Editing Collision theory (section)

==Alternative collision models for diluted solutions==
Collision in diluted gas or liquid solution is regulated by diffusion instead of direct collisions, which can be calculated from [[Fick's laws of diffusion]]. Theoretical models to calculate the collision frequency in solutions have been proposed by [[Marian Smoluchowski]] in a seminal 1916 publication at the infinite time limit.<ref name=Smoluchowski1916>{{cite journal
|last=Smoluchowski
|first=Marian
|title=Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen
|journal=Phys. Z.
|year=1916
|volume=17
|pages=557–571, 585–599
|language=German
|bibcode=1916ZPhy...17..557S}}</ref>

For a diluted solution in the gas or the liquid phase, the collision equation developed for neat gas is not suitable when [[diffusion]] takes control of the collision frequency, i.e., the direct collision between the two molecules no longer dominates. For any given molecule A, it has to collide with a lot of solvent molecules, let's say molecule C, before finding the B molecule to react with. Thus the probability of collision should be calculated using the [[Brownian motion]] model, which can be approximated to a diffusive flux using various boundary conditions that yield different equations in the Smoluchowski.

For the diffusive collision, at the infinite time limit when the molecular flux can be calculated from the [[Fick's laws of diffusion]], in 1916 Smoluchowski derived a collision frequency between molecule A and B in a diluted solution:<ref name=Smoluchowski1916></ref>

: <math>Z_{AB} = 4 \pi R D_r C_A C_B </math> 

where:
* <math>Z_{AB}</math> is the collision frequency, unit #collisions/s in 1 m<sup>3</sup> of solution.
* <math>R</math> is the radius of the collision cross-section, unit m.
* <math>D_r</math> is the relative diffusion constant between A and B, unit m<sup>2</sup>/s, and <math>D_r = D_A + D_B</math>.
* <math>C_A</math> and <math>C_B</math> are the number concentrations of molecules A and B in the solution respectively, unit #molecule/m<sup>3</sup>.

or
: <math>Z_{AB} = 1000 N_A * 4 \pi R D_r [A] [B] = k [A] [B] </math> 

where:
* <math>Z_{AB}</math> is in unit mole collisions/s in 1 L of solution.
* <math>N_\text{A}</math> is the [[Avogadro constant]].
* <math>R</math> is the radius of the collision cross-section, unit m.
* <math>D_r</math> is the relative diffusion constant between A and B, unit m<sup>2</sup>/s. 
* <math>[A]</math> and <math>[B]</math> are the molar concentrations of A and B respectively, unit mol/L.
* <math>k</math> is the diffusive collision rate constant, unit L mol<sup>−1</sup> s<sup>−1</sup>.