Page 73 - Gas Adsorption Equilibria

1. Basic Concepts 59

Likewise we have from Eqs. (1.31) combined with (1.27)

From equations (1.34), (1.35) the total mass adsorbed can be calculated
from density measurements and calculations of the sorptive gas and
given data of the corresponding helium experiments and after
choosing or calculating the reference density of the sorbate phase.

It should be noted that according to Eq. (1.30) at low gas densities,
or, equivalently low gas pressures, the absolute
mass adsorbed and the Gibbs surface excess are nearly equal

However, for high gas densities or, equivalently, high gas
pressures both quantities are becoming different. Consequences of this are
demonstrated in Figure 1.22 below showing of nitrogen
adsorbed on activated carbon Norit R1 Extra [1.50].

Both concepts of masses of an adsorbate discussed so far – the Gibbs
surface excess based on proposition (P1) and calculated by Eq. (1.27)
and the absolute mass adsorbed based on proposition (P2) and calculated
by either Eq. (1.34) or (1.35) – do have their physical limitations. Hence it is
desirable to mention other possibilities to define and to measure masses of
adsorbates in gas adsorption systems.

A fairly simple possibility to do this is to realize that contrary to a PSSS,
Fig. 1.20, the volume of an irregular porous sorbent being impenetrable
for molecules of a sorptive gas, generally will depend on the size of the gas
molecules, cp. Figs. 1.1, 1.21. This is well known in the mathematical theory
of fractal surfaces [1.67] and thermodynamic phases of fractal dimension
[1.68]. Also the range of surface forces cp. (1.14), of a sorbent
)
material is limited in space but also depend on the sorptive gas molecules.
*
Hence one may consider the volume of the joint sorbent/sorbate phase as

* )
The boundaries of the region (A) of surface forces of the sorbent can be defined as surface
on which the potential energy of the surface forces is equal to the (average) energy of the
thermal fluctuations of a sorptive gas molecule. Naturally these boundaries will depend on
the type of sorptive gas considered and – predominantly – on its temperature.