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

${\displaystyle Z=N_{\text{A}}{N}_{\text{B}}{\sigma }_{\text{AB}}\sqrt{\frac{8k_{\text{B}}T}{\pi {\mu }_{\text{AB}}}},}$

which has units of [volume][time]⁻¹.

Here,

• ${\displaystyle N_{\text{A}}}$ is the number of A molecules in the gas,
• ${\displaystyle N_{\text{B}}}$ is the number of B molecules in the gas,
• ${\displaystyle {\sigma }_{\text{AB}}}$ is the collisioncross section, the "effective area" seen by two colliding molecules, simplified to${\displaystyle {\sigma }_{\text{AB}}=\pi (r_{\text{A}}+r_{\text{B}}{)}^2}$, where${\displaystyle r_{\text{A}}}$ the radius of A and${\displaystyle r_{\text{B}}}$ the radius of B.
• ${\displaystyle k_{\text{B}}}$ is theBoltzmann constant,
• ${\displaystyle T}$ is the temperature,
• ${\displaystyle {\mu }_{\text{AB}}}$ is thereduced mass of the reactants A and B,${\displaystyle {\mu }_{\text{AB}}=\frac{m_{\text{A}}{m}_{\text{B}}}{m_{\text{A}}+m_{\text{B}}}}$

In the case of equal-size particles at a concentration${\displaystyle n}$ in a solution ofviscosity${\displaystyle \eta }$ , an expression for collision frequency${\displaystyle Z=V\nu }$ where${\displaystyle V}$ is the volume in question, and${\displaystyle \nu }$ is the number of collisions per second, can be written as:^[2]

${\displaystyle \nu =\frac{8k_{\text{B}}T}{3\eta }n,}$

Where:

• ${\displaystyle k_B}$ is the Boltzmann constant
• ${\displaystyle T}$ is the absolute temperature (unit K)
• ${\displaystyle \eta }$ is the viscosity of the solution (pascal seconds)
• ${\displaystyle n}$ 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${\displaystyle \nu }$.^[2]

• Chemical kinetics

• Articles with short description
• Short description is different from Wikidata