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## Area of Expertise - kinetic gas theory

The shock frequency ${z}_{\mathrm{A.}}(\mathrm{B.})$of a particle A and a particle B is a quotient of the number of these collisions $z$ per time unit $\Delta t$. is the collision frequency for two types of particles A and B:

- $$\begin{array}{l}{z}_{\mathrm{A.}}(\mathrm{B.})=\frac{z}{\Delta t}=\sigma {\overline{c}}_{\mathrm{A.}\mathrm{B.}}\frac{{N}_{\mathrm{B.}}}{V}\\ \sigma =\pi {r}_{\mathrm{A.}\mathrm{B.}}^{2}=\pi {({r}_{\mathrm{A.}}+{r}_{\mathrm{B.}})}^{2}\phantom{\rule{2em}{0ex}}{\overline{c}}_{\mathrm{A.}\mathrm{B.}}=\sqrt{\frac{8kT}{\pi \mu}}\end{array}\phantom{\rule{2em}{0ex}}\begin{array}{l}\sigma =\text{Impact cross-section}\\ {\overline{c}}_{\mathrm{A.}\mathrm{B.}}=\text{mean relative speed}\\ \frac{{N}_{\mathrm{B.}}}{V}=\text{Particle density of B}\\ {r}_{\mathrm{A.}\mathrm{B.}}=\text{Sum of the radii}{r}_{\mathrm{A.}}\text{and}{r}_{\mathrm{B.}}\\ k=\text{Boltzmann constant}\\ T=\text{absolute temperature}\\ \mu =\text{reduced mass}\end{array}$$

A particle A collides with all particles B, which are in the collision cylinder $\sigma {\overline{c}}_{\mathrm{A.}\mathrm{B.}}$ are located.

Multiplying the above equation by the particle density of A, the collision density becomes ${Z}_{\mathrm{A.}\mathrm{B.}}$ obtain:

- $${Z}_{\mathrm{A.}\mathrm{B.}}=\sigma {\overline{c}}_{\mathrm{A.}\mathrm{B.}}\frac{{N}_{\mathrm{A.}}}{V}\frac{{N}_{\mathrm{B.}}}{V}\phantom{\rule{2em}{0ex}}\frac{{N}_{\mathrm{A.}}}{V}=\text{Particle density of A}$$

The collision density indicates the number of collisions between a particle A and a particle B per unit of time and volume.

The collision frequency is important for the theoretical determination of the reaction rate in the gas phase.

See also: collision theory, collision laws

## Learning units in which the term is dealt with

### Mean free path of gas particles15 minutes.

#### ChemistryPhysical chemistrythermodynamics

The subject of the learning unit is the mean free path of gas particles and their derivation on the basis of the diameter and mean speed of the particles. Their importance in the construction of high vacuum systems is discussed.

### Shock frequency and shock density in gases60 min.

#### ChemistryPhysical chemistrythermodynamics

Shock frequency and shock density in gases are fundamental for the calculation of the mean free path of the gas particles, the speed of bimolecular gas reactions and the material parameters in transport phenomena. The learning unit shows how both quantities can be traced back to the number, mass and size of the gas particles by means of the collision cross-section, collision cylinder and collision axis. A special feature is the detailed derivation of the mean relative speed of the particles, which forms the conclusion of the learning unit and requires significantly higher prior knowledge of the reader than all previous sections of the learning unit.