The reaction ${\mathrm{NO}}_2+\mathrm{CO}\stackrel{k}{⟶}\mathrm{NO}+{\mathrm{CO}}_2$ follows the mechanism

${\mathrm{NO}}_2+{\mathrm{NO}}_2\stackrel{k_1}{⟶}{\mathrm{NO}}_3+\mathrm{NO}$        (slow)

${\mathrm{NO}}_3+\mathrm{CO}\stackrel{k_2}{⟶}{\mathrm{NO}}_2+{\mathrm{CO}}_2$        (fast)

The rate low of the reaction will be

Since the first step is slow, the reaction rate law is $-\mathrm{d}\left[{\mathrm{NO}}_2\right]/\mathrm{d}t=k{\left[{\mathrm{NO}}_2\right]}^2.$ Note that the rate law is not divided by 2 as one molecule of $N{O}_2$ is recovered in the second step.