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,
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