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 A and B is:[1]

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

Main article: Collision theory

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

where:

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

References

1. chem.libretexts.org: Collision Frequency