Collision frequency

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title: "Collision frequency" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["chemical-kinetics"] description: "Physics calculation for collisions" topic_path: "general/chemical-kinetics" source: "https://en.wikipedia.org/wiki/Collision_frequency" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Physics calculation for collisions ::

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 Z = N_\text{A} N_\text{B} \sigma_\text{AB} \sqrt\frac{8 k_\text{B} T}{\pi \mu_\text{AB}}, where : N_\text{A} is the number of A particles in the volume, : N_\text{B} is the number of B particles in the volume, : \sigma_\text{AB} is the collision cross section, the "effective area" seen by two colliding molecules (for hard spheres, \sigma_\text{AB} = \pi(r_\text{A} + r_\text{B})^2, where r_\text{A} is the radius of A, and r_\text{B} is the radius of B), : k_\text{B} is the Boltzmann constant, : T is the thermodynamic temperature, : \mu_\text{AB} = \frac{m_\text{A} m_\text{B}}{m_\text{A} + m_\text{B}} is the reduced mass of A and B particles.

Collision in diluted solution

In the case of equal-size particles at a concentration n in a solution of viscosity \eta, 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 \nu = \frac{8 k_\text{B} T}{3 \eta} n, where : k_B is the Boltzmann constant, : T is the absolute temperature, : \eta is the viscosity of the solution, : n is the number density.

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

References

1. (2 October 2013). "Collision Frequency".
2. Debye, P.. (1942). "Reaction Rates in Ionic Solutions". Transactions of the Electrochemical Society.

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