Concise Physical Chemistry

c10 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

REACTION MECHANISMS 155

Because of these complications, the termsorderandmolecularitymust be clearly

differentiated. The order is the sum of exponents in the rate equation, while the

molecularity is the number of molecules taking part in a simple reaction step.

The order and molecularity will be the same in only the simplest reactions. An

example in which the reaction order seems at first to be unrelated to the molecularity

is the important atmospheric process involving ozone

2O 3 →3O 2

which isnotsecond order. Rather, it follows the rate law:

−

dO 3

dt

=k

O 32

O 2

This can be explained by a reaction mechanism starting with aunimolecularstep

O 3 ←→O 2 +O

governed by the equilibrium constant

Keq=

O 2 O

O 3

The second step of the proposed reaction mechanism isbimolecular

O+O 3 →2O 2

and it is the slower step of the two. As in any sequential process, the slowest step

controls the rate of the entire process. In this case there are only two steps: a relatively

fast first step and a rate-controlling second step. The rate law for the bimolecular

collision between O and O 3 is

−

dO 3

dt

=k 2 OO 3

Solving forO, we obtain

O=

KeqO 3

O 2

Substituting forOin the previous equation,

−

dO 3

dt

=k 2 OO 3 =k 2

KeqO 3

O 2

O 3 =k

O 32

O 2

we get the observed rate law and rate constant.