In the reaction 2 NO(g) + O2(g) → 2 NO2(g)
when the NO concentration alone was doubled, the rate increased by a factor of 4; when both the NO and O2 concentrations were in-
creased by a factor of 2, the rate increased by a factor of 8. What is the rate law for the reaction?

rate = [NO]²[O2]

Explanation:

The rate law for the reaction:

2 NO(g) + O2(g) → 2 NO2(g)

Is expressed in terms of reactants as follows:

rate = [NO]ⁿ[O2]ˣ

Where n and x are the coefficients of the rate law.

If [NO] is doubled, the rate increased 4 times. That is only possible if:

rate = [NO]²[O2]ˣ

Now, as [NO] is doubled and increased the rate 4 times, and [NO] + [O2] when doubled increased the rate 8 times, doubled [O2] implies increased the rate 2 times. That is only possible is: