Rate Law and the Order of a Reaction

The rate law. For a reaction, the rate law is the experimentally determined equation

expressing the instantaneous rate of the reaction as a function of the molar concentrations of the

reactants, each raised to some power:

Here $k$ is the rate constant (or specific reaction rate) -- the rate of the reaction when every

reactant concentration is unity -- and its value is characteristic of a given reaction at a given

temperature. Critically, the exponents $x$ and $y$ in the rate law are not, in general, equal to

the stoichiometric coefficients of $A$ and $B$ in the balanced chemical equation. They must be

determined experimentally, usually by measuring how the initial rate changes as each reactant's

starting concentration is varied in turn while the others are held fixed (as illustrated in the worked

examples of the next section) -- never simply read off the balanced equation.

Order of reaction. The order of a reaction with respect to a particular reactant is the power to

which that reactant's concentration is raised in the experimentally determined rate law; the overall order of the reaction is the sum of all these individual exponents ($x + y$ for the rate law above).

Order is a purely empirical, experimentally measured number and, unlike molecularity (the next

section), it can take values that would be impossible for a single molecular collision step: it can be

zero (rate is independent of that reactant's concentration entirely), a fraction such as

$3/2$ (seen in some multi-step or chain reactions), or occasionally even negative (rate actually

decreases as a species' concentration increases, seen when a product inhibits the reaction). A

reaction is described as "first order in $A$" if $x = 1$, "second order overall" if $x + y = 2$, and

so on.

Units of the rate constant. Because rate always has units of $\text{concentration} \times \text{time}^{-1}$, and $[A]^n$ has units of $\text{concentration}^n$, the units of $k$ depend on the

overall order $n$ of the reaction:

For a zero order reaction ($n=0$), $k$ has units of $\text{mol L}^{-1}\text{time}^{-1}$ -- the same …