Question

propose a mechanism for the reaction consistent with the rate law you measured

Answer 1

The best example to prove this would be reaction between nitric oxide with oxygen,
2NO + O₂ ------------> 2 NO₂
whose experimentally determined rate law = K [NO]² [O₂]
The mechanism as suggested in literature will be bimolecular
2 NO <-----> N₂O₂ [ Fast step ]
N₂O₂ + O₂ -----------> 2NO₂ [ slow step ]
Here N₂O₂ is intermediate and cannot be included in the rate law hence the slow step cannot be
the rate determining step in this case. On the other hand the first elementary step i.e)
the fast step can be used
_k1 [NO]² = k₂ [N₂O₂]
_k1 / k₂  [NO]² = [N₂O₂]
Substitute the above equation into r₁ = k₃ [N₂O₂] [O₂]
(k₃ k₁ / k₂ ) [NO]² [O₂]
Let k₃ k₁ / k₂ = K (some constant)
rate law = K [NO]² [O₂] = experimental rate law