Ion Exchange Model for Reversible Sorption of Divalent Metals on

Comparison between the experimental data reported in the literature for the sorption of divalent metals on calcite and those predicted by the ion exch...
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Ion Exchange Model for Reversible Sorption of Divalent Metals on Calcite: Implications for Natural Environments Emmanuel Tertre,*,†,§ Jacques Page,‡ and Catherine Beaucaire‡,§ †

Université de Poitiers/CNRS, UMR 7285 IC2MP, Equipe HydrASA, rue Albert Turpain, Bat. B8, 86022 Poitiers, France CEA, Centre d’Etudes de Saclay, DANS/DPC/SECR/L3MR, 91191 Gif sur Yvette, France

‡

S Supporting Information *

ABSTRACT: Most of the thermodynamic models available in the literature describing the speciation of the calcite surface do not predict a significant concentration of sorbed Ca(II), whereas previous electrokinetics studies clearly show that Ca2+ is the main cation determining the potential of the calcite surface. This study proposes a new thermodynamic model based on ion-exchange theory that is able to describe the reversible sorption of Ca2+ on calcite. To constrain the model, concentrations of Ca(II) sorbed reversibly on the mineral surface were obtained as a function of pH. Such experimental data were obtained using solutions in equilibrium with both calcite and fixed pCO2(g) values (from 10−5 to 10−2 atm). The concentration of (de)sorbed Ca(II) is almost constant in the [7−9.5] pH range, having a value of approximately 1.2 × 10−6 ± 0.4 × 10−7 eq·g−1. Such a value agrees with total sorption site densities that were previously calculated by crystallography and is used to obtain a selectivity coefficient between H+ and Ca2+ species by fitting the experimental data. Then, selectivity coefficients between H+ and different metallic cations (Zn2+, Cd2+, Pb2+) that are able to accurately describe previously published data are proposed. Finally, the model is used to predict the contribution of calcite in the overall sorption of Cd(II) on a natural and complex solid (calcareous aquifer sand).

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ditions.5 Such results suggest that Ca2+ and CO32− (or HCO3−) are the main species in determining both the potential and the global charge of the calcite surface, as previously concluded by Cicerone et al.5 Note that previous structural observations showed that Ca2+ was effectively sorbed as outer sphere complexes at the calcite/water interface.9 Therefore, it seems crucial to explicitly consider the sorption of the constitutive ions of the mineral (e.g., Ca2+) in models describing the calcite/ water interface. Furthermore, the sorption of divalent metals (e.g., Zn, Cd, Ni, Co, Mn, Pb) on carbonate mineralsin particular, calcitewas studied (10−13 among others). Whatever the trace element used, the authors agree on a sorption in two stages: a first stage that is rapid, completed in a few hours, and attributed to a reversible surface phenomenon (sorption and/or exchange reaction), and a second slower stage that is potentially irreversible and occurs at a constant rate (diffusion, formation of solid solution, or coprecipitation, according to the authors). However, the exact contribution of these two stages in the global sorption process is rarely justified.10−12 For example, Davis et al.10 tested sorption reversibility of Cd2+ on calcite by

INTRODUCTION Carbonated minerals are known to be very reactive with respect to dissolution/precipitation processes and are strongly involved in the sorption processes of trace elements. Consequently, many authors have been interested in describing the surface reactivity of these minerals and particularly in investigating their surface charges (refs 1−3 among others). To accomplish these goals, acid−base titration and electrokinetic measurements were often used. However, it is now well documented in the literature (4−6 among others) that classical acid−base titration is unsuitable to obtain the proton surface charge of calcite, one of the main carbonated minerals in many natural environments. This feature is principally due to the difficulties in accurately accounting for other processes than H+ sorption/desorption occurring during titration, which can also consume and/or release significant H+, such as calcite dissolution and reactions with CO2(g). Furthermore, electrokinetic measurements (e.g., zeta potential) performed with calcite depend strongly on the chemical conditions chosen for the measurements (see discussion in Wolthers et al.7). For example, recent electrophoretic measurements performed on calcite suspensions in equilibrium with both calcite and pCO2(g) showed that the isoelectric point of calcite varied linearly with log (pCO2(g)).8 Moreover, several authors showed that the zeta potential of calcite in CaCl2 solutions was strongly dependent on the aqueous calcium concentration at pCO2(g) atmospheric con© 2012 American Chemical Society

