A rate law describes how the instantaneous rate of a reaction depends on the current concentrations of reacting species at a specified temperature.

For a reaction involving A and B, an experimentally observed rate law may have the form

$$\boxed{r=k[A]^m[B]^n},$$

where

• $r$ is the reaction rate,
• $k$ is the rate constant at the stated temperature,
• $m$ is the reaction order with respect to A,
• $n$ is the reaction order with respect to B.

The overall reaction order is $m+n$.

Reaction orders describe sensitivity to concentration. If a reaction is first order in A, doubling $[A]$ doubles the rate when other variables are fixed. If it is second order in A, doubling $[A]$ multiplies the rate by

$$2^2=4.$$

If it is zero order in A, changing $[A]$ does not change the rate within the regime where that rate law applies.

Reaction order is not ordinary stoichiometry

For an overall equation

$$a\mathrm A+b\mathrm B\rightarrow\text{products},$$

it is generally not valid to assume

$$r=k[A]^a[B]^b.$$

The exponents in an experimentally measured rate law need not equal the coefficients in the overall balanced equation. They reflect the molecular mechanism and must normally be determined from kinetic data.

Units of the rate constant

The units of $k$ depend on the overall reaction order because $r$ always has rate units. For example:

• zero order: $k$ has units $\mathrm{M,s^{-1}}$;
• first order: $k$ has units $\mathrm{s^{-1}}$;
• second order: $k$ has units $\mathrm{M^{-1},s^{-1}}$.

Example

Suppose

$$r=k[A][B]^2.$$

The reaction is first order in A, second order in B and third order overall. If $[A]$ is doubled while $[B]$ is unchanged, the rate doubles. If $[B]$ is doubled instead,

$$\frac{r_{new}}{r_{old}}=2^2=4.$$

If both are doubled, the rate changes by

$$2\times4=8.$$

A rate law is therefore an empirical mathematical model of kinetic behavior. Determining its exponents is a separate experimental task.