What are the units for the rate constant (k) of a first-order reaction?

• A. mol^{2} \, L^{-2} \, s^{-1}
• B. s^{-1}
• C. mol \, L^{-1} \, s^{-1}
• D. L \, mol^{-1} \, s^{-1}

Answer: (B)

Verified step by step guidance

1. Recall that the rate law for a first-order reaction is given by \(\text{rate} = k[A]\), where \([A]\) is the concentration of the reactant and \(k\) is the rate constant.
2. The rate of reaction has units of concentration per time, typically \(\text{mol} \, L^{-1} \, s^{-1}\), and the concentration \([A]\) has units of \(\text{mol} \, L^{-1}\).
3. To find the units of \(k\), rearrange the rate law to solve for \(k\): \(k = \frac{\text{rate}}{[A]}\).
4. Substitute the units into the expression: \(\text{units of } k = \frac{\text{mol} \, L^{-1} \, s^{-1}}{\text{mol} \, L^{-1}}\).
5. Simplify the units by canceling \(\text{mol} \, L^{-1}\), which leaves the units of \(k\) as \(s^{-1}\) for a first-order reaction.