Collision frequency explained

See main article: Collision theory.

Collision frequency describes the rate of collisions between two atomic or molecular species in a given volume, per unit time. In an ideal gas, assuming that the species behave like hard spheres, the collision frequency between entities of species A and species B is:^[1]

Z = N _{A} N _{B} \sigma _{AB} \sqrt (8 k _{B} T)/(\pi \mu _{AB}) , which has units of [volume][time]⁻¹.

Here,

N _{A} is the number of A molecules in the gas,N _{B} is the number of B molecules in the gas,\sigma _{AB} is the collision cross section, the "effective area" seen by two colliding molecules, simplified to \sigma _{AB} = \pi(r _{A+r} ^{2} ^{B )} , where r _{A} the radius of A and r _{B} the radius of B.k _{B} is the Boltzmann constant,T is the temperature,\mu _{AB} is the reduced mass of the reactants A and B, \mu _{AB} = ({m _{A})/(m _{B}) }

Collision in diluted solution

In the case of equal-size particles at a concentration

n in a solution of viscosity η , an expression for collision frequency Z = V\nu where V is the volume in question, and \nu is the number of collisions per second, can be written as:^[2] \nu = (8 k _{B} T)/(3η) n,

Where:

k _{B} is the Boltzmann constantT is the absolute temperature (unit K)η is the viscosity of the solution (pascal seconds)n is the concentration of particles per cm³

Here the frequency is independent of particle size, a result noted as counter-intuitive. For particles of different size, more elaborate expressions can be derived for estimating

\nu .

References

1. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/Modeling_Reaction_Kinetics/Collision_Theory/Collision_Frequency chem.libretexts.org: Collision Frequency
2. Debye. P.. 1942. Reaction Rates in Ionic Solutions. Transactions of the Electrochemical Society. en. 82. 1. 265. 10.1149/1.3071413. 0096-4743.