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IV. Rates of Adsorption and Desorption

IV. Rates of Adsorption and Desorption

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208



N. J. BARROW



(1978) for cadmium adsorption on manganese oxide. They showed different

rate curves for Cd adsorption and for H’, Na’, and K + displacement. This

rapid initial process is followed by a slow process. These will be examined in

turn.

A. THERATEOF THE ADSORPTIONPROCESS

The adsorption reaction involves the approach of charged particles to

charged surfaces. There might therefore be electrostatic effects on the rate of

the reaction. Unfortunately, this has not always been taken into account

(Mikami et al., 1983). It may be shown that the position of the rate-limiting

step relative to the electron-transfer steps determines the magnitude and

direction of the electrostatic effects (Barrow et al., 198lb). For phosphate

adsorption on goethite, Madrid and Posner (1979) observed that the

adsorption of phosphate was fastest at low pH. It was shown that this meant

that the rate-limiting step came before the electron-transfer steps and did not,

of itself, involve electron transfer (Barrow et al., 1981b). The effect of this is

that the electrostatic effect increases the rate of the forward (adsorption)

reaction when phosphate reacts with a positively charge goethite surface but

does not affect the rate of the backward (desorption) reaction. Further, the

equilibrium favors the product of the reaction, and hence the rate constant of

the forward reaction is larger than that of the backward reaction (Barrow et

al., 1981b). Therefore, if we disturb an equilibrium by adding phosphate, the

time required to reach a new equilibrium will be less than if we disturb the

equilibrium by removing the phosphate. It should not be assumed that a

period that suffices for the forward reaction to apparently reach equilibrium

will also suffice for the backward reaction. Some of the reported difficultiesin

inducing desorption may be due to this effect.

In this context it is appropriate to discuss the use of the word “irreversible”

to describe adsorption. This word is used in differing senses in the chemical

literature. A common meaning is that the equilibrium for a chemical reaction

is so far to the right that it goes virtually to completion. It therefore is

practically impossible to drive it in the opposite direction, that is, it is

practically irreversible. This sense is obviously inappropriate for adsorption

for, if the reaction went to completion, there would be no adsorbate left in

solution and adsorption-concentration curves could not be drawn. It is

therefore a contradiction in terms to speak of irreversible adsorption. If

desorption is found to differ from adsorption, there are only two possible

interpretations. One is that desorption is slower and that insufficient time has

been allowed. The other is that a further process has followed adsorption and

some of the reactant is, as a result, no longer “adsorbed” and thus not in



REACTION OF ANIONS AND CATIONS



209



equilibrium with the solution. The evidence for this further process is

considered next.

B. THESLOW PROCESS THAT FOLLOWS

ADSORPTION

There are three kinds of evidence that a molecular rearrangement may

follow the adsorption process. One is direct observation of overall rate. The

reaction often seems to consist of one process that appears to approach an

end point after periods of a few minutes followed by a much slower process.

This observation has been frequently made, and the following list of

references is meant to be illustrative rather than exhaustive: for acid-base

titration of goethite, see Madrid and Arambarri (1978); for reactions of

copper, zinc, cadmium, and lead with amorphous iron hydroxide see Benjamin and Leckie (1981); for reaction of copper with goethite see Padmanabham (1983); and for reaction of phosphate with goethite see Madrid and

Posner (1979) and Sigg and Stumm (1980).

The second kind of evidence is that high temperatures are observed to

increase the extent of the overall reaction [for phosphate on goethite, see

Muljadi et al. (1966); for cations on silica, see Bye et al. (1983)l. In both of

these cases, this observation was explained in terms of an effect of temperature on the position of an equilibrium and thus the value of an equilibrium

constant. However, in both cases, it was also observed that the maximum

amount of adsorption also increased. Muljadi et al. (1966) explained this in

terms of the breaking of surface bonds at high temperatures, thus increasing

the surface area. However, the temperatures used were not very high. Bye et

al. (1983) did not bring this aspect of their results to attention. A much

simpler explanation of these results is that a slow reaction followed adsorption and that the rate of this slow reaction was increased at high temperatures.

The third kind of evidence is that the longer the period that has elapsed

before desorption is started, the less complete the desorption. This has been

reported for the reaction of copper, zinc, and cobalt with goethite (Padmanabham, 1983a,b). Again, this can be explained by a slow reaction that follows

adsorption. Indeed, this is the only explanation that can explain observations

that, after an initial desorption, a resumption of adsorption may occur

(Hingston et al., 1974; Cabrera et al., 1981).

It is curious that such an extensive body of evidence has often been

ignored, especially when one considers that the slow and continuing process

that follows adsorption is very important in the long-term reaction of plant

nutrients and pollutants with soils. It is thus important both for the residual

value of fertilizers and for the retention of pollutants. It is even more curious



210



N. J. BARROW



when we realize that study of the mechanism of this slow process preceded

much of the work on the adsorption reaction. For example, Wei and

Bernstein (1959) reacted deuterium oxide vapor with boehmite (an aluminium oxyhydroxide) and showed that there was a rapid initial surface

exchange followed by a slower diffusion-controlled exchange within the

crystal. Berube et al. (1967) analyzed titration data with crystalline ferric

oxide and concluded that the slow step was controlled by diffusion of protons

into, or out of, the surface. They obtained a value of 20 kcal/mole for the

activation energy, that is, an increase in temperature would increase the rate

of the process.

