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CHAPTER 2. THERMODYNAMICS OF ADSORPTION                         29

    &ace;  at distance z = t,  this concentration reaches the constant value of  the gas
    phase  cg. This  form  of  hypothetical  variation  of  local  concentration is  shown
    schematically in Figure 2.la, where we also identify three zones (I, II and III).
      We shall assume that there is no penetration of gas into the solid (i.e. no absorp-
    tion) so that zone I is occupied solely by the adsorbent and therefore cs = 0. In zone
    a, the  adsorbable gas is at  sufficient distance from the  solid surface to  have a
    uniform concentration, cg, and here z > r.  In this region the concentration is depen-
    dent only on the equilibrium pressure and temperature. In Figure 2.la, zone Il is the
    ladsorbed layer', which is an intermediate region confined within the limits z = 0 and
    , Here, the local concentration, c, is higher than the concentration of the gas in
       t.
     =
    zone IJJ and is dependent on z.
      It follows from this simple picture that the volume, Va, of the adsorbed layer can
    be expressed as the product of the interfacial area, A, and the thickness, t. Thus


    We may define the amount adsorbed, na, of the substance in the adsorbed layer as









    In Figure 2. la, na is equivalent to the hatched area (d + e).
      The total amount, n, of  the  adsorbable  substance in the  whole  system can be
    divided into two parts, the amount adsorbed and the amount remaining in the gas
    phase:




    where the volume occupied by the gas at the concentration cg is Vg, therefore:



    It is evident that the exact evaluation of na requires a knowledge of either the exact
    value of  Vg or of the variation of  the local concentration, c, with respect to z.  In
    practice, it is not easy to attain either of these requirements.
      To overcome this problem, Gibbs (1877) proposed an alternative approach. This
    makes  use  of  the  concept of  'surface  excess'  to  quantify  the  amount adsorbed.
    Comparison is made with a reference system, which is divided into two zones (A, of
    volume V0 and B, of volume VgS0) by  an imaginary surface - the Gibbs dividing
    surface (or GDS) - which is placed parallel to the adsorbent sudace. The reference
    system occupies the same volume V as the real system, so that:


    h the reference system the concentration of the gaseous adsorptive remains constant
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