rateconstants

Rate constants (k) are the proportionality factors that relate the rate of a chemical reaction to the concentrations of reactants in a rate law. For a reaction aA + bB → products, the rate can be expressed as rate = -1/a d[A]/dt = -1/b d[B]/dt = d[Product]/dt, and more generally rate = k [A]^m [B]^n, where m and n are the reaction orders. These orders are determined experimentally and do not necessarily equal the stoichiometric coefficients.

The rate constant k depends on temperature and can be influenced by solvent, pressure, catalysts, and light exposure. It is not a universal constant; the same reaction at different temperatures or conditions can have markedly different k values. Temperature effects are commonly described by the Arrhenius equation, k = A exp(-Ea/(RT)), where Ea is the activation energy and A is the pre-exponential factor. Transition state theory provides another framework, for example k = (kB T/h) exp(-ΔG‡/(RT)).

Units of k depend on the overall order p = m + n. For a first-order reaction, k has units of s⁻¹; for a second-order reaction, units are M⁻¹ s⁻¹; higher orders have corresponding units. In many practical cases, a pseudo-first-order rate constant k' is used when one reactant is in large excess, giving rate ≈ k' [A].

Determination of k involves experimental data, typically via initial-rate methods or fitting to integrated rate laws. In complex mechanisms, multiple rate constants govern individual elementary steps, and the observed rate constant may reflect a combination of these steps rather than a single intrinsic value.