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]

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

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 collision cross 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 the Boltzmann constant,
• ${\displaystyle T}$ is the temperature,
• ${\displaystyle \mu _{\text{AB))}$ is the reduced 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 of viscosity ${\displaystyle \eta }$ , 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]