Received: Revised: Accepted: Published: 10055

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shaken mechanically for two days before separating the solid fraction by centrifugation. Then, salt excesses were discarded by performing three cycles including rinsing with ethanol for one day and separation of the solid from the solution by centrifugation. Then, the recovered solid was dried at 40 °C for two days and was preserved at room temperature in a polycarbonate flask. Solutions Pre-Equilibrated with Calcite at Different pCO2(g). Solutions used for sorption/desorption experiments were saturated with Ca-calcite (see preparation above) at three different pH values (i.e., 7.2, 7.6, and 9.0) by imposing a known pCO2(g) value (i.e., 10−1.8, 10−2.2, 10−5.0 atm). Moreover, all solutions were prepared at 20 °C and with a 10−2 mol·L−1 NaCl solution to fix the ionic strength. The saturation state of the solutions with respect to both calcite and CO2(g) was checked by measuring the pH, the aqueous calcium, and the alkalinity. For more details, we can refer to Tertre et al.15 Sorption and Desorption of 45Ca on Calcite. Three series of 45Ca sorption/desorption experiments were conducted with the solutions described above. Each series corresponded to a given calco-carbonic equilibrium (i.e., equilibrium with both calcite and a fixed pCO2(g) value) relative to one of the specific pCO2(g) value used for the pre-equilibrated solutions (see previous section). All experiments were performed in a glovebox flushed with a CO2−N2 gas mixture corresponding to the desired and fixed pCO2(g) (i.e., 10−1.8 or 10−2.2 or 10−5.0 atm). A series consisted of approximately ten measurements taken over time, and each measurement corresponded to a specific batch experiment. To measure significant sorption of 45 Ca in each of the series, different masses of calcite were used. For example, 0.6 g of calcite was used for experiments performed at pH = 7.2 and 7.6, whereas 6 g of calcite was necessary at pH = 9.0. For all of the experiments, Ca-saturated calcite was introduced in a 10-mL polycarbonate tube containing 9 mL of the pre-equilibrated solution. A precise volume of a labeled stock solution, containing the radioisotope (45Ca) with a specific certified activity, was added to each tube at the same time (t = 0). The tubes were mechanically shaken at room temperature for, depending on the experiment, a few hours to two months. Then, the tubes were centrifuged to separate the solution from the calcite slurry. Supernatants were filtered and fractioned in three aliquots: the first for pH measurements, the second for aqueous calcium concentration measurements, and the third for the measurement of the residual activity in solution. Immediately after the sampling of the aliquots, desorption studies were performed. A known mass of supernatant was removed and replaced by the same mass of a pre-equilibrated solution without the radioisotope. Then, the same protocol used for sorption was applied. The sorption/ desorption results were presented using distribution coefficients (i.e., Kd), expressed in mL·g−1 and calculated from the solution data as follows:

performing two types of experiments: increase in aqueous EDTA concentration and rapid isotopic exchange (with 109Cd). Unfortunately, the former test does not allow one to conclude clearly on the reversible nature of the sorbed Cd2+ since competition with another process (aqueous complexation with EDTA) occurs in the desorption step. The second test showed that rapid isotopic exchange is important at the beginning of the sorption experiments and that it increases regularly with increasing time. However, the fraction of sorbed Cd2+ which can participate in the rapid isotopic exchange decreases significantly with time. This means that the constant contribution of the first process, implying pure reversible sorption reactions, could not be obtained precisely with regards to the thermodynamic. In general, the discrimination of the different processes occurring at the calcite surface becomes questionable as the authors interpret their experimental data with their own formalisms. Indeed, formalisms describing rapid reactions such as cationic exchange (e.g., Ca2+/divalent metal) are based on the thermodynamics of chemical equilibrium, implicitly implying total reversibility. These formalisms are, for example, ion exchange models and surface complexation models.11,12 Note also that formalisms describing reactions occurring at a slower stage, such as solid-solution formation and coprecipitation are also based implicitly on the total reversibility.10,14 As a contrast incorporation into the crystal structure (i.e., pure diffusion) cannot be described by the thermodynamic of chemical equilibrium but rather by kinetics laws (12 among others); in this case reversibility does not have to be proven. Therefore, to predict and quantify reversible reactions occurring at the calcite/water interface (i.e., ion exchange reactions), it is important to propose an experimental methodology that exactly quantifies the reversible fraction of the sorption for whichever element is considered (trace metals as well as major elements such as Ca(II)). Moreover, note that aqueous metallic cations present in natural waters are always in competition with Ca2+ and H+ for sorption sites located on mineral surfaces. Therefore, these two latter species should be systematically included in all models predicting the sorption of divalent metals on calcite. The first aim of this study is to provide experimental data characterizing the reversible sorption process of Ca(II) on a calcite surface. As a thermodynamic formalism will be used to interpret the data, the independence of these latter with time, as well as the reversibility of the sorption, will be carefully checked. Modeling of the experimental data will be obtained using the ion exchange formalism, a theory that was never tested to our knowledge in the literature, to describe the reversible sorption of Ca2+ and H+ on a calcite surface. Then, based on this model, selectivity coefficients between H+ and divalent metallic cations able to accurately describe previously published data will be proposed. Finally, predictions will be made to calculate the contribution of calcite in the global sorption of a divalent metal on a multicomponent natural solid (e.g., calcareous aquifer sand).

