Page 45 - Adsorptionbypowders & poroussolids muyace

CHAPTER 2. THERMODYNAMICS OF ADSORPTION 3 1

in the volume Vg'O, i.e. up to the GDS. This is shown in pictorial form in Figure 2.1 b.
~n this model, the surface excess amount, nu, represented by hatched area d, is
defined as the difference between the total amount, n, of the adsorptive (hatched and
crossed areas) and the amount which would be present in the volume V8s0 of the ref-
erence system if the final equilibrium concentration cg were constant up to the GDS
(crossed area e + f). Thus:
nu= n - cBVg.0

It is convenient (although, in principle, not compulsory), for the sake of the physical
interpretation of the data, to locate the GDS exactly on the surface which is accessi-
ble to the adsorptive used, so that Vg'O = Va+ Vg. This is what was actually done in
Figure 2.lb. The experimental determination of VBsO in order to meet the above
requirement is examined in Section 3.4.1.
Under these conditions:

Combining with Equation (2.3), one gets:

na = no + cgV1
In Figure 2.lb, the surface excess amount nu is represented by hatched area d;
whereas the amount adsorbed nu, which also includes term cg Vn, is represented in
Figure 2.la by area (d + e).
Generally, the experimental conditions are such that the final concentration cg of
the gas is small and the volume V\f the adsorbed layer is negligible in comparison
with the gas volume Vg. Under these conditions

However, at high temperature or pressure it may become necessary to make some
allowance for the difference between these two quantities.
The amounts nkd nu are extensive quantities, which depend on the extent of the
interface. The related 'surface excess concentration', T, is an intensive quantity.
which is defined as

where the surface area, A, is associated with the mass ms of the adsorbent. The
specific surface area is therefore:

What is usually measured and recorded is the specific surface excess amount nu/ms,
where

As we have seen already, no/ms is dependent on the equilibrium pressure, p, and
the adsorbent temperature, T. The usual practice is to maintain constant temperature