1. The Langmuir Isotherm
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 (molecules or
atoms) which are bound to the surface of the solid.
As with all chemical
equilibria, the position of equilibrium will depend upon a number of factors :
- The relative stabilities of the
adsorbed and gas phase species involved
- The temperature of the system (both
the gas and surface, although these are normally the same)
- The pressure of the gas above the
surface
In general, factors
(2) and (3) exert opposite effects on the concentration of adsorbed species -
that is to say that the surface coverage may be increased by
raising the gas pressure but will be reduced if the surface temperature is
raised.
The Langmuir isotherm
was developed by Irving Langmuir in 1916 to describe the dependence of the
surface coverage of an adsorbed gas on the pressure of the gas above the
surface at a fixed temperature. There are many other types of isotherm (Temkin,
Freundlich ...) which differ in one or more of the assumptions made in deriving
the expression for the surface coverage; in particular, on how they treat the
surface coverage dependence of the enthalpy of adsorption. Whilst the Langmuir
isotherm is one of the simplest, it still provides a useful insight into the
pressure dependence of the extent of surface adsorption.
Important Note - Surface
Coverage & the Langmuir Isotherm
When considering
adsorption isotherms it is conventional to adopt a definition of surface
coverage (θ) which defines the maximum (saturation) surface coverage of
a particular adsorbate on a given surface always to be unity, i.e. θmax =
1 .
This way of defining
the surface coverage differs from that usually adopted in surface science where the more
common practice is to equate θ with the ratio of adsorbate species to surface
substrate atoms (which leads to saturation coverages which are almost
invariably less than unity).
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 (M), together with vacant surface sites, and the species
adsorbed on the surface. Thus, for a non-dissociative (molecular) adsorption
process we consider the adsorption to be represented by the following chemical
equation :
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