Which of the following would be a reasonable unit for the rate constant of a second order reaction?

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

Answer: (B)

Verified step by step guidance

1. Recall the general rate law for a reaction of order n: \(\text{rate} = k [A]^n\), where \(k\) is the rate constant and \([A]\) is the concentration.
2. For a second order reaction, the rate law is \(\text{rate} = k [A]^2\). The units of rate are typically concentration per time, such as \(\mathrm{mol\,L^{-1}\,s^{-1}}\).
3. Set up the units equation: \(\mathrm{mol\,L^{-1}\,s^{-1}} = k \times (\mathrm{mol\,L^{-1}})^2\).
4. Solve for the units of \(k\) by dividing both sides by \(\mathrm{(mol\,L^{-1})^2}\): \(k = \frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{\mathrm{mol^2\,L^{-2}}} = \mathrm{L\,mol^{-1}\,s^{-1}}\).
5. Therefore, the reasonable unit for the rate constant of a second order reaction is \(\mathrm{L\,mol^{-1}\,s^{-1}}\).