Page 54 - Adsorption Technology & Design, Elsevier (1998)

Fundamentals of adsorption equilibria 51

constant (Section 3.3.2) and As = (1 - sa/v) ~ identifies each adsorbate
molecule from s = 2 to s = n, the maximum number of molecules in the cage.
a and v are the effective volume of an adsorbate molecule and the cage
volume, respectively. When v < 2a only one molecule per cage can be
accommodated and equation (3.30) reduces to the Langmuir equation.
When v/a is sufficiently large there would be free mobility of adsorbate
throughout the zeolite structure. A family of curves, with qs the quantity of
adsorbate at full saturation as parameter, is obtained when q/q~ is plotted as
a function of Kp. When q~ = 1 a form equivalent to the Langmuir equation
(3.6) is obtained and when q~ = oo a form equivalent to the Volmer equation
(3.29) is obtained.

3.4 ADSORPTION OF GASEOUS MIXTURES

The techniques used to obtain single-component experimental isotherms
(see Chapter 4) may also be employed to gather data for multicomponent
isotherms with the additional premise that for every quantity of adsorbate
mixture adsorbed by the adsorbent the composition of the gas phase must be
determined. Thus, collecting experimental data for multicomponent
gaseous mixtures is very time-consuming. It has become customary,
however, to employ single-component adsorption data to predict the
adsorption properties of a binary or multicomponent gaseous mixture.
Success has been achieved for some binary gas mixtures although it is by no
means reasonable to assume that the methods of prediction to be described
are in any way universal.
Correlations based upon the Langmuir, Polanyi and Gibbs theories for
the adsorption of gases have emerged and the statistical thermodynamic
approach outlined by Ruthven has also been extended to incorporate the
adsorption of gaseous mixtures. Each of these different approaches is
described in the following sections and their relative applicability and
constraints noted.

3.4.1
The Extended Langmuir equation
The Langmuir isotherm can easily be extended to apply to gaseous mixtures
by simply assuming, as an additional constraint to those which are explicit in
the Langmuir theory, that for each gaseous component an equilibrium exists
between the amount adsorbed at the surface and the partial pressure of that
component in the gas phase. Fractional coverage Oi and partial pressure pi
are ascribed to each of the components, the total surface coverage being the