A reaction rate describes how quickly the composition of a reacting system changes with time.

For a reactant A, its concentration usually decreases as the reaction proceeds, so an average disappearance rate over a time interval is

$$-\frac{\Delta[A]}{\Delta t}.$$

For a product B, concentration increases, so its average appearance rate is

$$\frac{\Delta[B]}{\Delta t}.$$

The minus sign for a reactant makes the reported rate positive when reactant is being consumed.

For the balanced reaction

$$a\mathrm A+b\mathrm B\rightarrow c\mathrm C+d\mathrm D,$$

species concentrations do not generally change at the same numerical rate because the stoichiometric coefficients differ. A single reaction rate is defined by normalizing each concentration change by its coefficient:

$$\boxed{r=-\frac1a\frac{d[A]}{dt} =-\frac1b\frac{d[B]}{dt} =\frac1c\frac{d[C]}{dt} =\frac1d\frac{d[D]}{dt}}.$$

The derivative notation $d[A]/dt$ means the instantaneous slope of the concentration-versus-time curve. Typical concentration-based rate units are

$$\mathrm{mol,L^{-1},s^{-1}}=\mathrm{M,s^{-1}}.$$

Example

For

$$\mathrm{2NO_2\rightarrow2NO+O_2},$$

suppose oxygen is appearing at

$$\frac{d[O_2]}{dt}=0.015,\mathrm{M,s^{-1}}.$$

Because the stoichiometric coefficient of $\mathrm{O_2}$ is 1,

$$r=0.015,\mathrm{M,s^{-1}}.$$

The corresponding nitrogen dioxide disappearance rate is

$$-\frac{d[NO_2]}{dt}=2r=0.030,\mathrm{M,s^{-1}},$$

and nitric oxide appears at the same numerical rate,

$$\frac{d[NO]}{dt}=2r=0.030,\mathrm{M,s^{-1}}.$$

The balanced equation therefore connects the rates at which different species appear or disappear, while a rate law provides the separate relationship between reaction rate and the current composition of the mixture.