The mechanism

In the follwing we will consider the mechanism


where A2 is a molecule in the gas-phase, * is a vacant adsorption site, A2* is an adsorbed molecule and A* is an adsorbed atom. We assume that the first step is much faster than the second. Together these two steps describe a typical mechanism for the chemisorption of a diatomic molecule:

This mechanism is rather simple but it is complicated enough to illustrate the principles in the following.

As an adsorption site, *, is either free or occupied by A2* or A*, the coverage probabilities, , must add up to unity:


In the simplest case the reaction rates are proportional to the coverages.

Using


we find

where r+ is the adsorption rate and r- is the desorption rate. The difference between these two terms is the net adsorption rate, r. The two constants, k2+ and k2-, are known as the forward and backward rate constants, respectively.

At equilibrium the net adsorption rate is by definition zero. If we compare the rate equation to the conventional equilibrium equation


we find

Usually both k2+ and k2- have Arrhenius form


at least for small or moderate variations of T.

A is known as the preexponential factor while is known as the activation energy


Comparison of equation ? with equation ? shows that

As the adsorption energy, is negative, high pressures and low temperatures generally favour the formation of adsorbed molecules.

However, in the gas-phase the A2 molecule has three translational and two rotational degrees of freedom. In the adsorbed state these degrees of freedom are transformed into 6 vibrational degrees of freedom around the equilibrium position at the surface. This usually results in a negative adsorption entropy. At a given pressure the equilibrium between gas and adsorbate will shift towards desorption when the temperature is increased.

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Author Per Stoltze stoltze@fysik.dtu.dk