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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 densityZ 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 massm 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.
PAC, 1996, 68, 149 (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 160
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IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.
Last update: 2014-02-24; version: 2.3.3.
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