Various collision theories, dealing with the frequency of collision between reactant molecules, have been put forward. In the earliest theories reactant molecules were
regarded as hard spheres, and a collision was considered to occur when the distance
between the centres of two molecules was equal to the sum of their radii. For a gas
containing only one type of molecule, **A**, the collision density is given by simple collision theory as:
Here is the number density of molecules and is the mean molecular speed, given by kinetic theory to be
, where is the molecular mass, and
. Thus:
The corresponding expression for the collision density for two unlike molecules **A** and **B**, of masses and is:
where is the reduced mass, and
.
For the collision frequency factor these formulations lead to the following expression:
where is the Avogadro constant. More advanced collision theories, not involving the assumption that molecules behave
as hard spheres, are known as generalized kinetic theories.

Source:

PAC, 1996, *68*, 149*
(A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC
Recommendations 1996))
* on page 160