From AMS Glossary
A chemical reaction involving only one chemical species, in which the rate of decrease of the concentration of the reactant is directly proportional to its concentration.
The constant of proportionality is the first-order rate coefficient k, which has units of inverse time:
, where [A] is the concentration of species A. The first-order rate equation is often expressed in its integrated form,
, where [A]0 is the initial concentration of species A. A common example of a first-order reaction is a radioactive decay process. In the atmosphere, photolysis reactions obey first-order kinetics. Also, unimolecular decomposition reactions at their high-pressure limit empirically follow first-order kinetics.