Which of the following correctly lists the typical units of the rate constant k for zero-, first-, and second-order reactions?

• A. Zero order: s^-1; First order: M/s; Second order: M^-1 s^-1
• B. Zero order: M/s; First order: s^-1; Second order: M^-1 s^-1
• C. Zero order: M/s; First order: s^-1; Second order: M^-1 s^-1
• D. Zero order: M/s; First order: s^-1; Second order: M^-2 s^-1

Answer: (B)

The rate constant’s units come from how the rate law relates the rate to concentration and the reaction order. The rate of reaction is the change in concentration per unit time, typically expressed as d[A]/dt, which has units of concentration per time (M/s).

• For a zero-order process, the rate = k. Since the rate already has units M/s, k must have the same units: M/s.

• For a first-order process, the rate = k[A]. To get M/s from M, you divide by M, so k has units of s^-1.

• For a second-order process, the rate = k[A]^2. To convert M^2 to M/s, you divide by M^2, so k has units of M^-1 s^-1.

So the typical units are zero order: M/s; first order: s^-1; second order: M^-1 s^-1.