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MATERIALS AND METHODS Calcite. The raw material used in this study was a pure synthetic calcite distributed by Aldrich. Its specific surface area was determined to be 0.32 m2·g−1 by the BET method (Kr gas). To perform sorption/desorption experiments, surface sites of the initial Aldrich calcite were saturated with calcium ions. The saturation was performed by mixing ≈10 g of calcite with ≈500 mL of a 10−2 mol·L−1 CaCl2 solution. The suspension was

⎛A ⎞ V Kd s = ⎜ 0 − 1⎟ . s ⎝ A fs ⎠ M

(1)

⎡ (A ·V − A fs ·Vrec) ⎤ V − 1⎥ · d Kd d = ⎢ 0 s A fd ⎣ ⎦ M

(2)

where A0, Afs, Afd are, respectively, the initial activity in solution before sorption, the final activity in solution at the end of sorption, and the final activity in solution at the end of desorption (Bq·mL−1). Vs and Vd are the total volume of 10056

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solution during the sorption and desorption stages, respectively (mL). M is the mass of dried calcite (g), and Vrec is the volume of the recovered solution before the addition of the desorption solution (mL). Quantification of the Reversible Component in the Global Sorption of Ca(II). From the experimental data obtained using the methodology described above, reversible sorption/desorption of Ca(II) at the calcite surface was quantified using the isotopic approach developed by Badillo and Ly16 and further used by Tertre et al.15 Using this approach, Kds* and Kdd*, which correspond to the distribution coefficients related to the reversible component of the Ca(II) sorption and desorption, were calculated. This approach also calculated the concentrations of Ca(II) that were sorbed/ desorbed reversibly at the calcite surface. The details of this method are reported in the Supporting Information (SI). Analytical Measurements. Aqueous calcium was measured with a MetroSep C1METROHM ion chromatography apparatus. Analytical precision is approximately 2%. A cationic column Metrosep C12 was used with HNO3 2.5 × 10−3 mol·L−1 as an eluent. The [HCO3−]aq concentration was deduced from the alkalinity measurements from the titration with a 10−3 mol·L−1 HCl solution using a 794 Basic Titrino METROHM automatic titrator. The pH was measured with a combined Metrohm electrode calibrated at 20 °C with two NIST buffer solutions (pH = 4.01 and pH = 9.18). pH measurements were performed in a glovebox at the pCO2(g) chosen for each of the experiments. pH values stabilized after a few minutes to a precision of ±0.05 pH units. 45Ca(II) aqueous activity was determined by β liquid scintillation (Packard) with a precision better than 1%.

Figure 1. Concentration of protons (i.e., [>X-H]) and calcium (i.e., [>X2-Ca]) sorbed (or desorbed) reversibly on the calcite surface as a function of pH in CO2(g)−H2O−CaCO3(s) systems at equilibrium. The experimental data are marked by the symbols, and the dashed and solid lines show the predicted values according to the ion exchange model proposed in this study (the modeling is performed with logK2H/Ca = −9; see text and Table 1 for details). Note that predicted [>X-H] corresponds to maximum values predicted by our model, as logK2H/Ca value can be superior to −9 (see text for more explanations). For this reason, a gray shaded zone indicates the field for [>X-H] values predicted by our model assuming logK2H/Ca values rigorously superior to −9. Prediction of the Van Cappellen et al.4 model for the concentrations of sorbed calcium (i.e., [>CO3Ca+]) is also reported.

