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4.1 Basic Principles of Adsorption and Ion Exchange 269

if its shape is concae upward in an v X v ersus Y figure. In Figure 4.13, the characteristic
isotherm shapes are presented.
The parameter La and pro v e descrip- vides a quantitati is also called the “separation factor”
tion of the equilibrium regions: La = 0 for irreversible, La 1 for f orable, v a La 1 for lin-
ear, and La 1 for unf The same holds for orable adsorption. v a Fr in Freundlich’s isotherm.
Freundlich adsorption isotherm constants for seeral compounds on seeral adsor- v
v
bents/water systems at ambient temperature can be found in T Appendix I able I.24, .
Dubinin–Raduskevish (DR) Due to the great significance of vapor adsorption on
v
actiated carbons, the DR isotherm, which is the most widely used in such cases, will
v
be presented. It has seeral advantages (Dubinin, 1966):
• predicts quite fairly the experimental data oer a wide concentration range v
• it includes the effect of temperature
• it is based on physical parameters
• easy application.

Dubinin assumed that the amount of vapor adsorbed ( W ) by an acti at a rel- ated carbon, v
ative pressure P / P , is a function of the thermodynamic potential A :
s
P  s 
A RT ln  P    (4.18)

where:
R the uniersal gas constant v
T the absolute temperature
P s the saturated vapor pressure at temperature T
P the partial pressure of the adsorbate.
Dubinin reached the conclusion that the function was Gaussian after ha ving studied the
adsorption of simple organic compounds like benzene, and finally the classical expression of
Dubinin and Radushkevich (the D–R equation) was derived (Dubinin, 1966; Cheng et al .,
2004):

 A   2 
q e q o exp  k    (4.19)
     

where q o is the maximum amount that can be adsorbed and k is a parameter characterizing
f
the adsorbent. The parameter is called the “af or “similarity” coeficient and f
inity”
expresses the ratio of the characteristic free energy of desorption of the test vapors to the
free energy of desorption of the reference vapors. The affinity coefficients can be estimated
by ratios of molar polarizabilities (W 2001): ood,

(4.20)
ref