Physical Chemistry Third Edition

12.5 Chain Reactions 561

(5) H+O 2 +M−→HO 2 +M (termination)

(6) H+wall−→stable species (termination)

(7) HO+wall−→stable species (termination)

(8) HO 2 +wall−→stable species (termination)

In step 5, M represents any molecule that can collide inelastically with H and O 2.

This could be an H 2 or an O 2 molecule, but could be a molecule of another substance.

Steps 2 and 3 consume one chain carrier but provide two chain carriers, so that as these

steps occur the number of chain carriers increases and an explosion can occur. Since

several processes at the walls of the vessel are included in the mechanism the ratio

of the surface area to the volume is important in determining whether an explosion

will occur.

PROBLEMS

Section 12.5: Chain Reactions

12.36The chain mechanism for the

H 2 +I 2 
2HI

reaction is

(1) I 2 
2I

(2) I+H 2 
HI+H

(3) H+I 2 −→HI+I

Note that no reverse reaction is included in step 3, and

that the initiation step (step 1) is not included in adding

the steps to obtain the stoichiometric equation.

a.Find the rate law using the steady-state approximation.

b.Find the rate law using a hybrid of the rate-limiting

step approximation and the steady-state

approximation: Assume that step 1 is at equilibrium,

and assume a steady state for the concentration of H.

c.What must be assumed to make the results of parts

a and b agree with the experimental rate law, which is

first order in H 2 and in I 2 and second order overall?

12.37The thermal decomposition of acetaldehyde follows
the reaction equation CH 3 CHO−→CH 4 +CO.

The following mechanism is proposed^25

(1) CH 3 CHO−→CH 3 +CHO

(2) CH 3 CHO+CH 3 −→CH 4 +CO+CH 3

with the following termination steps, which make only

traces of C 2 H 6 and H 2 and are not included in the

stoichiometric equation:

(3) 2 CH 3 −→C 2 H 6

(4) 2 CHO−→2CO+H 2

a.Find the rate law assuming that the concentration of

CH 3 is steady.

b.Add a reverse reaction to step 1 and find the rate law

in the steady-state approximation.

c.Johnston^26 gives a mechanism in which step 2 is

replaced by the steps

(2a) CH 3 +CH 3 CHO−→CH 3 CO+CH 4

(2b) CH 3 CO−→CH 3 +CO

Repeat the steady-state solution using this mechanism,

again ignoring the termination steps. What must be

assumed to bring the two results into agreement?

Summary of the Chapter

A chemical reaction mechanism is the sequence of elementary steps that accomplishes

the reaction. A gas-phase elementary process involves a single molecular collision.

A liquid-phase “elementary” process is actually preceded and followed by diffusion

(^25) J. L. Latham,Elementary Reaction Kinetics, 2nd ed., Butterworths, London, 1969, p. 128.
(^26) H. S. Johnston,Gas Phase Reaction Rate Theory, Ronald Press, New York, 1966, p. 36.