Collision theoryIUPAC Term

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, strong A /strong , the collision density is given by simple collision theory as: \[Z_{\mathrm{AA}} \frac{\sqrt{2}\ \pi \ σ {2}\ u\ N_{{A}} {2}}{2}\] Here N A is the number density of molecules and u is the mean molecular speed, given by kinetic theory to be 8kB.Tπm, where m is the molecular mass, and σ π d AA 2. Thus: \[Z_{\mathrm{AA}} 2\ N_{{A}} {2}\ σ {2}\ \sqrt{\frac{\pi \ k_{{B}}\ T}{m}}\] The corresponding expression for the collision density Z AB for two unlike molecules strong A /strong and strong B /strong , of masses m A and m B is: \[Z_{\mathrm{AB}} N_{{A}}\ N_{{B}}\ σ {2}\ \sqrt{\frac{\pi \ k_{{B}}\ T}{μ }}\] 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: \[z_{\mathrm{AA}}\quad {or}\quad z_{\mathrm{AB}} L\ σ {2}\ \sqrt{\frac{8\ \pi \ k_{{B}}\ T}{μ }}\] 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.