2.3 Adsorption Kinetics  The Rate of Adsorption
The rate of adsorption, R_{ads}, of a molecule onto a surface can be expressed in the same manner as any kinetic process. For example, when it is expressed in terms of the partial pressure of the molecule in the gas phase above the surface:

R_{ads} = k' P^{ x} 
where: 
x  kinetic order 
If the rate constant is then expressed in an Arrhenius form, then we obtain a kinetic equation of the form :

R_{ads} = A exp ( E_{a} / RT ). P^{ x} 
where E_{a} is the activation energy for adsorption, and A the preexponential (frequency) factor.
It is much more informative, however, to consider the factors controlling this process at the molecular level....
The rate of adsorption is governed by
i.e. we can express the rate of adsorption (per unit area of surface) as a product of the incident molecular flux, F , and the sticking probability , S .

R_{ads} = S . F 
[molecules m^{2} s^{1 }] 
The flux of incident molecules is given by the HertzKnudsen equation

Flux , F = P / (2πmkT)^{1/2} 
[ molecules m^{2} s^{1} ] 
where 


P  gas pressure [ N m^{2} ] 
The sticking probability is clearly a property of the adsorbate / substrate system under consideration but must lie in the range 0 < S < 1; it may depend upon various factors  foremost amongst these being the existing coverage of adsorbed species (θ) and the presence of any activation barrier to adsorption. In general ,therefore ,

S = f (θ) . exp ( E_{a} / RT ) 
where, once again, E_{a} is the activation energy for adsorption and f(θ) is some, as yet undetermined, function of the existing surface coverage of adsorbed species.
Combining the equations for S and F yields the following expression for the rate of adsorption :
Notes :
For a discussion of some of the factors which determine the magnitude of the activation energy of adsorption you should see Section 2.4 which looks at the typical PE curve associated with various types of adsorption process.
Estimating Surface Coverages arising as a result of Gas Exposure
If a surface is initially clean and it is then exposed to a gas pressure under conditions where the rate of desorption is very slow, then the coverage of adsorbed molecules may initially be estimated simply by consideration of the kinetics of adsorption.
As noted above, the rate of adsorption is given by : R_{ads} = S . F
i.e.
where : N_{ads} is the number of adsorbed species per unit area of surface.
In general, this equation must be integrated to obtain an expression for N_{ads}, since the sticking probability is coverage (and hence also time) dependent.
However, if it is assumed that the sticking probability is essentially constant (which may be a reasonable approximation for relatively low coverages), then this integration simply yields: