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II. Methodologies Used in Kinetic Studies
D O N A L D L. SPARKS
The bulk of kinetic studies with soil and clay minerals have employed
batch techniques. These involve placing an exchanger and the adsorbate in a
vessel such as a centrifuge tube. The suspension is then agitated using a
reciprocal shaker or it is stirred. Then, the suspension is usually centrifuged to
obtain a clear supernatant solution for subsequent analysis.
The use of batch techniques to measure the rate of ionic reactions in clay
minerals and soils has a number of disadvantages. Unless the batch technique
of Zasoski and Burau (1978) is used, most batch techniques require centrifugation which requires about five minutes to separate the solid from the liquid
phases. Many exchange reactions are complete by this time or less (Harter
and Lehmann, 1983; Jardine and Sparks, 1984a). If the usual batch technique
is employed, one will never observe these reactions. This is a particular
problem in soils that contain organic matter, kaolinite, and montmorillonite,
and other layer silicates that have readily accessible sites for exchange. In
these systems, ion exchange kinetics are very rapid (Sparks and Jardine,
1984), and most batch techniques should not be used. However, if one uses
the batch technique of Zasoski and Burau (1978) which is a filtration
technique, one can observe rapid exchange reactions.
Also, to properly measure the kinetics of a chemical reaction, the technique
must not change the reactant concentration (Zasoski and Burau, 1978). Thus,
the sample and the suspension should have a similar solid to solution ratio at
all times. Unfortunately, this has not been true in most batch studies, as
Barrow (1983) discusses in an excellent review article. Most studies have
employed large solution: soil ratios where the concentration in the solution
and the quantity of adsorption both vary simultaneously. Exceptions are the
studies of Zasoski and Burau (1978), Van Riemsdijk (1970), and Van
Riemsdijk and DeHaan (1981). In the latter two studies, the solution
concentration was held constant. Thus, the relation between adsorption and
time should only be treated as a simple, two-dimensional relation if adsorption is constant. Unless a batch technique similar to that of Van Riemsdijk
and DeHaan (1981) is utilized, these conditions do not apply to experiments
in which a wide so1ution:soil ratio is used.
Another problem with the batch technique is mixing the solution and
exchanger. If mixing is inadequate, the rate of reaction will be limited.
However, vigorous mixing, which many investigators have used, can cause
abrasion of the exchanger particles leading to high rates of reaction and
alterations in the surface chemistry of the particles (Barrow and Shaw, 1979).
Barrow and Shaw (1979) studied the rate of phosphate adsorption by soil and
found that under prolonged agitation, breakdown of soil particles occurred,
increasing surface area, and causing greater phosphate adsorption. The
KINETICS OF IONIC REACTIONS
breakdown of particles during shaking was less marked at high so1ution:soil
ratios. The abrasion of colloidal particles could be a serious problem when
studying most ionic reactions, but particularly with potassium since release
could occur from potassium-bearing minerals.
A type of batch technique that has been employed by a number of
investigators is the isotopic exchange method. This has been particularly true
with soil phosphorus. Many authors have suggested that the fraction of total
soil phosphorus which is readily accessible to isotopic exchange may
represent the phosphorus available to plants (White, 1976).
Investigations using isotopic exchange methods are evaluated in several
ways. The earliest approach was to use a linear combination of exponential
terms analogous to a series of simultaneous first-order reactions as (Neuman
and Neuman, 1958):
x = 1 - a, exp(-k,t)
- u2 exp(-k,t)
where x is the fraction of the tracer in the adsorbed state at time t ; k,, k,, and
k, are the adsorption rate constants; and a,, a,, and u3 are constants such
that the sum is equal to 1.
However, the process of fitting experimental data to the above equation is
quite cumbersome. Probert and Larsen (1972) adopted a two-constant
formula to approximate the sum of exponential terms. Their formula was
1 - x = [(t
where y and b are constants. Probert and Larsen (1972) report that Eq. (2)
adequately described 32Pexchange data in several soils.
It must be pointed out that neither of the two equations above makes a
reference to adsorption or desorption rates per se. The equations simply
describe the rate of disappearance of the tracer from solution and its
exchange with solid-phase phosphorus. Presumably, this involves both
adsorption and desorption reactions, and the algebraic sum of both gives the
net adsorption rate of the isotope. For both of these equations, equilibrium is
asymptotically approached with increasing time.
Flow or miscible displacement techniques have been used to a lesser extent
to investigate the kinetics of reactions in clay minerals and soils (Sivasubramaniam and Talibudeen, 1972; Sparks et ul., 1980b; Sparks and Jardine,
1981; Jardine and Sparks, 1984a). However, flow techniques are increasingly
being recommended over batch studies to study sorption-desorption phenomena on colloids, particularly if one wishes to relate kinetic studies to solute
transport under field conditions (Murali and Aylmore, 1981, 1983a,b).
DONALD L. SPARKS
Perhaps Murali and Aylmore (1983b) best stated this:
It seems self-evident that adsorption studies should be performed under conditions close
to those encounteredin the field, viz., realistic water contents with no shaking or agitation,if
these results are to be related to solute transport models.
Most previous adsorption studies employing a batch technique were
performed at high solution-to-solid ratios with continuous shaking or
stirring. Such experiments usually yielded reaction rates that were instantaneous. Many investigators thus, incorrectly, concluded that all ion exchange
processes were instantaneous. This conclusion was often reached because one
could not measure short reaction times using the batch technique. However,
flow studies performed at realistic solution-to-solid ratios (usually I1)
clearly indicate that for many chemical species of interest, such as potassium,
phosphate, and selenite, the solute-solid interactions are much slower than
with batch techniques (Murali and Aylmore, 1983a,b; Sparks and Rechcigl,
The amount of solution in contact with colloidal particles is also an
important attribute of a flow technique. Supplied with a solution of the same
concentration, soil particles with solution flowing past them will be exposed
to a greater mass of ions (concentration x flow rate x time) than the soil
particles in a static system (concentration x solution volume) by the time
equilibrium is established. More importantly, with solution flowing through
the soil system, the solution not only brings in more ions but also removes the
desorbed ions of other species that were present originally at potential
sorption sites (Akratanakul et al., 1983). This is particularly important in
studying potassium reactions since small amounts of potassium in the
equilibrium solution will prevent further release of adsorbed potassium
which, consequently, results in marked hysteresis (Martin and Sparks, 1983).
Additionally, the number of introduced ions that can be adsorbed also
depends on how easily they can be exchanged with other ions of different
kinds already adsorbed by the soil surfaces, thus affecting the magnitude of
the heat of adsorption.
With a closed system, exchange cannot be complete without increasing the
concentration of the replaced ions in the bulk solution. This would, in turn,
drive these ions back into the adsorbed phase. However, in an open flow
system, the exchange can be complete, as the replaced ions are continuously
carried out of the system while more of the introduced ions can take their
place. Sparks et al. (1980b) developed a miscible displacement technique to
study kinetics of potassium adsorption from soils. With this technique, a soil
suspension is injected with a syringe into a 47-mm Nucleopore filter (Fig. 1).
The filter is attached to a fraction collector, and the sample is leached with
KCl and CaCl, for adsorption and desorption studies, respectively. The
KINETICS OF IONIC REACTIONS
FIG.1. Miscible displacement technique.
electrolyte is passed through the soil at a constant flow rate using a peristaltic
pump, and aliquots are collected at various times. Later, Jardine and Sparks
(1984a) modified the technique so that aliquots of leachate could be taken at
2-min increments. Thus, one could investigate very rapid ionic reactions
which could not be measured with a batch technique.
