# Collision frequency

Collision frequency is defined in chemical kinetics and collision theory, in the background of theoretical kinetics.

For a reaction between A and B, the collision frequency (Z) is the number of collisions between A and B occurring in the container per unit volume per unit time.

$Z=n_{\text{A}}n_{\text{B}}\sigma _{AB}{\sqrt {\frac {8k_{\text{B}}T}{\pi \mu _{AB}}}},$ 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 reaction 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 $m^{2}\ kg\ s^{-2}\ K)$ ,
• $T$ 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 $kg$ )
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