Page 57 - Partition & Adsorption of Organic Contaminants in Environmental Systems

48 FUNDAMENTALS OF THE ADSORPTION THEORY

where e s is the (molar) adsorption potential of the solute, e l the adsorption
potential of the solvent, e sl the adsorption potential of the solute from solu-
the respective molar volumes of the solute and solvent, C s the
tion, V s and V l
solute solubility in the solvent, and C e the solute concentration in the solvent
at equilibrium. Equation (4.12) may be further converted to give

e sl V = e s V - e l V = ( RT s V ) ( C s C ) (4.13)
ln
l
s
e
s
) is simply the
As seen, the net adsorption potential density of the solute (e sl /V s
) and solvent
difference between the potential densities of pure solute (e s /V s
). Thus one may in principle predict the adsorption of a partially mis-
(e l /V l
cible solute from solution from established or estimated correlation curves
of the pure solute and solvent. Equation (4.13) has been found most success-
ful for partially miscible liquid solutes in solution, in which the effective
) is practically the same as the molar
molar volume of the liquid adsorbate (V s
volume of the pure liquid. For solid solutes, the effective adsorbate molar
volume may well exceed that of the pure substance, because packing of the
condensed solid crystallite into fine-pore adsorption spaces may be hindered
significantly by crystalline structure; therefore, for solid solutes, adjustment of
molar volumes for packing efficiency is often required. Manes (1998) extended
the Polanyi theory to a wide range of vapor and solution systems, including
single and multiple vapors and solutes that are either completely or partially
miscible to each other.
In adsorption from solution, the net heat of adsorption for a partially mis-
cible solute (e sl ) is usually smaller than that of its single vapor-phase adsorp-
tion (e s ) because of the energy required to displace the solvent, as depicted by
Eq. (4.12). In such systems (i.e., where the solute separates out as a liquid
or a solid phase in adsorption space), the total molar heat of adsorption is
is the molar heat of solution of the solute. One
-(e sl +DH sol ), where DH sol
for solid solutes
may recall from the discussion in Chapter 3 that the DH sol
).
includes the associated heats of fusion (DH fus

4.6 SURFACE AREAS OF SOLIDS

The surface area of a solid (adsorbent) plays a fundamental role in the
physical adsorption of vapors. The BET method with appropriate adsorbate
gases has become a universal method for determining the solid surface area.
Suitable vapor adsorbates must be chemically inert, not subject to molecular
sieving by the solid pore, and confined only to the exterior of the solid (i.e.,
no vapor penetration into the interior network). The use of an inert vapor as
the adsorbate is to eliminate any specific interaction (or reaction) with either
solid surface or its interior network. Prevention of molecular sieving is ac-
complished by the use of small adsorbates. Measurement at low temperature