The reaction  has the following mechanism:
The rate of each species are:
These equations cannot be solved, because each one has values that change with time. For example, the first equation contains the concentrations of [Br],   and , which depend on time, as can be seen in their respective equations.
To solve the rate equations the steady state approximation can be used. The reactants of this reaction are  and , the intermediates are H and Br, and the product is HBr.
For solving the equations, the rates of the intermediates are set to 0 in the steady state approximation:
From the reaction rate of H,  , so the reaction rate of Br can be simplified:
The reaction rate of HBr can also be simplifed, changing  to , since both values are equal.
The concentration of H from equation 1 can be isolated:
The concentration of this intermediate is small and changes with time like the concentrations of reactants and product. It is inserted into the last differential equation to give
Simplifying the equation leads to
The experimentally observed rate is
The experimental rate law is very similar to the rate obtained with the steady state approximation, if  is  and  is .