Geoscience Reference
In-Depth Information
x
m
¼ KC
1
=
n
;
ð
5
:
4
Þ
where K and n are empirical constants, and the other terms are as defined previ-
ously. The value of 1/n represents a joint measure of both the relative magnitude
and diversity of energies associated with a particular sorption process (Karickhoff
1981
; Weber et al.
1992
). The linear form of the Freundlich equation is
m
¼
1
x
log
n
log C
þ
log K
:
ð
5
:
5
Þ
The Freundlich equation can also be derived theoretically by assuming that the
decrease in energy of adsorption with increasing surface coverage is due to the
surface heterogeneity (Fripiat et al.
1971
).
The main limitation of the Freundlich equation is that it does not predict a
maximum adsorption capacity, because linear adsorption generally occurs at very
low solute concentration and low loading of the sorbent. However, in spite of this
limitation, the Freundlich equation is used widely for describing contaminant
adsorption on geosorbents.
Composite linear isotherms express the natural conditions of heterogeneity
specific to geosorbents (Lafleur
1979
; McCarty et al.
1981
; Karickhoff
1984
). The
relative equation expressing composite conditions of geosorbents may be of the
type
!
C ¼ K
d
C
;
q ¼
X
x
i
q
i
¼
X
m
m
x
i
K
di
ð
5
:
6
Þ
i¼1
i¼1
where q is the total solute mass sorbed per unit mass of bulk solid at equilibrium, x
i
is the mass fraction of geosorbent constituting the reaction region or component i,
q
i
is the sorbed-phase concentration at equilibrium expressed per unit mass of that
region or component, K
di
is the partition coefficient for a reaction expressed per
unit mass of component i, and K
d
is the mass-averaged partition coefficient.
When one or more of the component elements of sorption is governed by a
nonlinear relationship between the solution and the sorbed phase, the composite
isotherm deviates from linearity. In these cases, modifications to the Freundlich
isotherm have been developed (e.g., Lambert
1967
; Weber et al.
1992
) to express
these conditions.
Overlapping patterns of some Langmuir-type sorption processes, which can
occur at different sites of a complex sorbent (such as a geosorbent) and show
different interaction energies, may be quantified by a Freundlich-type isotherm. A
meaningful thermodynamic interpretation of this equation has been developed by
Wauchope and Koskinen (
1983
), using a fugacity approach, with a proposed
standard state for a sorbed organic contaminant (herbicide). This interpretation
was based on the assumption that the organic fraction of the geosorbent forms a
