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II. Methodologies Used in Kinetic Studies

II. Methodologies Used in Kinetic Studies

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234



D O N A L D L. SPARKS



A. BATCHTECHNIQUES

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



235



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)



-



u3 exp(-k,t)



- a,exp(-k,t)



(1)



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



+



y)/y-b]



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.

B. FLOW

OR MISCIBLE

DISPLACEMENT

TECHNIQUES



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).



236



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,

1982).

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



237



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



238



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

ratio.



111. APPLICATION



OF CHEMICAL KINETICS TO SOIL

SOLUTIONS



A. THEORETICAL

ASPECTS

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



(3)

where [ i ] is the concentration of reactant i, t is time, and v is a stoichiometric

parameter.

The dependence of rate on reactant concentrations is expressed by the law

of mass action. Thus, for a given stoichiometric reaction,

v,A



+ v,B



-



vtC



+ odD



rate = - 1/ui d [ i ] / d t = - I / u i k [ ~ ] " [ B I b

-



(4)



KINETICS OF IONIC REACTIONS



239



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.



Table I

Equations Describing the Kinetics of Adsorption

Reactions in Clay Minerals and Soils Using a Miscible

Displacement Technique"

1. Elovich:

C, = a + b In t



2. Parabolic diffusion law:

C,/C,



=a



+ btIi2



3. First order:



log(1 - C,/C,) = a - bt

4. Zero order:

(1 - CJC,)

a



= a - bt



The terms in each equation are defined in the text.



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