Page 160 - Adsorption by Powders and Porous Solids

146 ADSORPTION BY POWDERS AND POROUS SoubS

location of the GDS on the surface excess amounts of components 1 and 2. Here ~0~
'L' provides the special condition for ny = 0.
Turning to Equation (5.53, we now require a GDS where nu (the whole surface
excess amount n: + nz) equals zero. In Figure 5.12, this is the case for GDS
where nz = -n:.
From Equation (5.55) we now obtain:
no(n) = n; = -ny =
2 L (5.59)
which shows that the reduced surface excess amounts of 1 and 2 are equal and oppo-
site in sign. It turns out that this remains true whatever the position of the GDS. A,
underlined by Defay and Prigogine (1951, p. 26), this representation in terms of the
reduced surface excess 'treats the components on an equal footing'. A practical con.
sequence is that the same curve (either U or S as illustrated in Figure 5.13) provides
the adsorption isotherm for both components. We also note that it is only when the
partial molar volumes of 1 and 2, together with their molecular cross-sectional areas,
are equal, that for ny + n; = 0 the GDS coincides with the real adsorbing surface.
By combining Equations (5.51), (5.54) and (5.53, we obtain the relationship
between the relative and reduced surface excess quantities:
ndl) = n;(")/x;
2 (5.60)
and:
rt) = rr)lx\ (5.61)
and also:
mu'" = m;'m'/w:
2 (5.62)
Adsorption isotherms expressed in reduced surface excess amounts
The reduced surface excess amounts, whose use is recommended by the IUPAC
(Everett, 1986), offer much more than a form of precise mathematical accounting of the
adsorption experiment: they also offer the most convenient way of reporting the exper-
imental results. For decades this presentation was intuitively chosen as a way of plot-
ting adsorption data, without any reference to the Gibbs formalism. The quantity
plotted to represent adsorption of component 2 was often in the form of either no A&
which is consistent with Equation (5.54), or [m, - mow:], which is consistent with
Equation (5.57). The isotherm obtained is generally termed a 'composite isotherm' or
an 'isotherm of apparent adsorption', or less often an 'isotherm of concentration
change'. The term 'composite' refers to the fact that this single isotherm contains infor-
mation about the adsorption of both components 1 and 2. This is shown in Figure 5.13,
which gives the two most important shapes of reduced surface excess (or 'composite')
isotherms (S-shape and inverted U-shape) for completely miscible liquids. Depending
on the axis chosen, one obtains the isotherm for component 2. These shapes were the
basis for a more detailed classification given by Schay and Nagy (1961).
When the adsorption is studied From dilute solutions (where by convention, we
shall consider that component 1 is the solvent), the experimental isotherms are still
plotted, strictly speaking, in terms of reduced surface excess. Nevertheless, since