The rate law expression for the reaction, $2\mathrm{NO}+{\mathrm{O}}_2⟶2{\mathrm{NO}}_2\text{ is rate }=\mathrm{k}[\mathrm{NO}{]}^2\left[{\mathrm{O}}_2\right]$ the unit of rate constant (k) is

Order of reaction $=2+1=3$
So, units of rate constant $={\mathrm{mol}}^{\mathrm{n}-1}{\mathrm{L}}^{\mathrm{n}-1}{\mathrm{s}}^{-1}={\mathrm{mol}}^{1-3}{\mathrm{L}}^{1-3}{\mathrm{s}}^{-1}$
                                         $={\mathrm{mol}}^{-2}{\mathrm{L}}^2{\mathrm{s}}^{-1}$