Final answer:
In the expression rate = k [A][B], the units of k for a second-order reaction are M^-1 time^-1, where time could be in seconds or minutes, hence the answer would be either M^-1s^-1 or M^-1min^-1.
Step-by-step explanation:
The units of k in the rate expression rate = k [A][B] depend on the units of the rate and the concentration terms used. Usually, the rate of reaction is given in Molarity per unit time (M/s or M/min), and the concentration of reactants is given in Molarity (M). If you see the expression rate = k [A][B], where [A] and [B] are the concentrations of reactants A and B in Molarity (M), and the rate is the change in concentration per unit time, then the units of k will depend on the order of the reaction.
For a second-order reaction, such as the one given by rate = k [A][B], each concentration ([A] and [B]) contributes to the order. Therefore, the units of k would be M-1 time-1, where time could be seconds, minutes, etc., depending on the rate measurement. If we have rate in M/s then the units for k would be M-1s-1. The units help to cancel out the Molarity units from the concentration of the reactants, leaving the rate units on one side of the equation. For a reaction where the rate is given as M/min, the units for k are M-1min-1.