The possible mechanism for the reaction
`2NO(g)+O_(2)(g) to 2NO_(2)(g)` is
(i) `NO+O_(2) overset(k)to NO_(3)` (fast)
(ii) `NO_(3)+NO overset(k_(2))to NO_(2)+NO_(2)(g)` (slow)
Write the rate law and order for the reaction.

Explanation

Rate law is derived from slow step
`(dx)/(dt) =k_(2)[NO_(3)][NO]`
From (i) `k=([NO_(3)])/([NO][O_(2)]) or [NO_(3)]=k[NO][O_(2)]`
Substituting value of `[NO_(3)]` in the above rate law, we get
`(dx)/(dt)= k_(2) xx k[NO]^(2)[O_(2)]^(1)`
It is rate law. The order of reaction is `2+1=3`.