Page 67 - Gas Adsorption Equilibria

1. Basic Concepts 53

of the sorbent, the surface potential and the sorptive fluid equations
of state Eqs. (1.11-1.13) allow one on principle to
calculate p = p(x), at the specific free enthalpy at any point
(x) within the sorbate phase. Hence we can assign a (total or absolute) mass to
the sorbate as

Here is the volume filled by the set (A) of all molecules of the
adsorbate, i. e. all molecules of the sorptive fluid influenced by or exerted to
* )
the surface forces of the sorbent material. Assuming the sorptive fluid far
away from the sorbent material to approach an equilibrium state of constant
density

we also can define the so-called Gibbs excess mass as

* ) This is basically an energetic criterion deciding whether a molecule from the fluid is
adsorbed on the surface of a solid material or not. It can be specified as follows: Let the
energy (E) of the molecule be

Here is the kinetic energy of the translational and possibly internal degrees of freedom
of the molecule. Let also and be the potential energies of interaction of the
molecule with other molecules from the fluid phase (f) and the surface atoms or molecules
of the solid (s). If
a) and
b)
we consider the molecule to be adsorbed even if it is not in direct contact with the surface of
the solid. Otherwise the molecule is considered to be not adsorbed. Consequently, molecules
from the fluid phase may change their status of being adsorbed or desorbed between two
molecular collisions and the “boundary” between adsorbed and not adsorbed molecules
from the fluid phase naturally will become fuzzy. In practice this boundary has to be defined
indirectly by an experimental procedure allowing one to actually measure the absolute or
total mass adsorbed. An example for such a procedure will be given in Section 5.2.