Express the rate constant k for the overall chemical reaction in terms of k1, k2, and (if necessary) the rate constants k-1 and k-2 for the reverse of the two elementary reactions in the mechanism.
k1
step elementary reaction rate constant
1 NO(g) + O2(9) --> NO2(g) + O(g) k1
2 NO(g) + O2(g) ---> NO2 (g) k2

The rate constant of the over all chemical reaction is k₁

Explanation:

The rate determining step for a reaction is the slow step. since , it is given that  k₁ ∠ k₂

The elementary step corresponding to the rate constant k₁ is the rate determining step.

NO(g) + O2(9) --> NO2(g) + O(g) k1  Slow

NO(g) + O2(g) ---> NO2 (g) k2 Fast

The rate is as follow

Rate = k₁[NO][O₂]

The rate constant for the over all chemical reaction is the rate constant of the rate determining step.

Therefore, the rate constant of the over all chemical reaction is k₁

you need to have a picture of the atom that way we can answer it