# Elementary reaction

An elementary reaction is a chemical reaction in which one or more of the chemical species react directly to form products in a single reaction step and with a single transition state.[1]

In a unimolecular elementary reaction, a molecule A dissociates or isomerises to form the products(s)

$\mbox{A} \rightarrow \mbox{products.}$

At constant temperature, the rate of such a reaction is proportional to the concentration of the species A

$\frac{d[\mbox{A}]}{dt}=-k[\mbox{A}].$

In a bimolecular elementary reaction, two atoms, molecules, ions or radicals, A and B, react together to form the product(s)

$\mbox{A + B} \rightarrow \mbox{products.}$

The rate of such a reaction, at constant temperature, is proportional to the product of the concentrations of the species A and B

$\frac{d[\mbox{A}]}{dt}=\frac{d[\mbox{B}]}{dt}=-k[\mbox{A}][\mbox{B}].$

The rate expression for an elementary bimolecular reaction is sometimes referred to as the Law of Mass Action as it was first proposed by Guldberg and Waage in 1864. An example of this type of reaction is a cycloaddition reaction. This rate expression can be derived from first principles by using collision theory for ideal gases. For the case of dilute fluids equivalent results have been obtained from simple probabilistic arguments.[2]

According to collision theory the probability of three chemical species reacting simultaneously with each other in a termolecular elementary reactions is negligible. Hence such termolecular reactions are commonly referred as non-elementary reactions and can be broken down into a more fundamental set of bimolecular reactions,[3][4] in agreement with the law of mass action. However it is not always possible to derive overall reaction schemes but solutions based on rate equations are possible in terms of steady-state or Michaelis-Menten approximations.

## Notes

1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "elementary reaction".
2. ^ Gillespie, D.T., A diffusional bimolecular propensity function, The Journal of Chemical Physics 131, 164109 (2009)
3. ^ Cook, GB and Gray, P. and Knapp, DG and Scott, SK, Bimolecular routes to cubic autocatalysis, The Journal of Physical Chemistry 93, 2749--2755 (1989)
4. ^ Aris, R. and Gray, P. and Scott, SK, Modelling cubic autocatalysis by successive bimolecular steps, Chemical Engineering Science 43', 207--211 (1988)