For a A + B → products the rate of the reaction is given by Rate = K [ A ] [ B ] 2 . The units of rate…

Rate of reaction =$=\mathrm{K}\left[\mathrm{A}\right][\mathrm{B}{]}^2$

The unit for the rate of reaction is $\mathrm{mol} {\mathrm{L}}^{-1}{\mathrm{S}}^{-1}$ and the unit of concentration is $\mathrm{mol} {\mathrm{L}}^{-1}$.

So, 

$$\begin{gathered} \mathrm{Rate} \mathrm{of} \mathrm{reaction}= \mathrm{K}\left[\mathrm{A}\right][\mathrm{B}{]}^2 \\ \mathrm{mol} {\mathrm{L}}^{-1}{\mathrm{S}}^{-1}=\mathrm{K}\times \mathrm{mol} {\mathrm{L}}^{-1}\times {\left(\mathrm{mol} {\mathrm{L}}^{-1}\right)}^2 \\ \mathrm{K}=\frac{\mathrm{mol} {\mathrm{L}}^{-1}{\mathrm{S}}^{-1}}{\mathrm{mol} {\mathrm{L}}^{-1}\times {\mathrm{mol}}^2 {\mathrm{L}}^{-2}}={\mathrm{mol}}^{-2}{\mathrm{L}}^2{\mathrm{S}}^{-1} \end{gathered}$$

Hence, the unit of rate constant $\mathrm{K}$ is ${\mathrm{mol}}^{-2}{\mathrm{L}}^2{\mathrm{S}}^{-1}$.