Using the miscible displacement technique of Jardine and Sparks (1984a),
one can investigate adsorption and desorption on the same soil sample. This
technique has proved extremely advantageous in studying the kinetics of
potassium reactions in soil since solution phase potassium is constantly
being removed and no inhibition of further potassium release occurs (Sparks
et al., 1980b; Sparks and Jardine, 1981; Sparks and Rechcigl, 1982; Jardine
and Sparks, 1984a). Thus Sparks and co-workers have obtained almost
complete reversibility in potassium exchange. This would not have been
possible using a batch technique. The miscible displacement technique
developed by Sparks et al. (1980b) was recently modified by Carski and
DONALD L. SPARKS
Sparks (1985) to allow the study of systems which are known to adsorb very
small quantities of ions.
In summary, the flow technique has several advantages over the traditional
batch technique for studying kinetics in clay minerals and soils: (1) it more
closely simulates ionic reactions under field conditions, (2) one can measure
short reaction times, (3) one avoids separation of liquid from solid phases by
centrifugation; and (4) one can maintain a relatively constant solid: solution
OF CHEMICAL KINETICS TO SOIL
Chemical kinetics is one of the most fascinating, yet one of the most
difficult areas in physical chemistry. Before applying chemical kinetics to soil
solutions, we shall discuss some of the theoretical aspects of this topic.
Chemical kinetics deals with chemical reaction rates and how these rates
can be explained in terms of reaction mechanisms (Laidler, 1965). There are
two salient reasons for studying the rates of chemical reactions: ( 1 ) to predict
how quickly a reaction mixture will move to its equilibrium state, and (2) to
reveal reaction mechanisms. Thus kinetics, unlike thermodynamics, provides
information along each step of a reaction pathway. Unfortunately, due to
theoretical and experimental difficulties, it is often arduous to apply pure
chemical kinetics to even simple homogeneous solutions! When kinetic
theories are applied to soil solutions, the problems are intensified.
To fully comprehend the above ideas, a knowledge of the rate equations or
rate law explaining the reaction system is required. Acquiring an empirical
rate law necessitates knowledge of the concentration of the reactants and the
stoichiometric equation, as well as the mechanism of product formation. One
can express the rate equation as
rate = - l/vi d[i]/dt
where [ i ] is the concentration of reactant i, t is time, and v is a stoichiometric
The dependence of rate on reactant concentrations is expressed by the law
of mass action. Thus, for a given stoichiometric reaction,
rate = - 1/ui d [ i ] / d t = - I / u i k [ ~ ] " [ B I b
KINETICS OF IONIC REACTIONS
where a and b indicate the reaction order for the individual constituents, [ A ]
and [B] are the concentrations of the reactants A and B, respectively, and k is
the rate constant.
One should realize that the rate law is determined by experimentation and
it cannot be inferred by simply examining the overall chemical reaction
equation. The rate law serves three primary purposes: (1) it permits the
prediction of the rate, given the composition of the mixture and the
experimental value of the rate constant or coefficient; (2) it enables one to
propose a mechanism for the reaction; and (3) it provides a means for
classifying reactions into various orders. The order of a reaction is the
summation of the powers to which the concentrations of the components are
raised in the rate law.
A number of equations have been employed to describe the kinetics of
reactions in clay minerals and soils (Chien et al., 1980; Sparks and Jardine,
1981,1984; Martin and Sparks, 1983; Jardine and Sparks, 1984a). These have
included the first-order, Elovich, parabolic diffusion, zero-order, secondorder, and two-constant rate equations. Since a comprehensive article on
kinetics as applied to soil solutions has not been previously published,
complete derivations of most of these equations will be given. The final forms
of some of the above equations for adsorption kinetics using a miscible
displacement technique are given in Table I.
Equations Describing the Kinetics of Adsorption
Reactions in Clay Minerals and Soils Using a Miscible
C, = a + b In t
2. Parabolic diffusion law:
3. First order:
log(1 - C,/C,) = a - bt
4. Zero order:
(1 - CJC,)
= a - bt
The terms in each equation are defined in the text.