Page 286 - Gas Adsorption Equilibria

272 Chapter 5

Similarly we have by combining eqs. (5.70, 5.57) the relation

As equations (5.74), (5.75) provide two linear relations for we get

From these equations the quantities can be calculated from measured
values of p, T), leading via the thermal equation of state of the sorptive
gas to its density All the other quantities included on the r.h.s.
of (5.76, 5.77), namely (b, can be determined from
auxiliary and calibration type experiments at the pendulum and the gas
storage system respectively. Note that eqs. (5.76), (5.77) also holds for
oscillometric-densimetric measurements mentioned in Sect. 4.2 in brief.

Experimental uncertainties of can be calculated
straightforwardly from eqs. (5.76, 5.77) using Gauss’ law of error
propagation. In our experiments relative values of uncertainties
always turned out to be about 5 %, thus indicating that
oscillometric-volumetric measurements tend to be somewhat less accurate
than oscillometric-gravimetric ones, cp. Sect. 3.3. As already indicated, this
situation can be improved by adding a microbalance to the installation Fig.
5.13 allowing one to measure the density of the sorptive gas by the buoyancy
of a sinker, cp. Fig. 5.15, [5.27].

4.4 Example

The solubility of carbon dioxide (Messer-Griesheim, 5.0) in
polymethylmethacrylate (PMMA) Makrolon 2400 (Bayer AG), cp. Tab. 5.3
and [5.29], and the swelling of the polymer have been measured at T=308 K
using the oscillometric-manometric method [5.27]. Results are presented in
Figure 5.19. The reduced masses resulting from
manometric measurements, cp. Eq. (5.74), are indicated by As clearly can
be seen, these data increase at low pressures (p < 3.5 MPa) to have a
maximum at p = 3.5 MPa, then to decrease and even assume negative values