rateconstant

Rate constant, denoted k, is a proportionality factor in the rate law of a chemical reaction that links the reaction rate to the concentrations of reactants. In a general form, the rate law is rate = k [A]^m [B]^n, where m and n are the reaction orders with respect to A and B, and the overall order is m + n. The rate constant is not a universal constant; it depends on the temperature, solvent, catalyst, and other conditions.

Units for k vary with the overall order of the reaction. For a zero-order reaction, rate has units of concentration per time, so k has units of M s^-1. For a first-order reaction, k has units of s^-1. For a second-order reaction, k has units of M^-1 s^-1. More generally, k has units of M^(1−n) s^-1, where n is the overall order of the rate law.

Temperature strongly influences k. The Arrhenius equation, k = A exp(-Ea/RT), describes how k increases with temperature; Ea is the activation energy, A is the pre-exponential factor, R is the gas constant, and T is temperature. Transition-state theory provides another framework for understanding k in terms of the formation and decomposition of the activated complex.

Determination of k typically involves experimental rate data fitted to the appropriate rate law. For first-order reactions, plotting ln[A] versus time yields a straight line with slope −k. For second-order reactions, plotting 1/[A] versus time yields a straight line with slope k. In many practical cases, a reactant in excess leads to pseudo-first-order behavior with k' = k[B] and an observed rate that depends linearly on [A].

Thus, the rate constant encapsulates the speed of a reaction under specific conditions and reflects the underlying mechanism and energy barriers.