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A reaction mechanism is a description of the path that a reaction takes. Many reactions as written are actually made up of several elementary steps, which when combined form the overall reaction.

A good example is the reaction of CO and NO2, CO(g) + NO2(g) -> CO2(g) + NO(g). At low temperature, this reaction occurs in two steps

NO2(g)+ NO2(g) -> NO3(g) + NO(g) +
CO(g) + NO3(g) -> CO2(g) + NO2(g) =
CO(g) + NO2(g) -> CO2(g) + NO(g)
The first two reactions are the two elementary steps in this reaction.

Each elementary step proceeds at a different rate. In the above equation, the first reaction is slow and the second is very fast. This means that the rate of the overall reaction is dominated by the rate of the first reaction: this is the rate determining step. The rate expression for the overall reaction is

k = [NO2]2
since the first elementary step is the rate determining step.

The rate expression for a complex reaction can be determined by looking at the overall steps: simply write down the elementary steps, figure out which is the slowest, then write the reaction rate expression in terms of that step. Occasionally, however, a reactive intermediate can be important in the reaction: these are difficult to deal with since their concentration is very low and there is usually no easy way to measure it, thus making the reaction rate expression not very useful. We can remove the intermediate term by noting that the fast reactions that form reactive intermediates typically quickly establish an equilibrium: we can then express the concentration of the reactive intermediate in terms of things in the fast reaction.

This sounds more complex than it is: conside the reaction of NO and Cl2 to form NOCl. This reaction occurs in two elementary steps: the first is fast, the second is slow.

NO(g) + Cl2(g) < = > NOCl2(g)    (fast)
NOCl2(g) + NO -> 2NOCl    (slow)
2NO(g) + Cl2 -> 2NOCl
We can write the rate expression as
rate = k2[NOCl2][NO]
however, NOCl2 is a reactive intermediate with a concentration we probably can't measure. We can remove it by noting that the first reaction quickly establishes an equilibrium: the rate of the forward reaction (rate = k[NO][Cl2]) is equal to the rate of the reverse reaction (rate = k-1[NOCl2]). Therefore
k[NO][Cl2] = k-1[NOCl2]
[NOCl2] = k1[NO][Cl2]/k-1
Now we can just substitute this into our original rate expression to find
rate = k2[NO][NOCl2]
rate = k2[NO]k1[NO][Cl2]/k-1
rate = k2k1[NO]2[Cl2]/k-1

Example: The reaction 2NO(g) + O2(g) ->NO2(g) possibly has the following mechanism:

NO + O2 < = > NO3    (fast)
NO3 + NO - > 2NO2    (slow)
What is the rate expression for this reaction?

Solution: the basic rate expression is dependant on the rate of the second reaction, so the rate for the overall reaction is

rate = k2[NO3][NO]
However, NO3 is a reactive intermediate and we must remove it from the reaction rate expression. To do this, note that the first reaction rapidly establishes an equilibrium and the forward and backwards rates are identical. Thus
k1[NO][O2] = k-1[NO3]
[NO3] = k1[NO][O2]/k-1
We can now substitute this into our original rate expression
rate = k2[NO3][NO]
rate = k2[NO] k1[NO][O2]/k-1
rate = k2k1[NO]2[O2]/k-1


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