Collision frequency

Main article: 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 A and B is:

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

SI unit of Z is number of collision $m^{-3}s^{-1}=1000N_{A}\ mol\ L^{-1}\ s^{-1}$, where $N_{A}$ is Avogadro constant.

where:

• $n_{A}$ is the number density of A in the gas (unit $m^{-3}$),
• $n_{B}$ is the number density of B in the gas (unit $m^{-3}$),
• $\sigma _{AB}$ is the collision cross section (unit $m^{2}$), the area when two molecules collide with each other, simplified to $\sigma _{AB}=\pi (r_{A}+r_{B})^{2}$, where $r_{A}$ the radius of A and $r_{B}$ the radius of B.
• $k_{B}$ is the Boltzmann's constant (unit $m^{2}\ kg\ s^{-2}\ K^{-1})$,
• $T$ is the temperature (unit $K$),
• $\mu _{AB}$ is the reduced mass of the reactants A and B, $\mu _{AB}={\frac {{m_{A}}{m_{B}}}{{m_{A}}+{m_{B}}}}$ (unit $kg$)

Collision in diluted solution

Collision in diluted gas or liquid solution is regulated by diffusion instead of direct collisions, which can be calculated from Fick's laws of diffusion.