What are the units for the rate constant (k) of a reaction with the rate law: rate = k[A][B]?

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

Answer: (A)

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], so the order is 1 + 1 = 2.
2. Recall that the rate of reaction has units of concentration per time, typically expressed as M/s (molarity per second).
3. Write the units of each concentration term: [A] and [B] both have units of M (molarity). Since the rate law is rate = k[A][B], the units on the right side are k × M × M = k × M^{2}.
4. Set up the equation for units: units of rate (M/s) = units of k × M^{2}. To find units of k, rearrange to k = (units of rate) / (units of M^{2}) = (M/s) / M^{2}.
5. Simplify the units for k to get M^{-1} s^{-1}, which means the rate constant has units of inverse molarity per second.