A novel derivation of collision theory rate constants for a bimolecular reaction

A novel exact derivation for the kinetic constant of a bimolecular reaction according to three well-known models of collision theory is reported. The use of probability density functions, with the introduction of a novel geometry to study the collision process, allows simplifying the derivation to such an extent, that, for a proper statistical background, it is is possible to recover the line-of-centers and the angular dependent line-of-centers models in no more than a couple of lectures. Although the derivation is introduced to recover the temperature-dependent kinetic constant, it is shown that the energy-dependent reactive cross section can be recovered as well. A possible confusion in the interpretation of the pre-exponential factor is commented.