than the Ca surface site density proposed by Zachara et al.17 who estimated it by isotopic exchange measurements extrapolated to time zero of a 45Ca sorption experiment. Indeed, these authors proposed a Ca(II) sorbed concentration of 3.6 × 10−6 mol·g−1 at pH = 8.3, when equilibrium with both calcite and atmospheric CO2(g) is assumed. However, our estimate remains consistent with crystallographic considerations.18 The total number of sites on the calcite (104) face is 8.22 × 10−6 mol·m−2, and the calcium to carbonate ratio at the surface is 1:1 (8). Each of the two types of sites (i.e., >CO3−H and >Ca−OH) have a site density of 4.11 × 10−6 mol·m−2. With this latter value and the specific surface area of Aldrich calcite measured in this study (0.32 m2·g−1; see Materials and Methods), a concentration of approximately 1.31 × 10−6 mol·g−1 for each of the sorption site types located on the calcite surface is proposed. According to the ion-exchange theory (see latter), each Ca2+ ion is virtually sorbed to two negative sites (i.e., >CO3−) at the surface. Therefore, 2 × 6 × 10−7 mol of sites by gram of solid (= 1.2 × 10−6 molsites·g−1) must be involved to interpret our Ca-sorption data. Therefore, this value is not strongly different from the sorption site density estimated for the >CO3H site from crystallography (1.2 × 10−6 molsites·g−1 vs 1.31 × 10−6 molsites·g−1). Consequently, in our experiments conducted at equilibrium with calcite and CO2(g) (from pCO2(g) = 5 × 10−5 to 2 × 10−2 bar), sorption sites are for about 90% occupied by Ca2+ species. Such a result is in agreement with a previous study5 dealing with the electrokinetic properties of the calcite/water interface, which reports that Ca2+ and CO32− are the main ions determining the potential of the calcite surface when calcocarbonic equilibrium is assumed. These observations are somewhat inconsistent with interpretations obtained by some

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RESULTS AND DISCUSSION For each sorption and desorption experiment of 45Ca on calcite, pH and concentrations of aqueous Ca(II) measured at equilibrium, as well as Kds and Kdd calculated from eqs 1 and 2 are reported in the SI (see Table S1). In this document, the parameters relative to the reversible sorption/desorption of 45 Ca, obtained according to the methodology detailed in the SI, are also tabulated (i.e., Kds*, Kdd* as well as concentrations of Ca(II) (de)sorbed reversibly). The file also contains data at pH = 8.2/8.3 obtained by Tertre et al.15 using the same methodology. Conceptual Model of the Calcite Surface. Concentrations of Ca(II) that are reversibly sorbed (or desorbed) at the calcite surface are plotted as a function of pH in Figure 1, for pH varying from 7 to 9.5. The values previously obtained at pH = 8.2/8.3,15 corresponding to an equilibrium with atmospheric CO2(g) (pCO2(g) ∼10−3.5 atm) were also reported. Note that a higher variability of the data is noticed at pH = 8.2/ 8.3 than at other pHs. Despite the fact that the method used to obtain the data is the same between the two studies, equilibrium of the CaCO3(s)/CO2(g)/H2O systems was better constrained in this study than in the first one.15 Indeed, in 15 pCO2(g) value (i.e., 10−3.5 atm), corresponding to atmospheric CO2(g), was not specifically regulated while pCO2(g) is regulated in this present work by using mixture of gases (see Materials and Methods). Considering the global scattering of the data, Ca(II) (de)sorbed concentrations are almost constant with pH and have a value of approximately 6 × 10−7 ± 2 × 10−7 mol·g−1 (i.e., 1.2 × 10−6 ± 0.4 × 10−7 eq·g−1). This value is much lower 10057

