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]

which has units of [volume][time]−1.

Here,

  • is the number of A molecules in the gas,
  • is the number of B molecules in the gas,
  • is the collision cross section, the "effective area" seen by two colliding molecules, simplified to , where the radius of A and the radius of B.
  • is the Boltzmann constant,
  • is the temperature,
  • is the reduced mass of the reactants A and B,

Collision in diluted solution

In the case of equal-size particles at a concentration in a solution of viscosity , an expression for collision frequency where is the volume in question, and is the number of collisions per second, can be written as:[2]

Where:

  • is the Boltzmann constant
  • is the absolute temperature (unit K)
  • is the viscosity of the solution (pascal seconds)
  • 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 .[2]

References

  1. chem.libretexts.org: Collision Frequency
  2. 1 2 Debye, P. (1942). "Reaction Rates in Ionic Solutions". Transactions of the Electrochemical Society. 82 (1): 265. doi:10.1149/1.3071413. ISSN 0096-4743.
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