collision theory

https://doi.org/10.1351/goldbook.C01170
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: ZAA=2 π σ2 u NA22 Here NA is the number density of molecules and u is the mean molecular speed, given by kinetic theory to be 8 kB Tπ m, where m is the molecular mass, and σ=π dAA2. Thus: ZAA=2 NA2 σ2 π kB Tm The corresponding expression for the collision density ZAB for two unlike molecules A and B, of masses mA and mB is: ZAB=NA NB σ2 π kB Tμ where μ is the reduced mass mA mBmA+mB, and σ=π dAB2. For the collision frequency factor these formulations lead to the following expression: zAAorzAB=L σ2 8 π kB Tμ 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 [Terms] [Paper]
Citation: 'collision theory' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.C01170 RIS BibTex EndNote
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