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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 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
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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: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.
Last update: 2014-02-24; version: 2.3.3.
DOI of this term: doi:10.1351/goldbook.C01170.
Original PDF version: http://www.iupac.org/goldbook/C01170.pdf. The PDF version is out of date and is provided for reference purposes only. For some entries, the PDF version may be unavailable.
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