Page 42 - Adsorption Technology & Design, Elsevier (1998)

Fundamentals of adsorption equilibria 39

component which could be adsorbed in a monolayer. Alternative ways to
express the ratio are on the basis of volume of gas adsorbed (at NTP) or on a
weight basis.
The simple derivation given assumes that a single molecule occupies a
single surface site and that there is no lateral interaction between adjacent
adsorbed molecules. Application of the kinetic theory of gases reveals that
the constant b can be identified as

1- v (27rmkT)'/~ exp( R~) (3.7)
b cr
where v is the pre-exponential factor of the desorption rate coefficient, tr the
condensation coefficient (defined as the fraction of those molecules that are
adsorbed with an activation energy greater than the energy of activation for
adsorption E~), m is the mass of the adsorbate molecule, k is the Boltzmann
constant and Q the heat of adsorption (the difference between the activation
energies Ed and E, necessary for desorption and adsorption, respectively).
It is important to note the implicit assumptions made in arriving at the
Langmuir isotherm. These are (i) the heat of adsorption Q is constant and
independent of coverage (a consequence of no lateral interaction between
adsorbate molecules), (ii) each adsorbate molecule occupies only one site
and (iii) the adsorption is localized (that is molecules remain at the site of
adsorption until desorbed).
Examples of gas adsorption onto porous solids which obey the Langmuir
equation are CH4 - sodalite and Ar - sodalite (Barrer and Vaughan 1971).
Other systems such as Kr- carbon (Sykes and Thomas 1960) and C3H8- 5A
zeolite (Ruthven and Loughlin 1972) show apparent conformity to the
Langmuir equation, as indeed do many other gas-solid systems, but on
closer examination reveal departures, especially at coverages approaching
saturation of the surface and at raised temperatures. Linearization of the
Langmuir equation, of which one form is
p/q = 1/bqm + plqm (3.8)
will yield values of b and qm. For obedience to the Langmuir isotherm,
values derived from the slopes and intercepts of plots of p/q against p should
remain constant over a wide range of both partial pressures and
temperature, while equation (3.6) should be tested for the full range of
coverage from 0 = 0 to 0 = 1. Figure 3.4 illustrates data for a system which
apparently conforms to the Langmuir isotherm.

3.3.2 Henry's law
At low pressures equation (3.6) reduces to the linear form