# 15.4: Untitled Page 234

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## Chapter 9

*k * I

*k * III

*E * *A *

*EA*

*E * *D *

(1)

*k * II

*k * IV

*E * *H*

*EH *

(2)

*k * V

in which we have used *H * to represent the inhibitor.

In this problem we assume that *k*

*k * in order to utilize (as an

III

II

approximation) the equilibrium relation given by

I

*c*

*K c c *

(3)

*EA*

*eq E A*

In addition we assume that the process illustrated by Eq. 2 can be approximated by the following equilibrium relation

II

*c*

*K c c *

(4)

*EH*

*eq E H*

In this problem you are asked to make use of the condition given by *c*

*c*

*c*

*c* o

(5)

*E*

*EA*

*EH*

*E*

in order to develop an expression for *R * in which the concentration of the *D*

inhibitor, *c *, is an unknown. Consider the special cases that occur when *H*

II

I

*K c*

*K * becomes both *large* and *small* relative to some appropriate *eq*

*H*

*eq*

parameter.

*Section* 9.3

9‐10. Indicate how Eqs. 9‐87 are obtained from Eqs. 9‐86.

9‐11. Beginning with the second of Eqs. 9‐90 derive Eq. 9‐93 using elementary row operations.

9‐12. In the analysis of the hydrogen bromide reaction described by Eqs. 9‐96, the concept of *local reaction equilibrium* was imposed on the reactive intermediates, H

and Br, according to

Local reaction equilibrium:

*R*

0 *, *

*R*

0

(1)

H

Br

437

Use of these simplifications, along with the chemical kinetic schemata and the associated mass action kinetics given by Eqs. 9‐97 though 9‐101, leads to the net rate of production of hydrogen bromide given by Eq. 9‐115. In reality, *R * and H

*R * will not be zero but they may be *small enough* to recover Eq. 9‐115. The Br

concept that something is small enough so that it can be set equal to zero is explored by Eqs. 9‐59 though 9‐63. In this problem you are asked to develop an analysis indicating that Eqs. 1 listed above are acceptable approximations when the following inequalities are satisfied:

*R*

2 *k c*

*k , *

*R*

2 *k c*

*k*

Br

I Br2

V

H

I Br2

V

(2)

*R*

*k c*

2 *k c*

*k*

H

II H2

I Br2

V

One should think of Eqs. 1 as being *assumptions* concerning the rates of production of the reactive intermediates, while Eqs. 2 should be thought of as *restrictions* on the magnitude of these rates.

9‐13. Use Eq. 9‐102a to verify Eq. 9‐103a.

9‐14. The global *stoichiometric schema* associated with the decomposition of N O

2

5

to produce NO and O can be expressed as

2

2

1

N O

2NO O

(1)

2

5

2

2

2

and experimental studies indicate that the reaction can be modeled as first order in N O . Show why the following elementary chemical kinetic schemata give 2

5

rise to a first order decomposition of N O .

2

5

*k * I

Elementary chemical kinetic schema I:

N O

NO NO

(2)

2

5

2

3

Elementary chemical kinetic schema II:

*k * II

NO

NO

NO O NO

(3)

2

3

2

2

*k * III

Elementary chemical kinetic schema III:

NO NO

2NO

(4)

3

2

438