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:
ZAA = 1⁄2√2πσ2uNA2
Here NA is the number density of molecules and u is the mean molecular
speed, given by kinetic theory to be (8kBT/πm)1/2, where m is the molecular
mass, and σ = πdAA2. Thus:
ZAA = 2NA
2σ2(πkBT/m)1/2
The corresponding expression for the collision density ZAB for two unlike
molecules A and B, of masses mA and mB is:
ZAB = NANBσ2(πkBT/µ)1/2
where µ is the reduced mass mAmB/(mA+mB), and σ = πdAB2.
For the collision frequency factor these formulations lead to the following
expression:
zAA or zAB = Lσ2(8πkBT/µ) 1/2
where L is the Avogadro constant.
More advanced collision theories, not involving the assumption that mole-
cules behave as hard spheres, are known as generalized kinetic theories.
1996, 68, 160
IUPAC Compendium of Chemical Terminology
2nd Edition (1997)