Sorption Isotherms - Transport and Fate of Chemicals in Soils: Principles and Applications - page 2

is analogous to the equilibrium constant for a chemical reaction. For b equal
unity, the Freundlich equation takes on the form of the linear equation:

(1.2)

S= KC
d

where K d is the distribution coefficient in L/kg or ml/g. As K d is used, this
implies a linear, zero-intercept relationship between sorbed and solution
concentration, which is a convenient assumption but certainly not univer-
sally true. This linear model is often referred to as a constant partition model
and the parameter K d is a universally accepted environment parameter that
reflects the affinity of matrix surfaces to solute species. The K d parameter
provides an estimate of the potential for the adsorption of dissolved contam-
inants in contact with soil. It is typically used in fate and contaminant trans-
port calculations. According to the U.S. Environmental Protection Agency
(1999), K d is defined as the ratio of the contaminant concentration associated
with the solid to the contaminant concentration in the surrounding aqueous
solution when the system is at equilibrium.

1.2 Langmuir Isotherm
The Langmuir isotherm was developed to describe the adsorption of
gases by solids where a finite number of adsorption sites in planer sur-
faces is assumed (Langmuir, 1918). Major assumptions include that ions
are adsorbed as a monolayer on the surface, and the maximum adsorption
occurs when the surface is completely covered. Other assumptions are that
the surface considered is homogeneous, the sites are of identical adsorption
energy or affinity over the entire surface, and that equilibrium condition
is attained.
As a result, a major advantage of the Langmuir equation over the linear
and Freundlich types is that a maximum sorption capacity is incorporated
into the formulation of the model, which may be regarded as a measure of
the amount of available retention sites on the solid phase. The standard form
of the Langmuir equation is

S ω

+ω

C

= (1.3)

S 1 C

max

where ω and S max are adjustable parameters. Here ω (ml μg -1 ) is a measure of
the bond strength of molecules on the matrix surface and S max (μg g -1 of soil)
is the maximum sorption capacity or total amount of available sites per unit
soil mass.