Collision frequency

Short description: Physics calculation for collisions

Main article: Chemistry: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=NANBσAB8kBTπμAB, where

NA is the number of A particles in the volume,
NB is the number of B particles in the volume,
σAB is the collision cross section, the "effective area" seen by two colliding molecules (for hard spheres, σAB=π(rA+rB)2, where rA is the radius of A, and rB is the radius of B),
kB is the Boltzmann constant,
T is the thermodynamic temperature,
μAB=mAmBmA+mB 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 η, an expression for collision frequency Z=Vν, where V is the volume in question, and ν is the number of collisions per second, can be written as[2] ν=8kBT3ηn, where

kB is the Boltzmann constant,
T is the absolute temperature,
η 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 ν.[2]

## References

1. ↑ "Collision Frequency". 2 October 2013. 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.
2. ↑ 2.0 2.1 Debye, P. (1942). "Reaction Rates in Ionic Solutions" (in en). Transactions of the Electrochemical Society 82 (1): 265–272. doi:10.1149/1.3071413. ISSN 0096-4743. https://doi.org/10.1149/1.3071413.

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