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surface complexation models4,8 based on the electrical double layer (EDL), which predict that H+ and OH− are the main ions compensating the surface charge of the calcite (see Figure 7 in ref 4, for example). As an example, we calculated the concentration of the calcium sorbed on the calcite as a function of pH according to the surface complexation model (Capacitance model) proposed by Van Cappellen et al.4 As seen in Figure 1, the Van Cappellen model predicts lower Casorbed concentrations than those obtained experimentally in this present study, whatever the pH investigated. That illustrates that additional models, as ours, are needed to interpret new experimental data obtained for reversible sorption of structural components of the calcite as well as for electrokinetic data obtained on this type of material (see Introduction). Furthermore, to resolve the apparent conflict between data obtained from electrokinetic studies and predictions of surface complexation models, Stipp9 proposed to modify these models by changing the location where Ca2+ and CO32‑ are sorbed in the EDL. In this new interpretation, sorption of Ca2+ and CO32− occurs on the hydrolyzed sites of calcite in the Stern layer to form outer sphere complexes. These complexes are weakly sorbed at the surface and can desorb again. Note that some of these hydrated complexes (e.g., >CO3, nH2O) were already observed by DRIFT spectroscopy.19 Considering that the charge of the calcite surface is always compensated by cations in the Stern layer, sorption reactions can be described as reversible ion-exchange reactions. Thus, a new model is proposed here to describe the calcite surface. This latter is considered to be an ion exchanger, as frequently proposed for clayey surfaces (see 20 for example). This ion exchanger is globally neutral and composed of one or several monovalent sites (e.g., >X-H) that are able to exchange aqueous cations, in particular Ca2+, with protons. Note that, in the case of calcite, the hypothetical site >X-H considered in our approach is formally identical to the >CO3-H site proposed in surface complexation approaches. Ion exchange reactions occurring between protons and aqueous cations on a >X-H site are explicitly taken into account by considering selectivity coefficients. Note that such coefficients are apparent thermodynamic constants because the ratio for the activity coefficients of the exchanged species is not known and assumed to be equal to 1. For example, H+/Ca2+ ion exchange reaction and the associated selectivity coefficient (i.e., K2H/Ca) can be defined as the following: 2>X‐H + Ca 2 + = >X 2‐Ca + 2H+

total site concentration (TSC) is required for modeling. In a solution containing only H+ and Ca2+ as cations, TSC expressed in eq·g−1 is defined as follows: TSC = [>X‐H] + 2 × [>X 2‐Ca]

where [>X-H] and [X2-Ca] are the concentrations of the sorbed species (in mol·g−1). A TSC value equal to 1.2 × 10−6 eq·g−1 is chosen according to the total concentration of sorbed (or desorbed) Ca(II) obtained above. Note that all values of logK2H/Ca superior to −9 reproduce our experimental data. The fact that there is not a unique solution for the ion exchange parameters interpreting our data is related to the TSC value we have chosen and which is equal to the measured concentration of Ca(II) sorbed reversibly on the calcite surface (see above). Figure 1 reports the concentrations of [>X2-Ca] predicted by our model considering a logK2H/Ca rigorously equal to −9 (see the dashed line in Figure 1; see Table S2 for predicted [>X2Ca] values). A sensitivity study is given in SI in Figure S1, illustrating the high sensitivity of the [>X-H] prediction to the value of the logK2H/Ca, while [>X2-Ca] is almost constant when logK2H/Ca is superior to −9. Furthermore, the [>X-H] values can be calculated according to the eq 5 reported below: −1 +

1 + 8K 2H/Ca ·

[>X‐H] = 4*K 2H/Ca ·

[Ca 2 +]·γCa [H+]2 ·γH2

·TSC

[Ca 2 +]·γCa [H+]2 ·γH2

(5)

All parameters in eq 5 were defined above. According to this latter equation and the maximum logK2H/Ca selectivity coefficient we propose (i.e., logK2H/Ca of −9; see above), the concentration of protons sorbed reversibly at the surface (i.e., [>X-H]) cannot exceed 10−7 mol·g−1 in our experimental conditions (equilibrium with both calcite and pCO2(g) values ranging from 5 × 10−5 to 2 × 10−2 bar). This supports the fact that H+ is not the main cation determining the potential of the calcite surface, as suggested by previous electrokinetic studies (see discussion above). Furthermore, when the aqueous phase is saturated with respect to calcite at a given pCO2(g) value (as ours is), the ratio between the activities of aqueous calcium and that of proton is completely determined by the calcite/CO2(g)/H2O system. This ratio is easily calculated according to the formula below: [Ca 2 +]·γCa

(Reaction 1)

+ 2

[H ]

with K 2H/Ca =

(4)

·γH2

=

Ks α ·pCO2(g) ·K a1·K a2

(6) −1.5

where α is the Henry coefficient (i.e., 10 at 25 °C), Ks is the solubility constant for calcite (10−8.47), Ka1 and Ka2 are the first and second acidity constants of carbonic acid, respectively (10−6.35 and 10−10.33), pCO2(g) is the partial pressure of CO2(g) in the system (in bar), and other parameters were already defined above. In the case of a system open to the atmosphere (i.e., pCO2(g) = constant = 10−3.5 atm) and when equilibrium with calcite is assumed, the ratio ([Ca2+]·γCa)/([H+]2·γ2H) is constant with varying pH; therefore, the concentration of sorbed protons (see eq 5) is also constant when pH varies, with a maximum value of approximately 10−8 mol·g−1. Metal Sorption on Calcite. Choice of the Experimental Data Published in the Literature. One objective of this study is to test the applicability of the conceptual model described in the previous section to describe sorption (i.e., pure exchange reactions) of metallic cations on a calcite surface. Data relative

[>X 2‐Ca]·[H+]2 γH2 [>X‐H]2 ·[Ca 2 +]γCa

(3) +

where [>X-H] and [X2-Ca] are the concentrations of H and Ca2+ sorbed reversibly on the calcite surface (mol·kg−1), [H+] and [Ca2+] are their respective aqueous concentrations (mol·L−1) and γ are the activity coefficients for the aqueous species, calculated using Davies approximations.21 To obtain the 2H/Ca selectivity coefficient from experimental data, modeling is performed with the PHREEQC software22 and the minteqv4 thermodynamic database.23 pH values for the modeling are chosen by considering the saturation of the aqueous phase with both calcite and a pCO2(g) value (from pCO2(g) = 5 × 10−5 to 2 × 10−2 bar), as performed in our experiments (see Table S2 in SI for precise values). Moreover, 10058

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example, Li et al.13 reported an error of ±0.02 m2·g−1 for the specific surface area of the calcite they used (i.e., 0.05 m2·g−1). For Zn(II), a good agreement is obtained between the two data sets selected (see Figure 2A). The authors of one of these data sets15 have checked that the data are relative to a completely reversible sorption process. Therefore, it seems reasonable to test the thermodynamic model proposed in the previous section to describe such experimental data. For Cd(II), the experimental data set proposed by MartinGarin et al.12 is different from that reported recently by Li et al.13 (see Figure 2B), even though similar chemical conditions were used (equilibrium with both calcite and atmospheric CO2(g)), pH varied slightly. Indeed, for a Cd(II) aqueous concentration close to 10−7 mol·L−1, the concentrations of sorbed Cd(II) reported by Martin-Garin et al.12 and Li et al.13 are 3 × 10−7 and 10−7 mol·g−1, respectively. The disparity could be due to the difference in the specific surface area of the calcite used by the different authors (0.28 m2·g−1 for Martin-Garin et al.12 versus 0.05 m2·g−1 for Li et al.13). Note also that the specific surface can vary notably during the sorption experiment, as mentioned by Martin-Garin et al., who observed an increase from 0.20 to 0.28 m2·g−1. Furthermore, the pH and aqueous concentration of calcium of the influent used by Martin-Garin et al.12 are 8.0 ± 0.1 and 2.6 ± 0.2 × 10−4 mol·L−1, respectively (see Table 2 in Martin-Garin et al.). These values are significantly different from those predicted by thermodynamics assuming a complete saturation of the aqueous phase with respect to calcite in atmospheric conditions (conditions of Martin Garin et al. experiments; pCO2(g) = 10−3.5 atm). The predicted values are close to 8.3 and 5 × 10−4 mol·L−1 for the pH and aqueous calcium concentration, respectively. Therefore, a slight undersaturation of the solution used by Martin-Garin et al.12 during their experiment can also explain the discrepancy between their data set and that of Li et al. Therefore, for Cd(II), the ion exchange model proposed in this study will be tested against the Li et al. data.13 Finally, in the case of Pb(II), the only experimental data proposed at pH = 8.2 by Rouff et al.24 were used because a significant fraction of irreversible sorption (i.e., coprecipitation) was observed for data obtained at other pH values (e.g., pH = 7.3 and 9.4). Such behavior was revealed by the authors themselves when interpreting sorption/desorption results and structural informations (i.e., XANES). Selectivity Coefficients for Metallic Cations and Data Analysis. According to the ion-exchange formalism proposed in this present study (see above), ion exchange between protons and divalent metallic cations (i.e., Me2+) can be described using a selectivity coefficient (i.e., K2H/Me) defined as

to three cationic metals (i.e., Zn(II), Cd(II), and Pb(II)), whose behavior is important to understand in many environmental conditions, were chosen from the literature. Data obtained in conditions of calco-carbonic equilibrium at atmospheric CO2(g) (i.e., pCO2(g) = 10−3.5 atm) were selected. Such experimental data were issued from Zachara et al.17 and from one of our studies15 for Zn(II), from Li et al.13 and Martin-Garin et al.12 for Cd(II), and from Rouff et al.24 for Pb(II). The data are plotted in Figure 2 in terms of sorbed concentration (mol·g−1) as a function of the total aqueous concentration at equilibrium (mol·L−1). Note that the sorbed concentrations are normalized to the mass of solid rather than by the specific surface area. Indeed, a higher error can be expected for specific surface area than for mass of the solid. For

