Page 196 - Instant notes

Physical chemistry 182

rate of formation of NO 2=2k 2[N 2O 2][O 2]

(The factor 2 appears in this rate law because two NO 2 molecules are formed in each
reactive collision encounter between N 2O 2 and O 2 so the rate of formation of NO 2 is
twice the rate at which the collisions occur.)
The steady state assumption is used to remove from the rate law expression the term
involving the concentration of the intermediate species N 2O 2. The net rate of formation of
N 2O 2 is given by the difference between its rate of formation (υia reaction 1) and its rate
of removal (υia reactions −1 and 2), and under the steady state assumption is
approximated to zero:

Rearranging gives:

so that the rate of formation of NO 2 in terms of reactants only is:

This rate law is more complex than the observed rate law. However, if it is the case that
the rate of decomposition of N 2O 2 (reaction −1) is much greater than its rate of reaction
with O 2 (reaction 2), then , (i.e. ) and the
formulated rate law becomes:

in agreement with the observed rate law. Furthermore, since the observed third order rate
constant is actually a combination of elementary reaction rate constants:

the observed negative temperature dependence is explained if the rate of increase with
temperature of rate constant k −1 is more rapid than the rate of increase of the product k 1k 2.
(Note that in the general case of rate law formulation using similar procedures it may not
be possible to invoke an approximation such as used above, in which case
both terms must explicitly remain in the derived rate law.)