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

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

Answer: (D)

Verified step by step guidance

1. Recall the general rate law for a second-order reaction: \(\text{rate} = k [A]^2\), where \(k\) is the rate constant and \([A]\) is the concentration of the reactant.
2. Understand that the rate of reaction has units of concentration per time, typically \(\mathrm{mol \\cdot L^{-1} \\cdot s^{-1}}\).
3. Since the rate is \(\mathrm{mol \\cdot L^{-1} \\cdot s^{-1}}\) and the concentration squared is \(\left(\mathrm{mol \\cdot L^{-1}}\right)^2 = \mathrm{mol^2 \\cdot L^{-2}}\), set up the units equation: \([k] \times \mathrm{mol^2 \\cdot L^{-2}} = \mathrm{mol \\cdot L^{-1} \\cdot s^{-1}}\).
4. Solve for the units of \(k\) by dividing both sides by \(\mathrm{mol^2 \\cdot L^{-2}}\): \([k] = \frac{\mathrm{mol \\cdot L^{-1} \\cdot s^{-1}}}{\mathrm{mol^2 \\cdot L^{-2}}} = \mathrm{mol^{-1} \\cdot L \\cdot s^{-1}}\).
5. Conclude that the SI units of the rate constant \(k\) for a second-order reaction are \(\mathrm{mol^{-1} \\cdot L \\cdot s^{-1}}\).