For a second-order reaction, what are the units for the rate constant k?

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

Answer: (B)

Verified step by step guidance

1. Recall the general rate law for a reaction: \(\text{rate} = k [A]^n\), where \(k\) is the rate constant and \(n\) is the order of the reaction.
2. For a second-order reaction, the rate law is \(\text{rate} = k [A]^2\).
3. The units of rate are typically concentration per time, which is \(\mathrm{mol \\ L^{-1} \\ s^{-1}}\).
4. The concentration term \([A]^2\) has units of \(\left(\mathrm{mol \\ L^{-1}}\right)^2 = \mathrm{mol^2 \\ L^{-2}}\).
5. To find the units of \(k\), rearrange the rate law to \(k = \frac{\text{rate}}{[A]^2}\) and divide the units of rate by the units of \([A]^2\), resulting in \(k\) having units of \(\mathrm{L \\ mol^{-1} \\ s^{-1}}\).