Physical Chemistry Third Edition

12.4 Reaction Mechanisms and Rate Laws 551

Solution

The mechanism could be

(1) aA+bB−→reactive intermediates (slow, rate-limiting)

(2) reactive intermediates−→cC+dD (fast)

However, ifa+b>3, this is not very likely, since collisions of more than three particles

are unlikely. Ifa1 andb3, a possible mechanism is

(1) A+B
F (fast)

(2) F+B
G (fast)

(3) G+B−→further intermediates or products (slow)

where F and G are reactive intermediates.

Exercise 12.14

Assuming that step 3 is rate-limiting, show that the above mechanism leads to the rate law

ratek[A][B]^3

EXAMPLE12.15

If the stoichiometry of a reaction is

B+F−→D+other products (12.4-37)

and if the rate law is

ratekapp[B]a+b[F]a[D]−a

find a mechanism that conforms to this rate law.

Solution

The first step in the mechanism cannot be rate-limiting. The following mechanism can produce

this rate law:

(1) B+F
A+D (fast in both directions)

(2) aA+bB−→products (slow, rate-limiting)

(12.4-38)

where A is a reactive intermediate. The equilibrium approximation applied to the first step

gives

[A]K 1

[B][F]

[D]

so that the rate expression is

ratek 2

(

K 1

[B][F]

[D]

)a

[B]bkapp[B]a+b[F]a[D]−a (12.4-39)