Page 71 - Gas Adsorption Equilibria

1. Basic Concepts 57

Hence we have from Eqs. (1.23, 1.24, 1.26)

This relation allows one to calculate the Gibbs surface excess from
mass and density measurements of the sorptive gas (m*, and
accompanying helium measurements leading to calibration parameters
Details of the experimental procedure by volumetric /
manometric measurements and several examples will be given in Chap. 2.

From a thermodynamic point of view (W. Schottky, M. Planck and others
[1.63-1.65]) all the mass of gas included in the sorbent surface-near-layer of
thickness (d) is adsorbed on the surface (Adsorption layer model [1.3],
Fig. 1.20). Hence the volume of the sorptive gas phase is the volume of
the Gibbs excess sorptive gas phase reduced by the volume of the
adsorbed phase i. e. we have

As the thickness (d) of the adsorbed layer is ill-defined we again have to use
an approximation for which may be related to the total mass adsorbed by

Here is an approximation for the average density of the sorptive
layer, cp. Fig. 1.20, a quantity which at least for technical porous sorbents
with a complicated, fractal-like surface structure cannot be measured up to
date, cp. Figure 1.21, [1.3]. Actually, there are two possibilities so far to get
physically reasonable numerical values for

a) One can choose as either the bulk density of the sorptive fluid in the
liquid boiling state at ambient pressure, or as the density in the liquid triple
state [1.66].