Reaction rate laws and order

A reaction's rate law expresses how fast it proceeds as a function of reactant concentrations: for a reaction involving reactants A and B, a typical rate law takes the form rate = k[A]^m[B]^n, where k is the rate constant (specific to that reaction at a given temperature) and m and n are the reaction orders in A and B respectively. The overall order of the reaction is the sum m + n.

The single most important fact about rate laws, and the source of the most common student error, is that the exponents m and n are not, in general, equal to the coefficients of A and B in the balanced chemical equation. This is not an inconsistency to be memorised away — it reflects something real about how reactions actually happen. A balanced equation describes only the overall stoichiometric relationship between reactants and products; it carries no information about the sequence of molecular-level steps (the mechanism) by which the reaction actually proceeds. Most reactions that look simple when written as a single balanced equation actually occur through several sequential elementary steps, and the observed rate law reflects only the slowest of these steps — the rate-determining step — because a multi-step process can never go faster than its slowest link. If a slow step involves only one molecule of A and none of B, the observed rate law will show first-order dependence on A and zero-order dependence on B, regardless of B's coefficient in the overall balanced equation.

The order in each species must therefore be determined experimentally, commonly using the method of initial rates: run the reaction several times with different starting concentrations of one reactant while holding the others fixed, measure how the initial rate changes, and infer the exponent from how the rate scales with concentration — doubling [A] while doubling the rate indicates first order in A, doubling [A] while quadrupling the rate indicates second order, and no change in rate at all when [A] is varied indicates zero order, meaning A does not participate in the rate-determining step even if it is consumed overall. Once the rate law and rate constant are known experimentally, they can be used to predict how the reaction rate will respond to any given set of concentrations, and the mechanism can often be inferred or tested against the observed order.