What are the units for the rate constant k in a reaction with the rate law: rate = k[a][b]?

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

Answer: (C)

Verified step by step guidance

1. Identify the overall order of the reaction by adding the exponents of the concentration terms in the rate law. Here, rate = k[a][b] means the reaction is second order overall (1 from [a] and 1 from [b]).
2. Recall the general rate law formula: \(\text{rate} = k [\text{A}]^m [\text{B}]^n\), where the units of rate are typically molarity per second (\(M\,s^{-1}\)) and the units of concentration are molarity (\(M\)).
3. Write the units of each term: rate has units \(M\,s^{-1}\), and the concentrations \([a]\) and \([b]\) each have units \(M\). So the units of the product \([a][b]\) are \(M \times M = M^2\).
4. Set up the equation for units: \(M\,s^{-1} = k \times M^2\). To find the units of \(k\), rearrange to \(k = \frac{M\,s^{-1}}{M^2} = M^{-1} s^{-1}\).
5. Conclude that for a second-order reaction with rate law \(rate = k[a][b]\), the units of the rate constant \(k\) are \(M^{-1} s^{-1}\).