Page 202 - Gas Adsorption Equilibria

188 Chapter 4

and

Now equations (4.2, 4.9) can be solved for . The result is

Here we have used the definition

The volume is determined by Eq. (4.6) and the helium approximation, i.e.
cp. (2.7). As immediately can be seen, solutions (4.12) become
singular if Indeed in this case equations (4.2, 4.12) become linearly
dependent and do not allow one to determine the masses of the adsorptive gas
Hence the volumetric – gravimetric method cannot be used for
isomeric gas components. It should be noted that equations (4.15) can only be
solved iteratively by starting with the ideal gas approximation for the
compressibility, i. e. choosing Z = 1. The results of this calculation can be
used to determine an approximate value of Z according to Eq. (4.3) via an
appropriate thermal EOS for the gas mixture. Repeating this procedure one
normally will get after a few steps stable and accurate numerical values
of the adsorptive masses from which the Gibbs excess masses of the

sorbate’s components immediately can be calculated via the
mass balance equations (4.1).