Skip to main content
Chemistry LibreTexts

3: The Langmuir Isotherm

  • Page ID
    25350
  • A continuous monolayer of adsorbate molecules surrounding a homogeneous solid surface is the conceptual basis for this adsorption model. The Langmuir isotherm is formally equivalent to the Hill equation in biochemistry.

    • 3.1: Introduction
      Whenever a gas is in contact with a solid there will be an equilibrium established between the molecules in the gas phase and the corresponding adsorbed species which are bound to the surface of the solid.  The position of equilibrium will depend upon a number of factors:  (1) The relative stabilities of the adsorbed and gas phase species involved, (2) The temperature of the system (both the gas and surface, although these are normally the same)  and (3) The pressure of the gas above the surface
    • 3.2: Langmuir Isotherm - derivation from equilibrium considerations
      We may derive the Langmuir isotherm by treating the adsorption process as we would any other equilibrium process - except in this case the equilibrium is between the gas phase molecules, together with vacant surface sites, and the species adsorbed on the surface.
    • 3.3: Langmuir Isotherm from a Kinetics Consideration
      The equilibrium that may exist between gas adsorbed on a surface and molecules in the gas phase is a dynamic state, i.e. the equilibrium represents a state in which the rate of adsorption of molecules onto the surface is exactly counterbalanced by the rate of desorption of molecules back into the gas phase. It should therefore be possible to derive an isotherm for the adsorption process simply by considering and equating the rates for these two processes.
    • 3.4: Variation of Surface Coverage with Temperature & Pressure
      Application of the assumptions of the Langmuir Isotherm leads to readily derivable expressions for the pressure dependence of the surface coverage.
    • 3.5: Applications - Kinetics of Catalytic Reactions
      It is possible to predict how the kinetics of certain heterogeneously-catalysed reactions might vary with the partial pressures of the reactant gases above the catalyst surface by using the Langmuir isotherm expression for equilibrium surface coverages.

    Contributors

    • Roger Nix (Queen Mary, University of London)