Adsorption Isotherms I

The Langmuir isotherm describes chemisorption by relating the amount of adsorbed molecules to pressure at constant temperature. It assumes adsorbate molecules form a reversible monolayer on identical, non-interacting surface sites. At equilibrium, the adsorption rate equals the desorption rate, yielding an equation that links fractional coverage to pressure through a parameter representing the ratio of adsorption and desorption rate constants.

At low pressures, fractional coverage increases linearly with partial pressure of gas molecules. As pressure increases, coverage rises more gradually and approaches saturation only at very high pressures where most surface sites are occupied. This behavior reflects the competition between adsorption collisions and desorption from occupied sites.

The Langmuir model assumes adsorption cannot exceed monolayer coverage, all surface sites are equivalent, molecules adsorb only at vacant sites, and there are no interactions between adsorbed molecules. These assumptions simplify the mathematical treatment of gas-surface interactions and make the model applicable to many chemisorption systems.

In non-dissociative adsorption, each molecule occupies one surface site and fills the surface rapidly. In dissociative adsorption, diatomic molecules dissociate into atoms that occupy separate sites, requiring a pair of adjacent vacant sites. This stoichiometric difference means dissociative adsorption progresses more slowly and shows different pressure dependence in the modified Langmuir equation.

The adsorption rate depends on pressure and vacant sites, governed by the adsorption rate constant. The desorption rate depends on occupied sites, governed by the desorption rate constant. At equilibrium, these rates are equal. The ratio of these constants, called alpha, directly determines how fractional coverage responds to changes in pressure.

The Freundlich isotherm is often more accurate than the Langmuir isotherm at intermediate pressures. Unlike Langmuir, it allows for multiple types of adsorption sites on the solid, each with different heats of adsorption. However, the Freundlich model is not valid at high pressures and is typically applied to adsorption of solutes from liquid solutions onto solids.

Dynamic equilibrium occurs when the rate of molecules colliding with and adsorbing onto the surface equals the rate of desorption from occupied sites. At this point, there is no net change in surface coverage. Equating the adsorption and desorption rate expressions and solving yields the Langmuir isotherm, which mathematically relates surface coverage to gas phase pressure.