rate law
Imagine a recipe that tells you not just what to mix but how the cooking speed depends on the ingredients: 'doubling the sugar makes it caramelise twice as fast, but adding more butter changes nothing.' A rate law is that recipe for a reaction — a formula that says how the reaction's speed depends on the concentrations of the substances present.
Formally, a rate law is an equation of the form rate equals a rate constant k multiplied by the concentration of each reactant raised to some power. Those powers are the orders, and they tell you how sensitive the speed is to each reactant. The whole point is that you cannot read a rate law off the balanced equation — it has to be discovered by experiment, because it reflects the hidden step-by-step mechanism, not the overall stoichiometry.
Rate laws matter because they let you predict and control how fast things happen: how long a drug lasts in the body, how quickly a pollutant breaks down, how to size an industrial reactor. Two cautions: the exponents need not be whole numbers and need not match the coefficients in the equation, and a rate law that fits at ordinary concentrations may break down at very high or very low ones.
For the reaction of nitric oxide with hydrogen, experiments give rate = k[NO]²[H₂]. Notice it is second order in NO but only first order in hydrogen — even though the balanced equation uses two of each, the real speed depends on them quite differently, a clue that the reaction happens in several steps.
The exponents come from experiment, not from the balanced equation.
A common error is to copy the stoichiometric coefficients straight into the rate law as exponents — that is only valid for a single elementary step, not for an overall reaction.