The reaction of nitric oxide with molecular hydrogen results in the production of molecular nitrogen and water as follows:

2NO(g) + 2H₂(g) N₂(g) +2H₂O(g).

A mechanism for the reaction is:

2NO(g) ^k1_k-1 N₂O₂(g) (FAST)

H₂(g) + N₂O₂(g) ^k2 N₂O(g) + H₂O(g)

H₂(g) + N₂O(g) ^k3 N₂(g) + H₂O

Derive the rate law expression for this reaction.

(The k's are supposed to be above/below the arrows with the subscripts.)