Agriculture Reference
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1.0
Olivier
0.8
0.6
1:1 line
0.4
Measured Fitted
Zn-Ca
Cd-Ca
0.2
0.0
Windsor
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Relative Concentration
FIGURE 7.6
Ion exchange isotherms of Cd-Ca and Zn-Ca for Olivier and Windsor soils (relative concen-
tration ( C / C T ) versus the sorbed fraction ( s /Ω). Solid and dashed curves are fitted using the
Rothmund-Kornfeld equation. (From H. M. Selim and M. C. Amacher. 1997. Reactivity and
Transport of Heavy Metals in Soils . Boca Raton, FL: CRC Press. With permission.)
several kinetic rate formulations have been proposed. Such formulations
have been applied to describe sorption-desorption kinetic results for heavy
metal ions. The pseudo first-order or mass action model is perhaps the most
commonly used approach, where one assumes the kinetic rate is a function
of the concentration gradient on the exchange surfaces. For the exchangeable
amount S (omitting the subscript i ) the rate equation can be expressed as
(Selim et al. 1992):
α−
S
t
=S S
eq
(
)
( 7.10 )
where α is an apparent rate coefficient ( d -1 ) for the kinetic-type sites. For
large values of α, S approaches S eq in a relatively short time and equilib-
rium is rapidly achieved. In contrast, for small α, kinetic behavior should
be dominant for extended periods of time. Illustrative examples of utilizing
the kinetic ion exchange concept are presented in a later section. It should
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