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:chem.libretexts.org: Collision Frequency
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: $Z = N_\text N_\text \sigma_\text \sqrt\frac,$
which has units of olumetime]⁻¹.

Here,
* $N_\text$ is the number of A molecules in the gas,
* $N_\text$ is the number of B molecules in the gas,
* $\sigma_\text$ is the collision cross section (physics), cross section, the "effective area" seen by two colliding molecules, simplified to $\sigma_\text = \pi(r_\text+r_\text)^2$, where $r_\text$ the radius of A and $r_\text$ the radius of B.
* $k_\text$ is the Boltzmann constant,
* $T$ is the temperature,
* $\mu_\text$ is the reduced mass of the reactants A and B, $\mu_\text = \frac$

Collision in diluted solution

In the case of equal-size particles at a concentration $n$ in a solution of viscosity $\eta$ , an expression for collision frequency $Z=V\nu$ where $V$ is the volume in question, and $\nu$ is the number of collisions per second, can be written as:

: $\nu = \frac{3 \eta} n,$

Where:

* $k_B$ is the Boltzmann constant
* $T$ is the absolute temperature (unit K)
* $\eta$ is the viscosity of the solution (pascal seconds)
* $n$ 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 $\nu$.

References

Chemical kinetics