What is the unit of measurement for the rate constant in a second-order reaction?

In a second-order reaction, the rate law can be expressed as rate = k[A]² or rate = k[A][B], where [A] and [B] are the concentrations of the reactants. The rate of reaction is measured in units of concentration per time, typically moles per liter per second (M/s).

To determine the units of the rate constant (k) for a second-order reaction, we can rearrange the rate equation. If we consider the general form of the rate equation:

rate = k[A]²

Rearranging gives:

k = rate / [A]²

Substituting the units for rate and concentration, we have:

k = (M/s) / (M²) = M/s * 1/M² = 1/(M·s)

Thus, the unit of measurement for the rate constant in a second-order reaction is indeed 1/M·s. This makes sense in terms of dimensional analysis and ensures that the units are consistent with the kinetic theory of reactions.