Page 98 - Gas Adsorption Equilibria

84 Chapter 2

that is the volume of the sorbent without that of the sorbate phase as “seen” by
helium molecules which are assumed not to be adsorbed at all on the surface
of the sorbent. Indeed under these conditions can be determined from
volumetric experiments performed with helium – preferably at room
temperature or even at higher temperatures – leading via (2.1 - 2.3) with
to

with

Here is the volume of the helium gas of mass at pressure
temperature T and is the compressibility or real gas factor of helium
[2.11, 2.12]. In view of the approximation (2.7), the sorbate mass in Eq.
(2.4) is the Gibbs surface excess mass (GSE) cp. Chap. 1. Inserting
Eqs. (2.5 - 2.7) in (2.4) this mass can be represented as

If the void volume in (2.4) is approximated by

cp. Chapter 1, in Eq. (2.4) is the absolute or total mass adsorbed which
equivalently to (2.8) via Eqs. (2.4 – 2.5, 2.8, 2.9) can be represented as

with as given by (2.8) and by (2.6).