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4.1 Basic Principles of Adsorption and Ion Exchange 267

Introducing the equilibrium parameter ( La ) as

1
La
1 KC o (4.8)

the dimensionless form of Langmuir equation is

X
Y (4.9)
(1
La La ) X
where

q
Y e (4.10)
q max

and

C
X e (4.11)
C o

By using the dimensionless equilibrium relationship, La can be expressed as

X (1 Y )
La (4.12)
Y (1 X )

Langmuir adsorption isotherm constants for seeral compounds on seeral v
v
adsorbents/water systems at ambient temperature are presented in T Appendix I able I.23, .
Freundlich Adsorbents that follow the Freundlich isotherm equation are assumed to have
a heterogeneous surface consisting of sites with different adsorption potentials, and each type
of site is assumed to adsorb molecules, as in the Langmuir equation (Perry and Green, 1999):

q
e kC Fr
Q e (4.13)
M

where q e is the solid-phase concentration in equilibrium with the liquid-phase concentra-
tion C , Q M is the fve capacity, and inal sorpti k and Fr are equilibrium constants. Another
e
form of the Freundlich isotherm is the follo wing:

q K C Fr (4.14)
e F e