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:[https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/Modeling_Reaction_Kinetics/Collision_Theory/Collision_Frequency chem.libretexts.org: Collision Frequency]

: $Z = N_\text{A} N_\text{B} \sigma_\text{AB} \sqrt\frac{8 k_\text{B} T}{\pi \mu_\text{AB}},$

which has units of [volume][time]⁻¹.

Here,

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

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:{{Cite journal|last=Debye|first=P.|date=1942|title=Reaction Rates in Ionic Solutions|url=https://doi.org/10.1149/1.3071413|journal=Transactions of the Electrochemical Society|language=en|volume=82|issue=1|pages=265|doi=10.1149/1.3071413|issn=0096-4743}}

: $\nu = \frac{8 k_\text{B} T}{3 \eta} n,$

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

Category:Chemical kinetics