Step 1: Units of the rate constant.
The units of the rate constant \( k \) depend on the order of the reaction. If the rate constant is measured in \(\text{s}^{-1}\), this indicates the units are consistent with the first-order reaction.
Step 2: Explanation of the options.
For a first-order reaction, the rate law is \( r = k[A] \), where the rate \( r \) has units of mol/L·s, and \([A]\) has units of mol/L. Therefore, the unit of \( k \) for a first-order reaction is \(\text{s}^{-1}\).
Step 3: Conclusion.
Thus, if the rate constant is measured in \(\text{s}^{-1}\), the reaction is first order, which corresponds to option (B).