13.1 Catalysis
573
Homogeneous Catalysis
Catalytic reactions in this class occur in a single gas or liquid phase.
Gas-Phase Catalysis
An example of a gas-phase homogeneously catalyzed reaction is the decomposition of
ozone
2O 3 − → 3O 2
(13.1-28)
This reaction is catalyzed by N 2 O 5 . The proposed catalyzed mechanism is 5
(1) N 2 O 5 − → NO 3 + NO 2
(13.1-29a)
(2) NO 2 + O 3 − → NO 3 + O 2
(13.1-29b)
(3) 2NO 3 − → 2NO 2 + O 2
(13.1-29c)
(1
) NO 3 + NO 2 − → N 2 O 5
(13.1-29d)
The fourth step is the reverse of step 1, so we label it as 1 . We have written it
separately to emphasize that the catalyst N 2 O 5 is regenerated. Step 2 must be doubled
for the equations of the mechanism to add up to the stoichiometric equation.
E X A M P L E 13.4
Find the rate law for the forward reaction of the O 3 decomposition according to the above
mechanism, using the steady-state approximation.
Solution
Since there are three independent steps in the mechanism, we write three differential equations: one for the rate of change of [O 3 ], which gives the rate of the reaction, and two for the
rates of change of [NO 3 ] and [NO 2 ]. The rates of change of the reactive intermediates [NO 3 ]
and [NO 2 ] are set equal to zero in the steady-state approximation:
rate −
1
2
d[O 3 ]
dt
k 2
2
[NO 2 ][O 3 ]
(13.1-30a)
d[NO 2 ]
dt
k 1 [N 2 O 5 ] − k
1 [NO 3 ][NO 2 ] + 2k 3 [NO 3 ] 2 − k 2 [NO 2 ][O 3 ] ≈ 0 (13.1-30b)
d[NO 3 ]
dt
k 1 [N 2 O 5 ] − k
1 [NO 3 ][NO 2 ] − 2k 3 [NO 3 ] 2 + k 2 [NO 2 ][O 3 ] ≈ 0 (13.1-30c)
Subtraction of Eq. (13.1-30c) from Eq. (13.1-30b) gives an equation that is solved to obtain
[NO 2 ]
2k 3 [NO 3 ] 2
k 2 [O 3 ]
(13.1-31)
5 H. S. Johnston, Gas Phase Reaction Rate Theory, Ronald Press, New York, 1966.