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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