C.2

o

*c*

*c , t * 0

(4)

*B*

*B*

Use the macroscopic mole balances for both species *A* and *B* along with the stoichiometric constraint

*R*

*R *

(5)

*A*

*B*

in order to derive an expression for *c * as a function of time. In this case one is *A*

forced to assume perfect mixing so that *c c * can be replaced by *c * *c * .

*A B*

*A*

*B*

8‐12. A batch reactor illustrated in Figure 8.12 is used to study the irreversible, decomposition reaction

*k*

*A *

products

(1)

The proposed chemical kinetic rate equation is

*R*

*k c *

(2)

*A*

*A*

and this decomposition reaction is catalyzed by sulfuric acid. To initiate the batch process, a small volume of catalyst is placed in the reactor as illustrated in Figure 8.12. At the time, *t * 0 , the solution of species *A* is added at a volumetric

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