Which of the following gives the correct units for k in a second-order reaction?

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

Answer: (C)

The main idea here is how the rate constant’s units balance a second-order rate law. The rate of reaction has units of concentration per time, typically M s^-1. For a second-order reaction, the rate law looks like rate = k [A]^2 (or rate = k [A][B]). The concentration term [A]^2 contributes two powers of concentration, so its units are M^2. To make both sides have the same units (M s^-1), k must supply the opposite of M^2, namely M^-2, but since time is in the denominator as well, k ends up with M^-1 s^-1. In short, the second-order rate constant has units of M^-1 s^-1. This is distinct from first-order (s^-1) and zero-order (M s^-1) constants.