Langmuir Isotherm - extension to dissociative adsorption

Dissociative adsorption of a homonuclear diatomic molecule, A 2 , can be represented by the following chemical equation :

2 (S -) + A2 (g) = 2 (S - A)

where :   S - , represents a vacant surface site

The same general expressions for the rate of adsorption and rate of desorption as were employed in consideration of molecular adsorption may be used,

 

but the coverage dependent pre-exponential factors are now very different. More specifically, the adsorption process will now exhibit a second order dependence on the concentration of vacant sites whilst the reverse desorption process will also exhibit a second order dependence on the concentration of adsorbed atoms.

This leads to the following expressions

Adsorption,   f (θ) = c (1-θ)2

i.e. proportional to the square of the fraction of sites that are unoccupied.

Desorption,   f '(θ) = c' θ 2

i.e. proportional to the square of the fraction of sites which are occupied by adsorbed atoms.

and equating the rates of adsorption and desorption now yields an equation of the form :

After rearrangement, this gives the following Langmuir Isotherm expression for dissociative adsorption.

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