collision theory

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 $d$ 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:

$Z AA = 2 π σ 2 u N A 2 2$

Here $N A$ is the number density of molecules and $u$ is the mean molecular speed, given by kinetic theory to be $8 k B T π m$ , where $m$ is the molecular mass, and $σ = π d AA 2$ . Thus:

$Z AA = 2 N A 2 σ 2 π k B T m$

The corresponding expression for the collision density $Z AB$ for two unlike molecules A and B, of masses $m A$ and $m B$ is:

$Z AB = N A N B σ 2 π k B T μ$

where $μ$ is the reduced mass $m A m B m A + m B$ , and $σ = π d AB 2$ . For the collision frequency factor these formulations lead to the following expression:

$z AA or z AB = L σ 2 8 π k B T μ$

where $L$ 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