Page 285 - Gas Adsorption Equilibria

5. Oscillometry 271

4.3 Theory

The mass of gas adsorbed or absorbed in a swelling sorbent material
of mass and volume in the sorbate state at given pressure (p) and
temperature (T) of the sorptive gas can be calculated from combined
oscillometric and volumetric/manometric measurements. To derive the
respective equations we consider again the result of oscillometric
measurements, i. e. equation (5.25)

The dimensionless quantity can be calculated from frequencies and
decrements of various rotational oscillations performed by the pendulum via
eq. (5.39). All quantities on the r.h.s. of eq. (5.70) have the same meaning as
explained in Sect. 3.3. Also eqs. (5.53-5.57) have to be taken into account in
what follows. The mass balance of the sorptive gas originally included
in the storage vessel of volume is

with the bulk sorptive gas mass

Here the volume is defined according to Fig. 5.13 by

However, it should be noted that in this quantity also the volumes and dead
spaces of all the tubes, valves, and circulation pump(s) within the
experimental installation which are filled with gas during the sorption process
should be included, cp. Fig. 5.13. In fact this quantity in practice must be
determined experimentally by – for example – nitrogen gas expansion
measurements.

The quantity in eqs. (5.70, 5.71) indicates the mass of sorptive gas
sorbed in the sorbent mass From eqs. (5.71, 5.72) we get