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270 4. Adsorption and Ion Exchange

The ratio of molar volumes in the liquid state can also be used:

V
(4.21)
V ref

By definition, benzene is standardized as the reference compound for carbonaceous mate-
alue of its affinity coefficient rials, and thus the v is 1. ant parameters of the D–R v The rele
isotherm can be found in paragraph I.4, Appendix I.
Other isotherms Some common isotherms are the follo wing:
Langmuir–Freundlich isotherm

X A
Y (4.22)
B (1 B X ) A

Redlich–Peterson isotherm

X
Y (4.23)
B B X ) A
(1
Sips isotherm

 X  A
Y   B (1 B X)   (4.24)

where A and B are equilibrium constants.
However, there is no reason to use more complicated isotherm models if tw o-parameter
models, such as Langmuir and Freundlich, can fit the data well. It should be clarified that
these models are only mathematical functions and that they hardly represent the adsorp-
tion mechanisms.
Ion ehange xc

Let us suppose that the solid phase is initially in the B form and that the liquid-phase ion
is A. The ion exchange can be represented as (Helf 1962) ferich,

B A B
A
Then, the separation f actor A B is defined as

qC YX
A B A B (4.25)
qC B A YX B A