Page 58 - Adsorption Technology & Design, Elsevier (1998)

Fundamentals of adsorption equilibria 55

mixture then the total number r/T of moles of mixture adsorbed is m o/Vm.
The number of moles ni of a component i, however, is x~.nT where x~ is the
mole fraction of component i. Provided no volume change is assumed for
mixing, then the partial molar volumes are additive so that Vm = ~x~V~
where V~ is the molar volume of component i for adsorption of the pure gas
at the same temperature and total pressure as the mixture is adsorbed.
Hence it follows that

n--~"- = 1 (3.35)

where n o is written for mo/Vi ~ The main advantage of a correlation like
equation (3.35) is that it contains both pure component and mixture data.
Figure 3.9 illustrates that hydrocarbons adsorbed on silical gel and on a
carbon obey the Lewis relation.

3.4.3 Grant and Manes model
This model for mixed adsorption (Grant and Manes 1966) is based upon the
idea of equipotential energies among the components of the adsorbed
mixture and is thus related to the Polanyi potential theory discussed in
Section 3.3.5. As previously recorded, Dubinin and Radushkevich (1947)
postulated a direct relation between the affinity coefficient fl; of a com-
ponent i and the molar volume Vm~ of the saturated pure liquid. The
equipotential energy concept for two components is thus (ei/fli) = (ej/flj).
Hence, by use of equation (3.18) for each component

In = ~ In (3.36)
Vmi pi Vmj pj
However, there were substantial deviations from the correlation given by
equation (3.36) when applied over a wide range of temperatures and
pressures. Grant and Manes (1966), by utilizing the molar volume V'm of the
liquid at its normal boiling point and fugacities rather than partial pressures,
showed that data could be correlated fairly well. Assuming that Raoult's law
applies to the partial pressure p~ of each component and its mole fraction x~
in the adsorbed phase, the correlation becomes

(e.)V,mi = RgT ln [ fi ' (3.37)

where (f~)i and fi are, respectively, the fugacity of the pure component i at its
saturated vapour pressure at temperature T and the fugacity of i in the gas
mixture. Assuming Raoult's Law is obeyed, fi is found from the relationship
fi = x~f,.* where fi* is the fugacity exerted by i if it were a pure adsorbate at the