For a second-order reaction, the rate law is:
\[
\text{Rate} = k[A][B].
\]
The unit of \( k \) is:
\[
\frac{\text{Rate}}{\text{Concentration}^2} = \frac{\text{mol litre}^{-1} \text{second}^{-1}}{(\text{mol litre}^{-1})^2} = \text{litre mol}^{-1} \text{second}^{-1}.
\]