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^{[better source needed]} $Z = N_{A} N_{B} σ_{AB} \sqrt{\frac{8 k_{B} T}{π μ_{AB}}},$ where

N_{A}

is the number of A particles in the volume,

N_{B}

is the number of B particles in the volume,

σ_{AB}

is the collision cross section, the "effective area" seen by two colliding molecules (for hard spheres,

σ_{AB} = π (r_{A} + r_{B})^{2}

, where

r_{A}

is the radius of A, and

r_{B}

is the radius of B),

k_{B}

is the Boltzmann constant,

T

is the thermodynamic temperature,

μ_{AB} = \frac{m_{A} m_{B}}{m_{A} + m_{B}}

is the reduced mass of A and B particles.

Collision in diluted solution

In the case of equal-size particles at a concentration $n$ in a solution of viscosity $η$ , an expression for collision frequency $Z = V ν$ , where $V$ is the volume in question, and $ν$ is the number of collisions per second, can be written as $ν = \frac{8 k_{B} T}{3 η} n,$ where

k_{B}

is the Boltzmann constant,

T

is the absolute temperature,

η

is the viscosity of the solution,

n

is the number density.

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 $ν$ .

References

↑ "Collision Frequency". LibreTexts Chemistry. 2 October 2013.
1 2 Debye, P. (1942). "Reaction Rates in Ionic Solutions". Transactions of the Electrochemical Society. 82 (1): 265–272. doi:10.1149/1.3071413. ISSN 0096-4743.

[1] "Collision Frequency". LibreTexts Chemistry. 2 October 2013.

[:0-2] 1 2 Debye, P. (1942). "Reaction Rates in Ionic Solutions". Transactions of the Electrochemical Society. 82 (1): 265–272. doi:10.1149/1.3071413. ISSN 0096-4743.