Frequently Asked Question

The extent of adsorption of a molecule A₂ that dissociates on the surface to form A fragments can be described using the Langmuir adsorption isotherm. Here's how:
Langmuir Isotherm for Dissociative Adsorption

Assumptions:

The surface is homogeneous and all adsorption sites are equivalent.

Adsorption occurs at a fixed number of sites and does not extend beyond a single layer.

There is no interaction between adsorbed molecules.

Derivation:

Consider a surface with 'S' total adsorption sites, and let 'θ' be the fraction of sites occupied by A fragments.

The rate of adsorption of A₂ is proportional to the partial pressure of A₂ (P) and the number of vacant sites (1-θ): Rate of adsorption = k₁P(1-θ)

The rate of desorption of A is proportional to the square of the fraction of occupied sites (θ²): Rate of desorption = k₂θ²

At equilibrium, the rates of adsorption and desorption are equal: k₁P(1-θ) = k₂θ²

Solving for θ, we get:

θ = (k₁P / (k₂ + k₁P))^(1/2)


Extent of Adsorption: The extent of adsorption (θ) represents the fraction of surface sites occupied by A fragments. In this case, it's directly related to the partial pressure of A₂ and the adsorption and desorption rate constants.
Important Points:

The expression for θ assumes that the adsorption of A₂ is dissociative, meaning that one A₂ molecule occupies two adsorption sites on the surface.
The Langmuir isotherm provides a good approximation for the extent of adsorption under low pressure conditions and for systems where the assumptions hold.
In real systems, the adsorption behavior can be more complex due to factors like surface heterogeneity, interactions between adsorbed molecules, and multi-layer adsorption.