The reaction-order

The reaction order is defined as the final exponent of the concentrations in the rate formula V.
Normally, this exponent is derived from the coefficients in the reaction equation.

Each reaction step below has its own 'order'.
Cl2 2 Cl·      V = k*[Cl2]
2NO2 N2O4      V = k*[NO2]2
CH3I + OH- CH3OH + I-       V = k*[CH3I]*[[OH-]
Back to the reaction: H2(g)+ Br2(g) 2HBr(g)
This seems to be a reaction of the second order (bimolecular), but rate measuring shows that the order of this reaction = 1½.
How to explain that?

The steps (including a radical mechanisme):
  1. Br2 pijlen (8K) 2Br·       this equilibrium is reached very quickly
  2. Br· + H2 HBr + H·       this is the slowest step
  3. H· + Br2 HBr + Br·       this is the fastest step

Step 2, the slowest one, is determining the total rate:
Vtotal =
Equilibrium 1 has as a condition:

If we combine the two (mathematical) equations, we can calculate:

 which means that the reaction order must equal 1½ (see exponent)