The
rather horrendous rate law for the HBr reaction,
arises because the true process is a chain
reaction that involves first the dissociation of Br2
molecules into atoms, then the reaction of atoms with other H2
and Br2 molecules:
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
constantk, the rate law simplifies to the 1�-order
expression that we saw previously: