The latter two equations constitute a chain reaction, each one yielding a molecule of HBr and producing the reactant atom for the other chain step. There also are reactions that either damp down or reverse the chain process:
 

With these reactions and a certain amount of algebra, one can arrive at the observed rate expression in a straightforward though tedious manner. Although the rate equation looks complicated, we can understand it in terms of the HBr mechanism. For example, as [HBr] increases, its presence in the denominator decreases the rate of reaction.

This happens because the chain-reversal reaction sends more HBr back to H2 molecules and Br atoms. At low HBr concentration, for which the ratio [HBr]/[Br2] is small in comparison with the rate constant k, the rate law simplifies to the 1-order expression that we saw previously: