3 Department of Geology and Geophysics, Yale University, P. O. Box 208109, New Haven, CT 06520-8109, U.S.A.

Experiments measuring synthetic gibbsite dissolution rates were carried out using both a stirred-flow-through reactor and a column reactor at 25°C, and pH range of 2.5 to 4.1. All experiments were conducted under far from equilibrium conditions (DG<-1.1 kcal/mole). The experiments were performed with perchloric acid under relatively low (and variable) ionic strength conditions.

An excellent agreement was found between the results of the well-mixed flow-through experiments and those of the (non-mixed) column experiments. This agreement shows that the gibbsite dissolution rate is independent of stirring rate and therefore supports the conclusion of Bloom and Erich that gibbsite dissolution reaction is surface controlled and not diffusion controlled.

The BET surface area of the gibbsite increased during the flow-through experiments, while in the column experiments no significant change in surface area was observed. The agreement between the dissolution rates of the mixed flow-through experiments that were normalized to the final surface area, with these of the column experiments, supports the assumption that the changes in surface area occurred early in the experiment, before the first steady state was approached. The significant differences in the BET surface area between the column experiments and the flow-through experiments, and the excellent agreement between the rates obtained by both methods, enable us to justify the substitution of the BET surface area for the reactive surface area.

The dissolution rate of gibbsite varied as a function of the perchloric acid concentration. At pH>3.5 the dissolution rate increased as a function of acid concentration, while at pH<3.5 it decreased with acid concentration. We interpret the gibbsite dissolution rate as a result of a combined effect of proton catalysis and perchlorate inhibition. Following the theoretical study of Ganor and Lasaga we propose specific reaction mechanisms for the gibbsite dissolution in the presence of perchloric acid. The mathematical predictions of two of these reaction mechanisms adequately describe the experimental data.

In nature, there are many environmental factors that govern the rate of mineral dissolution. The laboratory situation is somewhat simpler. One can conduct a series of experiments in which one factor is manipulated while all other factors are held constant. The outcome of such experiments is usually a simple rate law describing the effect of the manipulated variable on the rate. Many such experiments investigating the effect of variables such as temperature, pH, ionic strength, catalysis and inhibition by inorganic and organic compounds and deviation from equilibrium are reported in the geochemical literature. A large effort has been made in recent years, to formulate a general form of the rate law to generalize the simple rate laws. The form of the general rate law has improved as our understanding of the kinetics of heterogeneous reaction has deepened (compare for example, Lasaga, 1981; Aagaard and Helgeson, 1982; Lasaga, 1984; Nagy et al., 1991; Nagy and Lasaga, 1992; Lasaga et al., 1994; Lasaga, 1995 ).

A general form of rate law for one mechanism of heterogeneous mineral surface reactions can be written as :

(1)

where k0 is a constant, Sa is the reactive surface area of the mineral, Ea is the apparent activation energy of the overall reaction, R is the gas constant, T is the temperature (K), a_i and a_H+ are the activities in solution of species i and H⁺, respectively, n_i and n_H+ are the orders of the reaction with respect to these species, g(I) is a function of the ionic strength and f(DG) is a function of the Gibbs free energy. The much-studied pH dependence of the dissolution/precipitation reactions is represented by the term a_H+ⁿH+ in equation (1). Terms involving activities of species in solution other than H⁺, a_iⁿi, incorporate other possible catalytic effects on the overall rate. The g(I) term indicates a possible dependence of the rate on the ionic strength (I) in addition to that entering through the activities of a specific ion. The last term, f(DG), accounts for the important variation of the rate with deviation from equilibrium.

The formulation of equation (1) is very useful because it relates the reaction rate to activities of ions in solution that may be obtained directly from the chemistry of the solution. However, mineral dissolution is a surface process and therefore it is more appropriate to initially express the dependence of the rate on the concentrations (or activities) of ions adsorbed on the surface rather than on the bulk activities in solution. Therefore, equation (1) can be rewritten in terms of surface concentrations (Xi,ads):

(2)

The coefficients n_H+_,ads and n,_i,ads are the reaction orders with respect to the surface species.

The dissolution rate of gibbsite as a function of temperature, acid/base, ionic strength, degree of saturation and catalysis by inorganic anions has been addressed in previous works. Bloom studied the kinetics of dissolution of two synthetic gibbsite samples in nitric acid solutions with pH values that ranged from 1.5 to 3.3. The experiments were performed under relatively low (and variable) ionic strength conditions without adding high concentration of salt. Two different mechanisms with different rate-controlling steps were suggested by Bloom : At pH<2.1 a rate-controlling step of protonation of positively charged surface sites, and at pH>2.4 a rate-controlling step of water attack. Under high ionic strength conditions, Bloom and Erich found that the reaction order with respect to H+ within the pH range 1.5 to 4.0 varies from 0 to 1, depending on the anion. This behavior was explained by two parallel mechanisms. In solutions containing phosphate, anion attack predominated, and the rate of the reaction was independent of pH, while in solutions containing ions not specifically adsorbed, e.g., sulfate and nitrate, proton attack on the surface was the determining step, i.e., the dominant mechanism. For natural gibbsite, Mogollon et al. found a slight dependence of the dissolution rate on pH. The reaction order with respect to the activity of the proton was 0.29±0.05. The ionic strength of the experiments of Mogollon et al. was low (≤0.001) but not constant, and the pH range was 3.3 to 3.9. Mogollon and Perez-Diaz found a catalytic effect of SO42- on the dissolution rate of natural gibbsite. The reaction order with respect to the concentration of the anion was 0.4±0.1. A slight decrease in dissolution rate of natural gibbsite was observed by Mogollon and Perez-Diaz in the presence of other anions (NO3-, Cl-, and ClO4-). They explained this decrease of the rate by an ionic strength effect. A first order dependence on sodium hydroxide activity was found by Scotfoand Glastonbury .

The dissolution rate of gibbsite has been found to be a strong function of the degree of saturation . Nagy and Lasaga showed that near equilibrium (0 ≥ DGr ≥ -0.2 kcal/mole) the rates increase gradually with increasing undersaturation according to an approximately linear function of DGr. Over the range -0.2 ≥ DGr ≥ -0.5 kcal/mole, the rates increas. Far frome, DGr < -0.5 kcal/mole, the dissolution rates constant. Mogollon et al. show that the function that was used by Nagy and Lato describe the dissolution rate of synthetic gibbsite as a function of DGr at 80°C, adequately describes the DGr dependence of the dissolution rate of natural gibbsite at 25°C.

Essentially the same temperature dependence was exhibited by data from solutions using different anions (NO3-, SO42-, PO43-), and the activation energies (Ea) were therefore very similar, i.e., 59-67 kJ/mole . These values are much greater than Ea for reactions that are diffusion controlled, Ea < 20 kJ/mole , and they demonstrate that the dissolution reaction is surface controlled.

In this paper we reexamine the pH and anion effects on the dissolution rate of gibbsite under low ionic strength conditions (I<0.0032 M). The experiments were performed using different concentrations of HClO4 solutions. The drawback of such an experimental setting is that changing the acid concentration changes both the H+ and anion activities. By adding a high concentration of salt, Bloom and Erich were able to vary the pH and keep the anion concentration relatively constant. However, this is not suitable for experiments under low ionic strength. In our previous study we assumed that under low ionic strength conditions the acid effect is solely due to the proton effect. The present study re-examines this assumption and demonstrates that the perchloric acid effect is a result of a catalytic effect of the proton and an inhibitory effect of the anion.

Many different experimental designs, e.g., pH-stat, stirred batch, fluidized bed or stirred flow-through reactors and column experiments, have been used to determine dissolution rates. However, the consistency of results obtained by different methods has been rarely checked. The data in the present study were obtained by two methods: a mixed flow-through reactor and a column. We will show that under far from equilibrium conditions, there is no difference in dissolution rates obtained by the two methods, and will discuss some implications of this agreement to the comparison of results of laboratory dissolution experiments and weathering rates in the field.

Different crystal faces have different bonding properties and hence different surface free energies as well as different adsorption properties and different dissolution (or growth) rates. Surface reaction rate depends also on surface topography (e.g., kinks, edges and adatoms) and on the presence of defects. The use of mineral powders in kinetics experiments gives the advantage of reaction at a large number of surfaces of the mineral, thereby providing an average reaction rate. However, a potentially severe problem in interpreting these average heterogeneous kinetic results is our inability to measure the reactive surface area of the mineral powder, i.e., the surface area of the sites that significantly influence the reaction rate and are exposed to the aqueous phase. Therefore, the common practice in experimental kinetics is to normalize the dissolution rate to the total surface area measured by adsorption of non reactive gases to the surface of the dry powder (e.g., the BET method). The reactive surface area may be significantly less than the total (BET) surface area . Using measured total surface area of a dry sample to estimate reactive surface area of a sample in contact with solution may be problematic as well. In most studies the specific surface area of the mineral is not manipulated and therefore it is not possible to validate the assumption that the BET surface area represents the reactive surface area. Differences in the BET surface area between the column experiments and the flow-through experiments enable us to justify the substituting of the BET surface area for the reactive surface area.

The material used in this study is synthetic gibbsite ALCOA composition C-31 from Dave Wesolowski, Oak Ridge National Laboratory. Following Nagy and Lasaga gibbsite was pretreated at room temperature by the following procedures:

(1) Gibbsite was dry sieved using 43 mm polyester macro filter.

(2) The <43 mm fraction was suspended in distilled, deionized water.

(3) The suspension was stirred and then allowed to sit for 2 to 20 hours, and suspended material was decanted.

(4) Stages (2) and (3) were repeated in sequence about 15 times .

(5) Gibbsite was stirred and washed 3 times for about an hour in a 1 M HCl to dissolve ultra-fines and amorphous surficial particles.

(6) Stages (2) and (3) were repeated in sequence about 20 more times.

The BET-determined initial surface area of the gibbsite after the pretreatment was 0.37±0.04 m2 g-l using 3-point N2 adsorption isotherms.

The columns used measured 7.50 cm in length with a diameter of 0.9 cm, and were fully immersed in a water bath held at a constant temperature of 25±0.1°C using a Techne temperature-controller. The columns were constructed from Lexan plastic, which is transparent and acid resistant. Flow was directed upward in the experiments to avoid the presence of air bubbles. The flow rates were controlled with an Ismatec brand peristaltic pump. Variations in flow rate were less than 3%, (in most cases less than 1%). Darcy velocity (which is the flow rate divided by the cross section area of the column) ranged from 204 m/yr to 321 m/yr (Table 1). Solutions were filtered with a 0.45 mm Durapore (Millipore) membrane at the top of the column before flowing through the output tubing. To avoid losses of the material, a similar membrane was placed at the bottom of the column. An O-ring, resistant to extreme pH, was used to complete the seal. No solid was observed in any input or output solution. Input and output tubing was made out of Norprene black plastic. The initial gibbsite mass was 2.527 g. Details of the experimental design are given in Mogollon et al. .

Experiments were carried out using a stirred-flow reactor (30-45 ml in volume) which was fully immersed in a water bath held at a constant temperature of 25±0.2°C. Details of the design of the reaction vessel are given in Nagy et al. . The flow rates were controlled by a peristaltic pump and ranged from 0.021 to 0.040 ml min-l yielding a residence time within the cell of about 15 to 36 hours. Stirring of gibbsite and fluid was controlled by a stirring plate placed directly beneath the bath. A Teflon-coated stir bar was mounted on a pin to avoid grinding the gibbsite. Solutions were filtered on the output side of the vessel through a 0.45 mm Durapore membrane (Millipore). In any one run, the flow rate and the input pH were held constant for a long enough time such that steady state conditions were achieved. Achievement of steady state was verified by a series of constant Al output concentrations, where constancy was defined as standard deviation of output concentrations of less than 6%. After steady state conditions were reached, dissolution rates were evaluated and the flow rate and/or the input pH were changed to achieve a different steady state. Each experiment was composed of 1 to 3 such stages. After the end of the last stage thecell was dismantled and the final specific surface area was measured. The experimental conditions of each stage are described in Table 2.

The mass of gibbsite in the cell was decreased during the experiment as a result of its dissolution. The dissolved mass at each experiment was calculated daily based on the outflux of aluminum and was subtracted from the initial mass (Table 2). The daily total surface area was calculated by multiplying the mass by the final (BET) specific surface area. Calculated total dissolved material throughout the experiments was less than 1% of the starting mass of gibbsite. Nonetheless, a significant difference was observed between the initial and final BET specific surface areas of the gibbsite (Table 2).

Input solutwereprepareagent grade concentrated perchacid with di, deioni. Output bottles were replaced once a day and the solutions were analyzed Al and pH. Total Al was analyzed colorimetrically with a UV-visible spectrophotometer, using the catechol violet method . The uncertainty in measured Al was ± 3% and the detection limit 0.5mM . The pH of input and output solutions was measured at experimental temperature on an unstirred aliquot of solution using a Ross combination electrode with a reported accuracy of ± 0.02 pH units (± 4.5% in H+ activities). The pH electrode was standardized at experimental temperature against NBS buffers prepared from reagent grade salts.

The overall dissolution reaction of gibbsite at acidic pH is expressed as:

(3)

The deviation from equilibrium with respect to gibbsite dissolution is calculated in terms of Gibbs free energy of reaction (DGr),

(4)

where R is the gas constant, T is temperature and IAP and Keq are actual and equilibrium ion activity products of the solution, respectively. Assuming that activity of water is 1 (a reasonable assumption for low ionic strength, I<0.0032 M), the ion activity product for the gibbsite dissolution reaction is:

(5)

Ion activity products of steady-state solutions were obtained by calculating the distribution of all aqueous species using appropriate thermodynamic data (Table 3). Activity coefficients were calculated using the extended Debye-Huckel equation with parameters from Wolery .

For both mixed flow-through and column experiments, steady state is needed to carry out dissolution rate calculations. Based on the precision of the measurement techniques and the variability of flow rate, variation of less than 6% in the output Al concentration of three successive samples was chosen as a practical criterion for establishing steady state.

The dissolution rate, R, (mole m-2 sec-1) in a well-mixed flow-through experiment is obtained from the expression:

(6)

where Cj,inp and Cj,out are the concentration of component j in the input and the output (mole m-3), nj is the stoichiometry coefficient of j in the dissolution reaction, t is time (sec), Sa is the total surface area of the mineral (m2), V is the volume of the cell (m3) and q is the fluid volume flux through the system (m3 sec-1) . The dissolution rate in such an experiment may be readily obtained if steady state is reached, i.e., if the composition of the output solution reaches a constant value (). In this case, the dissolution rate is balanced by the difference between input and output solutions:

(7)

The analytical error in the rate calculated from equation (7) is ±11%. This error includes the uncertainty of the flux (2%), the output aluminum concentration (3%) and is dominated by the uncertainty of the BET surface area measurement (±10%).

Mogollon et al. show that under far from equilibrium conditions the dissolution rate of gibbsite in a column experiment similar to that of the present study may be obtained from the expression:

(8)

where R is the dissolution rate of gibbsite (moles m-3 sec-1), v is the true fluid velocity in the column (m/sec) (that is v=v_D/f, where v_D is the Darcy velocity and f is the porosity), Cinp and Cout are the input and the output concentrations (M), respectively, and L is the column length (m) . For an input aluminum concentration equal to zero, equation (8) becomes:

(9)

To obtain the dissolution rate in units of moles m-2 sec-1, we multiply both sides of equation (9) by V, the total volume of solution (m3), and divide by Sa, the total surface area of the gibbsite (m2),

(10)

where qv is the volume flow rate of the fluid (m3 sec-1), Sa is the product of the mass (g) and the BET specific surface area (m2 g-1). Note that in our formalism, the rate is defined to be negative for dissolution and positive for precipitation (hence the minus sign has been added in equation (10). The error in the rate calculated from equation (10) is ±11%, the same as calculated from equation (7). This error includes the uncertainty of the volume flow rate (2%), the output aluminum concentration (3%) and is dominated by the uncertainty of the BET surface area measurement (±10%).

The variation in the output concentration of Al and in the output pH as a function of time are shown in Fig. 1a and 1b, respectively. The vertical lines represent changes in the input pH and/or flow rate between the different stages. Figure 1 shows that once the flow rate and the pH are stable, constant output concentration, i.e., steady state, is reached in the column experiments in less than 100 hours, as determined from the first two to five samples. New steady state constant output concentrations are obtained after each change in the pH and/or flow rate. Averages and standard deviations of the pH and Al concentration for each steady state reached during the experiment are given in Table 1. Al and pH analyses used to calculate these average steady states are marked with black symbols in Fig. 1. Dissolved material, calculated based on integrating the Al concentrations in the outputs, was less than 0.2% of the starting mass for the entire experiment. No significant difference (within the precision of the technique) was observed between the initial BET surface area (0.37±0.04 m2/g) and the final BET surface area (0.44±0.04 m2/g).

The variation of the output concentration of Al and of the output pH as a function of time are shown in Figs. 2a to 2f. Each experiment was composed of 1 to 3 stages, where each new stage was initiated by a change in the flow rate. The vertical lines in the figures delineate the different stages. Much of the noise in the non-steady state data results from instabilities in flow rate and or stirring. Successive samples showing constant aluminum concentration were considered not at steady state if the flow rate and/or stirring were not stable. Average pH and Al concentrations for each steady state are compiled in Table 2. Al and pH analyses used to calculate these average steady states are marked by black symbols in Figs. 2a to 2f. In all of the experiments, the final surface area (Table 2) was much higher than the initial surface area (0.37±0.04 m2/g). Dissolution rates at steady state (Table 2) were calculated using the measured final surface area, the flow rate and the output Al concentration (the input solutions in all experiments contained no Al).

Dissolution rates at steady state (Tables 1 & 2) were calculated for the column and the mixed-flow-through experiments using equations (10) and (7), respectively. Two important differences exist between a column reactor and a mixed-flow-through reactor: a) The volumetric instantaneous water/rock ratio in the column is small and in a well-wetted experiment is equal to the porosity, while in a mixed flow-through reactor the water/rock ratio>>1. b) At steady state, the solution composition at a specific location in the column is constant with time but varies with position along the column, while in a well-mixed experiment all the solid is exposed to the same solution. Therefore, it is important to verify that the resulting dissolution rates are independent of tanalytical method that was used. This is especially important when one triesto evaluatkineticvariables, suchas pH or temperadeof the dirat, bon daobtained by the two methods. Fig. 3a compares the dissolution rate of synthetic gibbsite at 25°C in the mixeflow-through and the column reacat various pH values. The two methods show excellent agreement, allowing use of the entire data set for the following discussion. This agrbetweresults of well-mixed flowthrough experiments and results of (non mixed) column experiments shows that the dissolution rate is independent of the rate of stirring and therefore supports the conclusion of Bloom and Erich that the gibbsite dissolution is surface controlled and not diffusion controlled. Casey et al. argued that one of the limitations in using experimental dissolution rates to study natural conditions is that the fluid to solid ratio is high in experiments but very low in the field. The comparison in Fig. 3a shows a good agreement between experiments with high and low fluid-to-solid ratio. Although a well-wetted column experiment has higher water/rock ratio than most natural soils, the agreement between the two types of experiments demonstrates that laboratory dissolution experiments with high water/rock ratios may be relevant in interpreting systems with much lower water/rock ratios which are more similar to natural systems.

By substituting the BET surface area (SBET) as the reactive surface area (Sa) in equations (10 & 7) to calculate the dissolution rate, we make the assumption that the BET surface area can be substituted for the reactive surface area. Even though they are probably not identical, the substitution would be kinetically feasible if the distribution of the sites that significantly influence the reaction rate (i.e., defects, kinks, etc...) correlates with the total surface area, and therefore the BET surface area is linearly proportional to the reactive surface area, i.e.,

(11)

The proportional coefficient, kBET, should be independent of the experimental design and environmental conditions such as temperature and pH. As long as these assumptions are valid, calculation of the parameters affecting the rate (equation 1) will not be influenced by replacing the reactive surface area with the BET surface area. The only parameter in equation (1) that will be influenced by using of the BET surface area is the rate constant k0 that will be replaced by an apparent rate constant k'o, i.e.,

(12)

For all practical purposes, the usage of k0' instead of k0 is adequate, as long as we use the BET surface area systematically.

Under far from equilibrium conditions, constant ionic strength, temperature and concentrations of all possible catalysts and inhibitors, the general rate law (equation 1) is reduced to:

(13)

where kp is a rate coefficient that is constant under these conditions. Rearranging equation (11) and substituting into (13) gives

(14)

where kp' is an apparent rate coefficient. Fig. 4 is a theoretical plot of dissolution rate (not normalized to surface area) vs. surface area. The slope of the line connecting each data point to the origin is the rate coefficient kp (equation 13). As we plot the BET surface area in Fig. 4 the slopes of the lines connecting the data points to the origin become the apparent rate coefficient kp' (equation 14). As long as the BET surface area is linearly proportional to the reactive surface area (i.e., equation 11) the slope (and the obtained rate coefficient) is independent of the surface area (Fig. 4a). On the other hand, if the assumption of equation (11) is wrong then the rate coefficient will vary as a function of the BET surface area (Fig. 4b). In most studies the specific surface area of the mineral is not manipulated and therefore it is not possible to validate the assumption of equation (11).

The BET surface area of the gibbsite exhibited variations between the initial and final measured values in the different flow-through experiments (Table 2). Up to 10-fold increase in the gibbsite surface area was observed between the initial and final BET measurements. Nagy and Lasaga observed a similar increase in the surface area of gibbsite in their dissolution and precipitation experiments. They proposed that the change in measured surface area is a result of mechanical disaggregation taking place early in the experiments and not a result of dissolution or precipitation reaction taking place throughout the duration of the experiments. Nagy and Lasaga supported their interpretation by three lines of evidence. Firstly, they published SEM images showing that the unreacted pretreated gibbsite consisted of clusters of smaller grains while the reacted gibbsite always occurred as single grains. Secondly, the SEM image did not demonstrate extensive pitting of the dissolved surfaces or irregular growth on the precipitated surfaces. Thirdly, experiments remained at steady state for as long as 85 days, which shows that there was no significant change in surface area after the experiments reached steady state. Following the reasoning of Nagy and Lasaga we calculate the dissolution rates assuming that the changes in surface area occurred early in the experiment, before the first steady state was approached. In the following discussion we show that the comparison between the results of the mixed flow-through and the column dissolution experiments supports this assumption. Moreover, substitution of the BET surface area for the reactive surface area is borne out by the experimental data as well.

In the column experiments we did not observe a significant change in surface area as was observed in the well-mixed flow-through experiments. This is in agreement with suggestion of Nagy and Lasaga , that the change in surface area is a result of mechanical disaggregation and not a result of a dissolution or precipitation reaction. Fig. 3a and 3b compare dissolution rates of column experiments with dissolution rates of mixed flow-through experiments. In Fig. 3a the dissolution rates of the flow-through experiments are normalized to the final surface area and in Fig. 3b to the initial surface area. The agreement between the dissolution rates of the mixed flow-through experiments that were normalized to the final surface area with these of the column experiments supports the assumption that the changes in surface area occurred early in the experiment, before the first steady state was approached. Having two sets of dissolution experiments with significantly different BET surface area enables us to learn about the relation between the reactive surface area and the total (BET) surface area. In the following section we demonstrate that the agreement between the column and the flow-through experiments indicates that the reactive surface area is linearly proportional to the BET sarea.

We obtained dissolution rates (mole g-1 sec-1) that are independent of the measured BET surface area by calculating the dissolution rate per mass unit of the gibbsite instead of per surface area unit, i.e., by replacing the surface area in equation (7) by the mass, m (g),

(15)

Fig. 5 plots the mass normalized dissolution rate vs. the measured (final) BET specific surface area for experiments at pH 3.05 and 3.6. The regression lines for both pHs cross through the origin and therefore may be described by equation (14), where kp' , the slope of the trend line, is the rate constant. By substituting equation (14) into equation (13) we can obtain equation (11) and therefore show that the BET surface area is linearly proportional to reactive surface area, i.e., that the assumption of equation (11) is valid. This linearity is not influenced by the drying of thegibbafter the ex. Yet,we can not prove that the propocoefficis independent of environmentalcond, i.e., ththe ratio kp/kp' (=kBET) is not influenced by the different variathat influence the values of the coefficients kp and kp' .

Curreour understanding of the surface reaction mechanism is limited, and we do not know what type of surface sites (e.g., kinks, dislocations) controls gibbsite dissolution. The relative reactivity of the various crystal faces is also unknown. The observation that the reactive surface area is linearly proportional to the BET surface area implies that the dithe density of surface sites that signinfluence the reaction rate remains constant as the change in total surface area occurs. A simple explanation for this observation is that the reactive surface sites are evenly distributed on all crystal faces (e.g., basal plains, edges), and therefore the dissolution rate is the same on all crystal faces. According to this explanation the change in the total surface area involved changes in the relative exposure of the different crystal faces to dissolution, but the dissolution rates on the different faces are controlled by the same reaction mechanism and therefore dissolution rate remains constant. However, there is no independent evidence that supports the suggestion that different crystal faces have the same reactivity.

An alternative and more likely explanation is that only a few types of crystal face dominate both the reaction rate and the total surface area. For example, this will be the case if the dissolution rate is dominated by dissolution of the basal plane and each gibbsite crystal has the shape of a plate in which a@b>>c . In this case, the total surface area is dominated by the surface area of the basal planes (2.a.b), while the surface area of the edges (2.a.c+2.b.c) is negligible. Therefore, cleaving the gibbsite perpendicular to the c axis will double both the total and the basal plane surface area which control the reactive surface area. The important requirement for explaining the rate-surface area relationship is that the relative amounts of the dominant faces do not change significantly as the total area changes. For example, if the surface area is changed by adding more of the same material in an experiment, this condition would obviously be met. On the other hand, Nagy and Lasaga (1992) showed that the unreacted pretreated gibbsite consisted of 10-40 mm clusters of smaller crystals of 1-10 mm, and that during dissolution experiments these clusters were disaggregated into single grains. Therefore, we suggest that the grains were randomly oriented in the clusters so the representation of each crystal face on the clusters - fluid interface was equal to its relative surface area. Therefore the ratio between the surface area of the crystal face that dominates dissolution rate and the total surface area remained constant as the clusters were disaggregated and the change in total surface area occurred.

The dissolution rate of gibbsite varies as a function of the acid concentration. Fig. 6 plots the log of gibbsite dissolution rate as a function of -pH (=log(aH+)). The main feature in Fig. 6 is a maximum at dissolution rate around pH=3.5. The increase in dissolution rate as the pH decreases between pH 4.1 and 3.5 may be challenged due to the scatter of the data at pH 4.1. However, a similar trend was demonstrated previously by Mogollon et al. . Close examination of the column data (figure 1 and Table 1) should be convincing that the stepwise decrease in dissolution rate between pH 3.5 and pH 2.5 is clear. Every change in pH (Fig. 1b) results in a change in Al output concentration (Fig. 1a). In all cases, decreasing the pH results in a decrease in Al concentration whereas increasing in pH results in an increase in Al concentration. (Note that the decrease in Al concentration between stage 1.05 and 1.06 is a result of changes in flow rate and not in pH). Such close examination of figure (1) demonstrates that even the drop in dissolution rate between pH 3.2 and 3.0 is real.

A simple rate law for the pH dependence of the rate may be calculated by linear regression to be,

(16)

In all our experiments, CClO4- @ CH+, and therefore from a mathematical point of view (assuming that the activity coefficient gH+=1), we may equally view Fig. 6 as a plot of log dissolution rate as a function of log perchlorate concentration. A different rate law, equivalent to that of equation (16) is,

(17)

Equations (16 & 17) suggest that the observed changes in dissolution rate may be interpreted as a result of differences in the pH and/or the ClO4- concentration. To correctly interpret the actual dependencies of the dissolution rate, one should separate these two possible effects from each other as well as from other possible effects of parameters such as output Al concentration, ionic strength and the degree of saturation, which vary between the experiments.

The effect of deviation from equilibrium on dissolution rate is described by the highly non linear f(DG) function (equation (1) and (2)) observed originally by Nagy and Lasaga for synthetic gibbsite at pH=3 and 80°C. According to this function (Fig. 7), near equilibrium (0 ≥ DGr ≥ -0.2 kcal/mole) the rates increase gradually and approximately linearly with increasing undersaturation. Over the range -0.2 ≥ DGr ≥ -0.5 kcal/mole, the rates increase sharply. Far from equilibrium, at DGr £ -0.5 kcal/mole, the dissolution rate is independent of the degree of saturation. This region in Rate vs. DGr space where the function f(DG) is flat is termed the dissolution plateau . The results of Mogollon et al. show that the dissolution plateau for gibbsite at 25°C is in very good agreement with the results of Nagy and Lasaga at 80°C. Tables 1 and 2 show that for all output solutions DGr< -1.1 kcal/mole, i.e., all experiments were conducted on the dissolution plateau regime. Under these far from equilibrium conditions the last term in equation (1) and (2) equals 1, and therefore the observed changes in dissolution rate did not result from changes in the degree of saturation between the experiments.

The input solutions of all our experiments contain only H+ and ClO4-. As a result of the gibbsite dissolution, Al is added to the solution in the reaction cell. Therefore, H+, ClO4- and the Al aqueous species are the only potential catalysts / inhibitors. The existence of a dissolution plateau, observed by Nagy and Lasaga and Mogollon et al. , implies that under far from equilibrium conditions the dissolution rate is independent of Al concentration. Therefore, we rule out the possibility that Al species have catalytic or inhibitory effects on gibbsite dissolution rate. Hence, under constant temperaand far from equilibrium conditions when protons and perchlorate are the only potential catalysts/inhibitors in the system, the dissolution rate (normalized to surface area) is determined by the pH, the perchlorate ion activity and the ionic strength (see equation (1) and (2)).

Proton catalysis is a reasonable explanation for the increase in dissolution rate as a function of acidity between pH 4 and 3.6 (Fig. 6). The maximum in dissolution rate around pH=3.5 and the decrease in dissolution rate between pH 3.6 and 2.5 are more difficult to interpret. We suggest that the surface is saturated with respect to protons around pH 3.6. Any increase in perchloric acid concentration will not change the surface concentration of the protons and the dissolution rate will be govby either inhibition by perchlorate ions or ionic strength effect. The ionic strength of the solution is dominated by the concentration of the pacid, because thconcenof althe other aqueous species are negligible in our e. Therefore, itis impossible to use oudata set to diffebetwethe effect of thperchlorate and that of the ionic strength.

Mogollon and Perez-Diaz showthat the dissolution rate of natural gibbsite under ionistrengof up to 0.01 M decreases as a function of ionic strength. They show that log dissolution rate decreases linearly as a function of the square root of the ionic strength with a slope of 3.0±0.5. They explain this effect by the primary kinetics salt effect. According to transition state theory, reaction rate is proportional to the concentration of the activated complex that is in equilibrium with the reactants. The activity of the reactants depends on their activity coefficients (g). By analogy with ions in solution Mogollon and Perez-Diaz suggested that log(g) is lto the square root of the ionic strength as predicby the Debye-Hückel equation. As a result, the log of the rate is proportional to the square root of the ionic strength :

(18)

where Q is a coefficient, A is a constant depending on temperature, Z₁ and Z₂ are the charges of the ions that form the activated complex and I is the ionic strength of the solution. This and other possible theoretical explanations for the effect of ionic strength on gibbsite dissolution rate were thoroughly discussed by Mogollon and Perez-Diaz . In this respect, our Fig. 8 plots log dissolution rate vs. the square root of the ionic strength of all samples with pH≤3.6. The plot shows a near linear negative slope of 18±3. As the A parameter in the Debye-Hückel equation is very close to 0.5 at 25°C the absolute value of the predicted slope should be approximately the product of the charges of the ions that form the activated complex (equation 18). The slope of -3±0.5 that was found for natural gibbsite by Mogollon and Perez-Diaz is reasonable and may be obtained if the absolute value of the charges are 1 and 3, and therefore can be interpreted as a result of ionic strength effect. A slope of -18, on the other hand, requires that at least one of the charges will be very high, which is not very probable. Therefore, a possible alternative explanation is that the decrease in dissolution rate below pH 3.6 results from perchlorate inhibition. In the following discussion we assume no ionic strength effect and interpret the measured dissolution rates as the result of a combined effect of proton catalysis and perchlorate inhibition.

Ganor and Lasaga presented a mechanistic model describing the effects of an inhibitor on mineral dissolution rate in the presence of a catalyst. The model is fairly simple and consists of fast adsorption of a catalyst and/or an inhibitor on the mineral surface followed by a slow hydrolysis step. The surface reaction mechanism envisions four plausible reaction paths and the formation of four types of reaction intermediate surface clusters: 1) clusters with adsorbed catalyst; 2) clusters with adsorbed inhibitor; 3) bare clusters and 4) clusters with both adsorbed catalyst and adsorbed inhibitor. The rate of each of these reaction paths depends on the effect of the adsorbed surface species on the strength of the bonds and on the molar fraction of the surface cluster. To relate the rate law to activities of species in solution, adsorption isotherms of the catalyst and the inhibitor were introduced into the models. The adsorption isotherm of the catalyst and the inhibitor may depend on each other or may be independent. Accordingly, Ganor and Lasaga proposed two end member mechanisms. In the first mechanism the catalyst and the inhibitor compete with each other, i.e., they have a full mutual (negative) dependence, and therefore clusters with both adsorbed catalyst and adsorbed inhibitor can not exist. In the second mechanism the adsorption of the catalyst and the inhibitor are absolutely independent of each other.

There have been many studies of water-rock interactions in recent years, producing extensive experimental data sets. However, understanding of these data requires models that address more and more details of chemical processes occurring on the mineral surface. To this end, the geochemical community has used adsorption models, for example Langmuir models, to interpret the kinetic data. However, the discussion of possible competition between ligands and the role of multiple sites can still be much more developed. Therefore, it is important to extend the current discussion of these adsorption phenomena in new directions, especially when new kinetic data are available. We discuss such models in the following section. Even though these types of models can and will be refined as more spectroscopic and surface data become available, the basic results stemming from the treatment of several ligands adsorbing on surface sites are very useful to cast the kinetic data in much more mechanistic mode. The fact that the models are not unique and several possible modes cannot be ruled out, is to be expected and, in fact, forms the basis for guiding future research.

Following the general mechanisms of Ganor and Lasaga , two theoretical ways in which perchlorate affect the rate may be anticipated: 1) Competition between the perchlorate ions and the protons on the same adsorption sites decreases the concentration of protons on the surface; 2) Independent adsorption of perchlorate on the surface at a site near the adsorbed proton strengthens the bond. The first possibility, of competition between perchlorate ions and protons, is unreasonable because of the charge difference between these two adsorbates. In any case, thorough examination of this possibility shows that the "competition mechanism" must be ruled out because it can not predict a maximum in dissolution rate at finite value of acid concentration.

To examine the validity of the second possibility, a specific reaction mechanism for the gibbsite dissolution in the presence of perchloric acid is postulated. This mechanism involved several reaction paths. In these paths adsorption of the catalyst (H+) and/or inhibitor (ClO4-) on the surface close to the Al-OH-Al bond influence the bond strength and thus affect the dissolution rate. Proton adsorption decreases the bond strength, while adsorption of perchlorate strengthens the Al-OH-Al bond. Four types of surface clusters will be discussed: 1) clusters with adsorbed proton, Al-OH2+-Al; 2) clusters with adsorbed perchlorate, Al-ClO4-OH-Al; 3) bare clusters, i.e., clusters with neither adsorbed proton nor adsorbed perchlorate, Al-OH-Al; and 4) clusters with adsorbed proton and adsorbed perchlorate, Al-ClO4OH2-Al. If no other species are adsorbed to the Al-OH-Al bonds, then

(19)

where square brackets denote the molar fraction of a surface cluster. Assuming that allother surface sites with adsorbed proton and/or adsorbed perchlorate are negligible, the total fraction of the sites with adsorbed proton, XH+,ads, is

(20)

and the total fraction of the sites with adsorbed inhibitors, XClO4-,ads, is

(21)

The strength of the Al-OH-Al bonds varies as a function of the adsorbed species. Therefore, the rate of the respective reaction path varies accordingly. The faster reaction path, associated with the Al-OH2+-Al clusters, is the proton-promoted breakdown of the Al-OH-Al bond. The proton-promoted path consist of fast adsorption H+ followed by slow hydrogen-ion-mediated hydrolysis steps.

(22)

The rate of this proton-promoted reaction path is

(23)

where kH (sec-1) is the apparent rate constant of the proton-promoted path and rr (mole m-2) is the density of reactive surface sites on the mineral surface.In the above reaction path the rate-determining step is the breakdown of the Al-OH-Al bond. In the absence of competing ions, assuming Langmuir adsorption isotherms, the molar fraction of the Al-OH2+-Al cluster is

(24)

where bH+ is a consrelated to the energy of adsorption, CH+ is the protconcentration in solutionand FH is the maximum mofraction surface coof H+. Substitthe Langmuir adsorpisotherm (equation 24) into equation (23), gives

(25)

The noncatalytic breakdown of Al-OH-Al bonds maybe described by the reaction path

(26)

The dissolution rate of this reaction path is

(27)

We refer to the proton-promoted mechanism as catalysis, as long as the overall dissolution rate increases by increasing the proton surface concentration, i.e., as long as the rate of the non-catalytic breakdown of Al-OH-Al bonds (equation 26) is slower than the proton-promoted reaction path (equation 22). If the proton is a strong catalyst, i.e., when

(28)

the rate of the bare cluster reaction path (eq27) is negligible. A reaction path similar to that of equation (22) can be postulated for the perchlorate affected dissolution reaction path.

(29)

The rate of this perchlorate affected reaction path is

(30)

The adsorption of perchlorate strengthens the Al-OH-Al bond, and as a result the rate of this inhibited path (equation 30) is even slower than that of the bare cluster path. Therefore, the rate of this inhibited path is negligible as well. The reaction mechanisms for Al-ClO4OH2-Al clusters is described by

(31)

The dissolution rate for this reaction path is

(32)

Neglecting the dissolution from sites without catalysts, Al-OH-Al and Al-ClO4-OH-Al, the overall rate is the sum of the rates of equations (23) and (32)

(33)

In the proposed mechanism we assume that the adsorption of the proton and the ClO4- are independent of each other, i.e., that the adsorption of the proton near the Al-OH-Al bond is independent of the presence or absence of perchlorate on that cluster. By assuming that the adsorption of the proton and the perchlorate are independent of each other we envisage that the adsorption energy for the proton is the same both for a cluster with adsorbed perchlorate, and for a cluster with no perchlorate. If so, the equilibrium constant of the adsorption reaction

(34)

is equal to the equilibrium constant of the adsorption reaction

(35)

In other words, it means that the equilibrium constant of the surface reaction

(36)

equals 1 (K=1). The above assumption implies that the proportion of clusters with an adsorbed proton (XH+,ads) in the total population of clusters, must be equal to the proportion of clusters with both an adsorbed proton and an adsorbed perchlorate in a total population of clusters with an adsorbed perchlorate (XClO4-,ads), i.e.,

(37)

where XH+,ads, and XClO4-,ads, are defined by equations (20) and (21) respectively. Rearranging equation (37) gives

(38)

Substituting equation (38) into equation (20) and rearranging gives

(39)

Substituting equations (38) and (39) to the overall rate of equation (33) gives

(40)

Rearranging equation (40) gives

(41)

Further rearranging equation (41) gives

(42)

where kr is the relative difference between the apparent rate constant of the proton-promoted reaction path, kH, and the rate constant of the inhibited reaction path, kHClO4, i.e.,

(43)

Substituting Langmuir adsorption isotherms for the proton and the perchlorate into equation (42) gives

(44)

In each of our experiments, the concentration of ClO4- is about equal to that of H+, i.e.,

(45)

Substituting equation (45) into equation (44) gives,

(46)

The coefficients: k1 (mole m^-2 sec^-1) =rr . kH . FH, k2=kr . FClO4, bH+ and bClO4- were calculated from a non linear regression of equation (46) using least squares. For the regression, we utilized all the data in the 2.5 to 4.1 pH range. The regression coefficient R2=0.75 and the resulting coefficients are:

k1=-3.7x10-11 mole m^-2 sec^-1, k2=1, bH+=5229 and bClO4-=5229.

Rearranging equation (46) and substituting the resulting coefficients gives,

(47)

Comparison of the prediction of equation (47) with the experimental data is shown by the green line in Fig. 9. The best fit curve adequately describes the experimental data. Therefore, the independent adsorption reaction mechanism of Ganor and Lasaga is a viable explanation for the experimental results. It is important to note that an uncertainty of few orders of magnitude is associated with each of the coefficients obtained from the regression of the experimental data. The reason for these large uncertainties is that different combinations of the four coefficients yield similar curves that adequately describe the experimental data. For example the red line in Fig. 9 was obtained using the coefficients: k1=-1x10-10 mole m^-2 sec^-1, k2=1, bH+=2420 and bClO4-=13810. In other words, the best fit plot obtained by the regression (equation 47) is not unique and therefore the value of the coefficients should be refined as more spectroscopic and surface data become available. Using these coefficients to understand the surface properties of the kaolinite will be erroneous in the absence of such supporting data.

In the above mechanism we assume that perchlorate is adsorbed on the surface at a site near the adsorbed proton and as a result strengthens the Al-OH-Al bond and the dissolution reaction is inhibited. Alternatively, perchlorate ion may adsorb onto an adsorbed proton and partly (or completely) impair the proton effect. This last perchlorate inhibited reaction path may be described by

(48)

The dissolution rate for this reaction path is

(49)

Iperchlorate is adsorbed only on protonated clusters than its surface coverage is limited by the surface coverage of the protons (equation 24). The maximum surface coverage of perchlorate, FClO4, is a fraction, F'ClO4, of the proton surface coverage and therefore the perchlorate adsorption on the protonated sites may be described by the following Langmuir adsorption isotherms:

(50)

The surface concentration of free protons will therefore be

(51)

The overall rate is the sum of the rates of equations (23) and (49)

(52)

Substituting equations (45), (50) and (51) into equation (52) gives

(53)

The rate law of equation (53) is identical to the rate law of equation (46). Therefore, the good fit of equation (47) to the experimental data indicates that the inhibition mechanism of impairing the proton effect by perchlorate ions that become adsorbed on top of the prot, is a viable explanation for the experimental results.

It follows from the identity of equations (46) and (53) that the prediction of the "independent adsorption" reaction mechanism (equation 46) is identical to the prediction of the "perchlorate adsorption onto the adsorbed proton" reaction mechanism. Therefore, from our treatment of the two mechanisms, it is mathematically impossible to prefer one over the other. Only measurements of the surface distribution of ClO4- and / or molecular bonding studies may help to differentiate between the two alternative mechanisms.

Dissolution rates of synthetic gibbsite were examined by two different experimental methods: a mixed flow-through reactor and column. The two methods showed an excelagreement. From thathe results of well-mixed flow-through experiments high fluid to solid ratio anthe results of (non mixed) column experiments wlow fluid to solid rait follows that: 1) The gdissolution rate is independent of the rate of stirring and thersupports the conclusion of Band Erich that gibbsite dissolution reaction is controlled and not diffusion controlled. 2) Laboratory dissolution experiments with high water/rock ratio may be relevant in interpreting dryer natural situations.

The BET surface area of the gibbsite in the flow-through experiments exhibited variations between the initial and final measured values, while in the column experiments we did not observe a significant change in surface area. These observations are in agreement with the suggestion of Nagy and Lasaga , that the change in surface area is a result of mechanical disaggregation and notresult of dissolution or precipitation reactions. Thagreement between the dissolution rates of the mixed flow-through experiments that were normalized to the final surface area with these of the column experiments supports the assumption that the changes in surface area occurred early in the experiment, before the first steady state was approached. Differences in the BET surface area between the column experiments and the flow-through experiments enable us to demonstrate that the BET surface area is linearly proportional to the reactive surface area and therefore it is justified to substitute the BET surface area for the reactive surface area.

The dissolution rate of gibbsite varies as a function of the perchloric acid concentration. At pH>3.5 the dissolution rate increases as a function of acid concentration, while at pH<3.5 it decreases with acid concentration. We interpret the gibbsite dissolution rate as a result of a combined effect of proton catalysis and perchlorate inhibition. Following the theoretical study of Ganor and Lasaga , we propose two specific reaction mechanisms for gibbsite dissolution in the presence of perchloric acid. In both mechanisms the proton is adsorbed on the Al-OH-Al bond and as a result decreases the bond strength. In each of the postulated mechanisms the perchlorate inhibits the rate differently: 1) Independent adsorption of perchlorate on the surface at a site near the adsorbed proton strengthens the bond; 2) adsorption of the perchlorate onto the adsorbed proton impairs the protons' effect. Examination of the proposed mechanisms shows that both the "independent adsorption" and the "perchlorate adsorption onto the adsorbed proton" reaction mechanisms adequately describe the experimental data, and therefore they are viable explanations for perchloric acid effect on gibbsite dissolution rate. The mathematical predictions of these two reaction mechanisms are identical and therefore it is impossible to prefer one over the other.

This research was carried out with the financial support of NSF EAR-9017976, NSF EAR-9219770, DOE DE-FGO2-90-ER14153 and of the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel grant No. 94-00089. J. Ganor would like to thank the Lady Davis Fellowship Trust for their support. We would also like to acknowledge Fundacion Gran Mariscal de Ayacucho for the financial support of J.L. Mogollon. We wish to express our gratitude to K. L Nagy, T. Burch and Y. Xiao for hours of fruitful discussions and to T. Vujic , S. Riney and A. Goodhune for the technical assistance. We would also like to gratefully acknowledge thorough reviews by two anonymous reviewers.