Lecture 28 : Elementary Reactions and Reaction Mechanisms
28.3
Examples of reaction Mechanisms
Decomposition of ozone 2 O3 (g) 3 O2 (g)
(28.14)
This reaction is known to occur by the following mechanism
O3 (g) + M(g) O2 (g) + O(g) + M(g)
(28.15)
O3 (g) + O (g) 2O2 (g)
Here M is molecule that collides with O3 molecules and decomposes the latter through a collision. The intermediate in this reaction is O which we treat using the steady state approximation.
The rate equation for [O] is d [O] / dt = k1 [O3] [M] - k -1 [O2] [O] [M] - k2 [O3] [O]
(28.17)
Setting d [O] / dt = 0, we get the concentration of [O] as
[O] = k1 [O3] [M] / k -1 [O 2] [ M ] + k 2 [O 3]
(28.18)
The rate of change of O3 is given by
d [O3] / dt = - k 1 [O3] [ M ] + k-1 [ O2] [ O] [M] - k 2 [O] [O3]
(28.19)
Using the SSA for [O] we have,
d [ O3] / dt = 2 k 1 k2 [O3] 2 [ M ] / k -1 [ O2 ] [ M ] + k 2 [ O3 ]
(28.20)
Needless to say, the result is quite involved. The rate law depends on the value of [M], the concentration of colliding molecules. For small [M] or small pressure or concentrations of M, the rate is nearly first order if k-1 is small. For large [M] and small values of k2, the rate law is of second order.
3 O2 (g) 
O2 (g) + O(g) + M(g) 
2O2 (g) 