A question that then arises is whether ignoring this diffusive process

invalidates studies on the supposed equilibrium. One defense is that equilibrium models have usually been tested against data obtained from a fairly

short period of reaction, so that the diffusive process is less important.

Another is that the immediate source of the diffusive process is the surface

concentration of adsorbate, not the solution concentration. If we assume that

diffusion is into a plane and ignore, for the time being, changes in surface

potential which the diffusion process will itself induce, then

2

M , = -r,@



&



where M , is the amount of substance i penetrating at time t, Ti is its surface

concentration, and D is a solid-state diffusion coefficient. (The mathematics

of. solid-state diffusion are more complex than indicated here, but this

complexity will not affect the current argument.) If we accept that diffusive

penetration of the surface occurs, then the amount of “adsorption” observed

is really true adsorption plus penetration, that is, M , + Ti. It would therefore

be better called “sorption” or “retention.” After a given period, the observed

retention is proportionately higher than true adsorption. The parameters of

“adsorption” models are therefore overestimated. This is especially true of

the maximum adsorption.

A further question is, By what molecular mechanism does diffusion occur?

Diffusion in crystals is basically an atomic process, with the diffusing

molecules undergoing a series of jumps through the crystal. Mechanisms

include exchange, in which two atoms change place, and vacancy mechanisms, in which an atom moves in one direction and the vacancy, or hole, in the

other (Manning, 1968). The vacancy mechanism is most likely to occur if the

crystals are imperfect. Wei and Bernstein (1959) noted that hydrogen occurs

in bonded sheets in boehmite crystals and suggested that diffusion of

hydrogen is more rapid than diffusion of oxygen. Similarly, Padmanabham

(1983a,b) suggested that copper, zinc, and cobalt atoms might occupy the



REACTION OF ANIONS AND CATIONS



211



lattice positions normally occupied by iron. They could therefore diffuse into

goethite by an exchange mechanism. Padmanabham (1983b) found that lead

could be more easily desorbed than copper, zinc, or cobalt and suggested that

the large lead atoms could not replace iron atoms in the crystal. For larger

ions such as phosphate, a vacancy mechanism seems more likely, and

imperfections in the crystal would therefore be important. Cabrera et al.

(1981) found that reaction of phosphate with the iron lepidocrocite continued

for a longer period than reactions with goethite. They noted that lepidocrocite appeared to consist of small crystals forming large aggregates with

micropores between them. The resolution that can be obtained with electron

microscopy is now so good that such boundaries between microcrystals can

be examined in detail. Cornell et al. (1983) have shown that a sample of

goethite was highly coherent across such boundaries, that is, there were not

many vacancies or micropores. An interesting research project would be to

test whether samples of iron oxides with less well-organized boundaries are

more prone to continue to react with, say, phosphates.

It is largely because of the diffusion process that follows adsorption that

desorption does not seem to follow the same path as retention (hereafter the

word “retention” is used to describe the sum of adsorption and penetration).

This difference between retention and desorption is often more clearly

expressed, and certainly more extensively documented, with soils and is

discussed further in the content.



V. TRANSFERRING THE VARIABLE-CHARGE MODELS

TO SOILS

A. THEOBSERVATIONS

To BE DESCRIBED

A large proportion of all the studies on soil chemistry have involved

reactions with the variable-charge components of soil. It is obviously

impractical to deal with more than a small fraction of this work here, and

hence only the main aspects will be considered.



1. Spec$city and Concentration

It is a common experience that many ions react specifically, that is, when

several species of ions are present in solution, some are retained by soil in

much greater proportions than their proportion in solution. For example,

phosphate is strongly preferred over, say, chloride, and zinc is strongly

preferred over, say, sodium. Nevertheless, some of the specifically reacting



212



N. J. BARROW



-



10,000



.SI



2 1000rn



I



P



L



Q



8



L



n



10



I,



0.01



I



I



I



1.o

10

Phosphate concentration ( p g P/ml)



0.1



FIG.12. Relation between retention of phosphate and concentration over a wide range of

concentrations for three soils of widely differing phosphate retention. The lines drawn are taken

from a model of the effect of pH and concentration on retention. They are a section in the

concentration dimension of Fig. 16.



ions remain in solution, and plots may be prepared of the amount retained

against the concentration remaining in solution (Fig. 12). Such curves are

often called “adsorption isotherms.” However, it is now becoming clear that

the process involved is not simply adsorption, and the term “isotherm”

implies that temperature is the only other variable affecting the curve. I have

therefore argued that this impressive-sounding terminology be avoided

(Barrow, 1978). A better terminology is Q/Z (quantity/intensity) plots or

retention curves.

Much effort has been expended in seeking a mathematical description of

these Q/Z plots. The reasons for this effort have not always been clear. I have

argued that the only good reason is to seek a way of summarizing behavior

by a few numbers (Barrow, 1978). For this purpose, the fewer the numbers the

better. A simple equation that often describes Q/Z plots is the Freundlich

equation

S



= acb



(16)



were S is the amount retained and should include any adsorbate initially

present, c is the concentration remaining in solution, and a and b are

constants. If this equation holds, logarithmic plots of S against c give a

straight line. This is often a convenient approximation over important

concentration ranges, but over larger ranges the nonlinearity becomes more

important (Figs. 12, 13,14, and 15). The Langmuir equation, or versions of it,

have been widely used to describe Q/Z curves on the grounds that they are



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