K 2H/Me =

[>X 2‐Me]·[H+]2 γH2 [>X‐H]2 ·[Me 2 +]γMe

(7)

where [>X2-Me] (with Me = Zn, Cd or Pb) corresponds to the sorbed concentration of the metallic cation (in mol·kg−1), and [Me2+] is the aqueous concentration of the metallic cation at equilibrium (in mol·L−1). All other terms are defined above for eq 3. Using the 2H/Ca selectivity coefficient obtained above (i.e., maximum logK2H/Ca = −9) and considering the equilibrium with both calcite and pCO2(g) = 10−3.5 atm, selectivity coefficients between H+ and the metallic cations (i.e., K2H/Me) that best fit the experimental data mentioned in the last section are reported in Table 1. To determine the 2H/Me selectivity

Figure 2. Comparison between the experimental data reported in the literature for the sorption of divalent metals on calcite and those predicted by the ion exchange model proposed in this study (see text and Table 1 for details). Sorbed concentrations are plotted as a function of the concentration in solution at equilibrium. Zn(II) (A), Cd(II) (B), and Pb(II) (C). 10059

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Table 1. Selectivity Coefficients (i.e., K2H/Me with Me = Ca, Zn, Cd, or Pb) Proposed in This Study To Interpret the Reversible Sorption of Divalent Metallic Cations (Including Ca2+) on a Calcite Surfacea

log KCa/Meb

interpret the Rouff et al. data,24 at least when Pb(II) aqueous concentrations are less than 10−6 mol·L−1 at equilibrium (see Figure 2C). For higher values (see Figure 2C), the precipitation of Pb-carbonates and Pb-hydroxides phases is suggested by the near-vertical increase of the concentration of sorbed Pb(II) versus concentration of aqueous Pb(II) at equilibrium. The model proposed in this study is based only on ion exchange reactions and is not relevant to these specific conditions. Finally, note that sorption of carbonated complexes has not been taken into account in the modeling, despite the fact that some of these complexes could dominate the aqueous speciation (especially for Pb(II); see above). The reason is that even though structural studies have revealed the presence of carbonates complexes sorbed on calcite (especially for Pbcomplexes), no quantitative data were found in literature to constrain precisely selectivity coefficients between H+ and such carbonates complexes in calco-carbonic equilibrium conditions; these latter conditions being difficult to assess in most of the papers dealing with this topic. Predictive Modeling of Metal Sorption on Complex and Carbonated Solids. The ion exchange model proposed in this study is used to assess how calcite can contribute quantitatively to the sorption of divalent metals on a complex and natural carbonated material. Our model was not tested on natural materials rich in clay minerals due to the stronger sorption properties of these minerals compared to those of carbonates. In contrast, materials dominated by quartz, feldspars, and carbonates were preferred due to the very low sorption properties of quartz and feldspars compared to those of carbonates, such as calcite. The experimental data reported by Fuller and Davis27 for the sorption of Cd(II) on a calcareous aquifer sand (i.e., “Borden Sand”) were selected. Data reported for this carbonated sand were obtained in conditions of calcocarbonic equilibrium. Therefore, such data are representative of reversible sorption (i.e., ion exchange reactions), and other sorption processes, such as coprecipitation and incorporation into the crystal structure, had to be limited. Detailed mineralogical and chemical information of the Borden Sand, reported from the study of Fuller and Davis, are given in SI Table S3. Fuller and Davis27 presented data sets that were obtained at different pHs (ranging from 6.0 to 7.2) for sorption of Cd(II) on the Borden Sand. These data are reported in Figure 3 in terms of the Cd(II) sorbed concentration as a function of the total Cd(II) aqueous concentration at equilibrium for four different pHs (i.e., 6, 6.5, 7, and 7.2). To predict the contribution of calcite to the global sorption of Cd(II) on the carbonated sand, the ion exchange model proposed in this study is used. To predict this contribution, the sorption site density due to calcite alone must be evaluated. Fuller and Davis27 mention that the calcite contributes to 14 wt % of the mineralogical composition of the sand. According to the total site concentration proposed in this study for pure calcite (i.e., 1.2 × 10−6 eq·g−1), the sorption site density due to the calcite phase in the sand is estimated to be 1.7 × 10−7 eq·g−1 of sand. Fuller and Davis reported a cation exchange capacity (CEC) close to 7 × 10−6 eq·g−1 for their bulk material. This discrepancy between the measured CEC and the CEC obtained by solely considering the contribution of calcite could be due to the presence of organic/inorganic coatings on the quartz and feldspar grains, as mentioned by the authors themselves.27 Note, for example, that 14 wt % of pure calcite (the estimation of the authors) with only 0.8 wt % of pure montmorillonite

