Adsorption kinetics

Rate of adsorption : From kinetic theory the rate of collision, r_c, is the rate at which molecules of a gas strike a bare surface per cm² per sec at pressure p. The r_c is given asmolecules /cm². sec, where ‘k_B' is Boltzmanns constant, ‘m' is mass and ‘T' is temperature.

Then the rate of adsorption is ---------------------------------------[1]

The ‘s' is known as the sticking coefficient and defined as fraction of molecules bombarding or impinging on the catalyst surface that stick to the surface on impact. The ‘s' is also called the sticking probability.

Now whether a molecule will be adsorbed (chemisorbed) depends on two main parameters: activation energy and configuration. Only those molecules possessing the required activation energy can be chemisorbed. Even if the molecules possess the necessary energy they may not be chemisorbed if the configuration of the molecule and surface site do not allow the activated complex to be traversed. The fraction of molecules possessing the required energy is , where E_a is the activation energy for chemisorption.

The configuration probability that a molecule will occupy a single site is proportional to the fraction of unoccupied surface, 1-θ, where θ is the fraction of surface covered.

Therefore , -----------------------------[2]

α is the proportionality constant often known as ‘condensation coefficient. It is the fraction of those molecules with energy greater than E_a that is adsorbed.

Combining equation [1] and [2] gives

 

or -------------------------[3]

 

For non- dissociative adsorption, f(θ)= fraction of surface uncovered = (1- θ). It is for non dissociative adsorption. For dissociative adsorption into two fragments, f(θ) = (1- θ)² and f(θ) = (1-θ)³ for three fragments. The type of adsorption depends on extent on interaction between adsorbate and adsorbent surface molecules.

In actual adsorption, the observed rate decreases rapidly with increasing surface coverage which implies that the activation energy increases with the surface coverage, θ. The condensation coefficient α also var ies with θ. These variations are caused by surface heterogeneity, that is the activity of the adsorbent sites varies and different sites posses different values of α and E_a. The most active sites are associated with lowest activation energy. Hence probability of occupation of these sites by adsorbate molecules is higher. Further, the interaction between occupied and unoccupied site also affects the rate of adsorption. Hence α and E_a should be represented as function of θ.

Rates of desorption

The rate of desorption is given by Polanyi –Wigner equation as

---------------------------[4]

w here, E_d is activation energy for desorption, v is the pre-exponential factor of the desorption rate coefficient, N_a is the number of binding sites for the adsorbed molecules and m is kinetic order for desorption process. Kinetic order suggests the nature of elementary steps that governs the desorption. A zero-order kinetics indicate s that desorption occurs from multilayer where desorption is independent of coverage. A first order kinetics indicates the presence of single surface species whereas second order kinetics indicates recombination of adsorbate atoms leading to production of a diatomic molecule that is then desorbed.