Nitric oxide reacts with oxygen to produce nitrogen dioxide.
`2NO(g)+O_2(g) rarr 2NO_2(g)`
What is the predicted rate law, if the mechanism is ,
`NO+O_2 overset(k)(rarr)NO_2("fast")`
`NO_2+Noverset(K_1)(rarr)NO_2+NO_2("slow")`

Explanation

As the second step is the slowest step ,
Rate = `k_1 = [NO_3] [NO]`
From the first elementary step,
Equilibrium constant. `K = ([NO_3])/([NO][O_2])`
`therefore` `[NO_3]=K[NO][O_2]`
Substituting in (i)
Rate =`k_1K[NO] [O_2] [NO]`
Rate = `k[NO]^2[O_2]`.where `k=k_1xxK`