Page 69 - Gas Adsorption Equilibria

1. Basic Concepts 55

If one is interested only in the Gibbs surface excess mass defined by Eq.
(1.16), one has to assume the sorptive gas phase to extend to the surface of the
sorbent material, i. e. to have a mass of

Then from the mass balance of the sorptive gas, i. e. equalization of gas mass
prior to and after adsorption equilibrium has been attained,

it follows

Let us now introduce a reference gas density namely the density the
sorption gas would have if no sorbent surface forces were acting on its
molecules, i. e.

or

Then we get for in view of (1.18), (1.20), (1.21)

This formula also holds for more complex geometries of the sorbent material
than that simple one sketched in Figure 1.20, cp. Figure 1.21 showing the
structure of zeolite molecular sieve UOP/Linde MS 13X. Formula (1.23)
allows one to calculate the Gibbs surface excess from measured data
if the volume of the sorbent material (which is impenetrable for
the gas molecules) is known. And here is where often difficulties start, as
normally is unknown, at least for most technical sorbents which are a mixture
of the true sorbing material and some cement or glue and possibly some other
components providing mechanical stability to sorbent pellets or grains. Hence
one has to use some approximation for the most common of which will
discussed in brief in the next Section.