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, if a + b > 3, this is not very likely, since collisions of more than three particles
are unlikely. If a 1 and b 3, 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
rate k[A][B] 3
E X A M P L E 12.15
If the stoichiometry of a reaction is
B + F − → D + other products
(12.4-37)
and if the rate law is
rate k app [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
rate k 2
K 1
[B][F]
[D]
a
[B] b k app [B] a+b [F] a [D] −a
(12.4-39)