2NO(g) + O2(g) --> 2NO2(g)

Derive the theoretical rate law and indicate whether or not this is a possible mechanism for the above reaction:

(1) 2NO(g) <-->* N2O2(g) (fast)
(2) N2O2(g) + O2(g) --> 2NO2(g) (slow)

Extra Info: This reaction is third order overall. NO is second order, and O2 is first order.

* indicates equilibrium arrows

Thank you!