reference of the experimental data used for the fit

reaction

log K2H/Me

2 > X‐H + Ca 2 + = > X 2‐Ca + 2H+

−9.0c

−

this study

2 > X‐H + Zn 2 + = > X 2‐Zn + 2H+

−6.5

2.5

2 > X‐H + Cd2 + = > X 2‐Cd + 2H+

−5.5

3.5

Zachara et al.17 and Tertre et al.15 Li13

2 > X‐H + Pb2 + = > X 2‐Pb + 2H+

−4.6

4.4

Rouff et al.24

Values were obtained assuming a total site concentration of 1.2 × 10−6 eq·g−1 and using an ion-exchange formalism (see text for details). b log KCa/Me is calculated according to the following equation: log KCa/Me = log K2H/Me − log K2H/Ca and by considering log K2H/Ca = −9.0. cAll log K2H/Ca values equal or superior to −9.0 can interpret concentrations of Ca(II) that are reversibly sorbed (or desorbed) at the calcite surface (experimental data reported in Figure 1; see also text and Figure S1 for more explanations). a

coefficient, modeling is performed with the PHREEQC code22 and the minteqv4 database.23 A comparison between the experimental data and the predictions is shown in Figure 2. For Zn(II), the proposed model accurately describes all of experimental data (see Figure 2A). Note that the predicted results from the model are slightly different for Zachara et al.’s data and for Tertre et al.’s data. For a given aqueous concentration of Zn(II) at equilibrium, the predicted sorption is slightly less for the case of high chloride normality (Zachara et al. case; I = 0.1 M NaCl) than for the low chloride normality case (Tertre et al. case; I = 0.01 M NaCl). In the 0.1 M NaCl solution, the contribution of the ZnCl+ species to the Zn(II) aqueous speciation is approximately 3%, whereas this contribution can be neglected in the 0.01 M NaCl solution (X2-Ca] and [>X-H] values predicted by our model considering different values for logK2H/Ca (from −8 to 11); mineralogy and some physicochemical parameters of the calcareous aquifer reported from 27. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions §

These two authors equally contributed to this work.

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Environmental Science & Technology

Article

Notes

(20) Tertre, E.; Beaucaire, C.; Coreau, N.; Juery, A. Modelling Zn(II) sorption onto clayey sediments using a multi-site. Appl. Geochem. 2009, 24, 1852−1861. (21) Davies, C. W. Ion Association; Butterworth: London, 1962. (22) Parkhurst, D. L.; Appelo, C. A. J. Phreeqc2 User’s Manual and Program; U.S. Geological Survey, 1999. Available at http://www.geo. vu.nl/users/posv/phreeqc.html. (23) MINTEQA2/PRODEFA2, A Geochemical Assessment Model for Environmental Systems: User Manual Supplement for Version 4.0. U.S. Environmental Protection Agency, 1998. Available at www.epa.gov/ ceampubl/mmedia/minteq/. (24) Rouff, A. A.; Elzinga, E. J.; Reeder, R. J.; Fisher, N. S. The influence of pH on the kinetics, reversibility and mechanisms of Pb(II) sorption at the calcite-water interface. Geochim. Cosmochim. Acta 2005, 69, 5173−5186. (25) Sposito, G.; Holtzclaw, K. M.; Charlet, L.; Jouany, C.; Page, A. L. Sodium-calcium and sodium-magnesium exchange on Wyoming bentonite in perchlorate and chloride background ionic media. Soil Sci. Am. J. 1983, 47, 51−56. (26) Tertre, E.; Prêt, D.; Ferrage, E. Influence of the ionic strength and solid/solution ratio on Ca(II)-for-Na+ exchange in montmorillonite. Part 1: Chemical measurements, thermodynamic modeling and implications for trace elements geochemistry. J. Colloid Interface Sci. 2011, 353, 248−256. (27) Fuller, C. C.; Davis, J. A. Processes and kinetics of Cd2+ sorption by a calcareous aquifer sand. Geochim. Cosmochim. Acta 1987, 51, 1491−1502.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was financially supported by the CEA (Commissariat à l’Energie Atomique). REFERENCES

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