Geoscience Reference
In-Depth Information
Fig. 5.3 First-order plots of potassium adsorption on clay, where K
t
is the quantity of potassium
adsorbed at time t, and K
?
is the quantity of potassium adsorbed at equilibrium (Sparks and
Jardine
1984
)
however, show that the pre- and post-Elovichian sections, in many cases, are not
observed, which leads to the incorrect conclusion that the entire rate process may
be explained by one single kinetic law.
Sparks (
1989
) discusses the application of various kinetic equations to earth
materials based on the analysis of a large number of reported studies. Even though
different equations describe rate data satisfactorily, Sparks (
1989
) uses linear
regression analysis to show that no single equation best describes every study.
According to the Arrhenius law, the rate of reaction is correlated linearly to the
increase in temperature, with the rate constant k given by
k ¼ Ae
E
=
RT
;
ð
5
:
9
Þ
where A is a frequency factor, E is the energy of activation, R is the universal gas
constant, and T is the absolute temperature. A low activation energy usually
indicates a diffusion-controlled process, while higher activation energy indicates
chemical-reaction-controlled processes (Sparks and Huang
1985
; Sparks
1986
).
Data on the effect of temperature on the rate of potassium release from potassium-
bearing minerals were presented by Huang et al. (
1968
) and are reproduced in
Table
5.3
. Huang et al. (
1968
) showed that a 10 K rise in temperature during the
reaction period resulted in a twofold to threefold increase in the rate constant.
