Adsorption isotherms

Adsorption is the accumulation of gas or dissolved molecules onto a solid (or liquid) surface, distinct from absorption, in which molecules are taken up into the bulk of a material rather than sticking only to its surface. A naive model might expect the amount adsorbed to simply grow in proportion to gas pressure, but real adsorption data consistently shows the amount adsorbed rising steeply at low pressure and then levelling off toward a maximum at high pressure — a saturation behaviour that a simple proportional model cannot explain, but that the Langmuir isotherm accounts for directly.

The Langmuir model rests on a small set of physically motivated assumptions: the solid surface offers a fixed number of identical adsorption sites, each site can hold at most one adsorbed molecule (monolayer coverage), and adsorbed molecules do not interact with each other. Crucially, the model treats adsorption as a dynamic equilibrium rather than a one-way process: molecules continuously adsorb onto empty sites at a rate proportional to both the gas pressure and the fraction of sites still empty, while adsorbed molecules continuously desorb at a rate proportional to the fraction of sites currently occupied. Setting the adsorption and desorption rates equal at equilibrium and solving for the fractional surface coverage θ yields the Langmuir isotherm equation, θ = KP/(1 + KP), where P is the gas pressure and K is an equilibrium constant reflecting how strongly the gas binds to the surface.

This equation reproduces exactly the saturation behaviour seen experimentally. At low pressure (KP much less than 1), the isotherm reduces to θ ≈ KP — coverage increases roughly linearly with pressure, since plenty of empty sites remain available and adsorption dominates over desorption. At high pressure (KP much greater than 1), the isotherm approaches θ ≈ 1 — coverage saturates near complete monolayer occupation, since essentially every site is filled and further pressure increases can add very little more. This finite-sites, saturating behaviour is the qualitative signature the Langmuir model is built to capture, and though real surfaces often deviate from its simplifying assumptions (multiple adsorption layers, non-identical sites, interactions between adsorbed molecules — addressed by more elaborate isotherms such as the BET model), the Langmuir isotherm remains the essential starting point for understanding gas-solid adsorption, with direct application to heterogeneous catalysis, where the reaction rate on a catalyst surface often depends directly on how much of that surface is covered by reactant molecules.