Which one of the following sets of units is appropriate for a second-order rate constant?

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

Answer: (A)

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. Understand that the units of rate are typically concentration per time, such as \(\mathrm{mol \\cdot L^{-1} \\cdot s^{-1}}\).
3. For a second-order reaction, the rate law is \(\text{rate} = k [A]^2\), so the units of \(k\) must balance the units so that the rate has units of \(\mathrm{mol \\cdot L^{-1} \\cdot s^{-1}}\).
4. Set up the units equation: \([k] \times (\mathrm{mol \\cdot L^{-1}})^2 = \mathrm{mol \\cdot L^{-1} \\cdot s^{-1}}\).
5. Solve for the units of \(k\): \([k] = \frac{\mathrm{mol \\cdot L^{-1} \\cdot s^{-1}}}{(\mathrm{mol \\cdot L^{-1}})^2} = \mathrm{L \\cdot mol^{-1} \\cdot s^{-1}}\).