Page 97 - Gas Adsorption Equilibria
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2. Volumetry / Manometry 83
In this equation M is the molar mass of the sorptive gas, R = 8.314 J/molK the
universal gas constant and Z = Z (p, T) the compressibility factor or real gas
factor of the gas which can be determined from p, V, T-measurements.
Analytic expressions for Z are given for example in [2.9, 2.10], numerical
values for a variety of technical gases over a considerable range of pressure
and temperature can be found in [2.11 – 2.15]. For an ideal gas we have Z = 1
for any value of p, T. The volume of the sorptive gas in Eq. (2.2) can be
calculated from the relation
where indicates the so-called void volume of the sorbent material and the
sorbate phase which can not be penetrated by the sorptive’s gas molecules.
Equations (2.1-2.3) can be combined to present the result of volumetric
measurements:
Here has been introduced as an abbreviation being defined by
with the sorptive gas density, cp. (2.2),
It should be emphasized that the auxiliary quantity only includes
measurable quantities. Hence its numerical value is known from the gas
expansion experiment. According to Eq. (2.4), can be called “reduced
mass” of the adsorbed phase as it is the difference between the mass of the
adsorbed phase and the mass of the sorptive gas that would be included
in the void volume of both the sorbent and the sorbate phase [2.3, 2.7].
As this quantity also is unknown, some model assumptions for it have to be
introduced to calculate the adsorbed mass from Eq. (2.4).
As outlined in Chapter 1, is often approximated by the so-called
helium volume,