Collision frequency

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, ${\displaystyle \mu _{\text{AB}}={\frac {{m_{\text{A}}}{m_{\text{B}}}}{{m_{\text{A}}}+{m_{\text{B}}}}}}$