### Adsorption at the solid/gas interface

Surface excess amount of adsorbed substance (Gibbs adsorption), ( ) is the excess of the amount of component actually present in the interfacial layer over that which would be present at the same equilibrium gas pressure in the reference system, in which the gas phase concentration is constant up to the Gibbs surface, and the reference concentration of component is zero beyond the Gibbs surface in the surface layer of the solid (see Figure 2).

The general expression for 1.1.8) becomes in this instance:

where the interfacial layer is divided into two regions, the adsorption space and surface layer of the solid (see §1.1.5), by the Gibbs surface. The second term is usually assumed to be zero or negligible.

For a multicomponent gas mixture the total surface excess amount of adsorbed substance is

If the area of the solid surface is known, then the surface excess concentration (or Gibbs surface concentration) of component , denoted by , is

Similar definitions can be given for the surface excess number of molecules of component , , and of the surface excess mass of , , and of the surface excess volume of gas of ( ) preferably expressed as the volume of gas calculated for 273.15 and 101.325 (0 and 1 atm): the equation of state used in the calculation should be stated.

The operational definition of is

where is the total amount of component present and is the volume of the gas defined by the Gibbs dividing surface. The position of the Gibbs surface is often defined experimentally as that surface which encloses the volume of space from which the solid excludes helium gas (the so-called helium dead-space), and is associated with the assumptions that the volume of the solid is unaffected by the adsorption of , and that helium is not adsorbed by the solid. This requires that the measurement of the helium dead-space be made at a sufficiently high temperature.

The amount of adsorbed substance is defined as

where is the volume of the interfacial layer which has to be defined on the basis of some appropriate model of gas adsorption and is the local concentration of component as exemplified in Figure 2. An equivalent, alternative, but somewhat more operational definition may be formulated as follows:

where is the volume of the adsorption space depicted schematically in Figure 2. When the adsorption of component is not too weak and its equilibrium partial pressure sufficiently low, then the second term on the right hand side becomes negligibly small so that:

This last identification is usually justified in measurements of gas adsorption at lower pressures. Under these conditions the surface excess amount of adsorbed substance and the amount of adsorbed substance become indistinguishable and the latter term (often abbreviated to amount adsorbed) is usually used for both concepts.

Adsorption isotherm, in the case of a single adsorptive, is the function relating the amount, mass or volume, or corresponding excess of substance adsorbed by a given amount of solid to the equilibrium pressure () at constant temperature ()14

Adsorption isobar is the function relating the amount, mass, or volume, or corresponding excess of substance adsorbed by a given amount of solid to the temperature at constant pressure.

Adsorption isostere is the function relating the equilibrium pressure to the temperature at a constant value of the amount, or excess amount, of substance adsorbed by a given amount of solid.

When the specific surface area () is measured by adsorption methods15 then it is given by the product of the specific monolayer capacity, , the Avogadro constant, and the area occupied by a molecule adsorbed in a complete monolayer ():

In the case of microporous solids the interpretation of adsorption measurements in terms of surface area may lose its significance when the size of the adsorbed molecules is comparable with the dimensions of the pores. Nevertheless it may be convenient to define a monolayer equivalent area, in which is replaced in the above equation by the amount needed to fill the micropores (§1.1.7).