Adsorption of Chromium (VI) on Calcium Phosphate: Mechanisms and Stability Constants of Surface Complexes

Abstract

first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessArticle Adsorption of Chromium (VI) on Calcium Phosphate: Mechanisms and Stability Constants of Surface Complexes by Ahmed Elyahyaoui 1,*, Kawtar Ellouzi 1, Hamzeh Al Zabadi 2, Brahim Razzouki 3, Saidati Bouhlassa 1, Khalil Azzaoui 4, El Miloud Mejdoubi 4, Othman Hamed 5, Shehdeh Jodeh 5,* and Abdellatif Lamhamdi 4,6 1 Laboratory of Radiochemistry, Department of Chemistry, Faculty of Sciences, Mohamed V-Agdal, B.P 1014 Rabat, Morocco 2 Public Health Department, An-Najah National University, P.O. Box 7, Nablus 44830, Palestine 3 Laboratory of Spectroscopy, Molecular Modeling, Materials and Environment, Department of Chemistry, Faculty of Sciences, Mohamed V, B.P 1014 Rabat, Morocco 4 Laboratory LMSAC, Faculty of Sciences, Mohamed 1st University, P.O. Box 717, Oujda 60000, Morocco 5 Department of Chemistry, An-Najah National University, P.O. Box 7, Nablus 44830, Palestine 6 National School of Applied Sciences Al Hoceima, Mohamed 1st University, P.O. Box 717, Oujda 60000, Morocco * Authors to whom correspondence should be addressed. Appl. Sci. 2017, 7(3), 222; https://doi.org/10.3390/app7030222 Received: 4 December 2016 / Accepted: 7 February 2017 / Published: 28 February 2017 (This article belongs to the Special Issue Wastewater Treatment and Reuse Technologies) Download Download PDF Download PDF with Cover Download XML Download Epub Browse Figures Versions Notes Abstract: The adsorption of chromate on octacalcium phosphate (OCP) was investigated as a function of contact time, surface coverage, and solution pH. The ion exchange method was adapted to establish the interaction mechanism. Stoichiometry exchange of H+/OH− was evaluated at a pH range of 3–10, and obtained values ranged between 0.0 and 1.0. The surface complexes formed between chromate and OCP were found to be > S ( HCrO 4 ) ¯ and > S ( CrO 4 ) ¯ . The logarithmic stability constant logK1-1, and the logK10 values of the complexes, were 6.0 in acidic medium and 0.1 in alkaline medium, respectively. At low pH and low surface coverage, the bidentate species > S ( HCrO 4 ) ¯ 2 with logK10.5 of about 2.9, was favored at a hydration time of less than 150 min. The contribution of an electrostatic effect to the chromium uptake by the OCP sorbent, was also evaluated. The results indicate that the adsorption of chromate on OCP is of an electrostatic nature at a pH ≤ 5.6, and of a chemical nature at a pH > 5.6. Keywords: octacalcium phosphate; chromium (VI); adsorption; environmental; ion exchange Graphical Abstract 1. IntroductionThe hexavalent chromium Cr (VI) generated from various industrial processes, such as metallurgy, dyes, paints, inks, and plastics, is a major global concern, due to its harmful effects on humans and nature [1].As a result, the presence of this metal cation in nature is well controlled. The maximal concentration level of Cr (VI) allowed in drinking water, as determined by the US-Environmental Protection Agency (EPA), is 0.05 mg/L [2]. Compliance with the EPA’s chromium rule requires additional industrial monitoring. Designing a treatment process which reduces the number of chromium ions in industrial effluent to an acceptable level, has become crucial. A number of methods for this purpose have already been developed, among which are reduction and precipitation [3], ion exchange [4], solvent extraction [5], adsorption [6], and electrochemical precipitation [7]. When considering these methods, adsorption is the most promising technique [8]. This process is usually performed using conventional adsorbents, such as silica, zeolites, iron(III) (hydr)oxides, and activated carbon, or nonconventional adsorbents, such as red mud, sewage sludge, and bone char [9,10,11]. Phosphate materials (synthetics and minerals) have also been used as effective adsorbents for heavy metals from wastewaters and polluted soils. They have an excellent stabilization efficiency for several metal ions. For this reason, they are highly efficient metal adsorbents [12,13,14], particularly calcium phosphate. This material has a large specific area, high thermal and geochemical stability, low solubility, high ionic exchange capacity, and high stability towards ionization by radiation. For these reasons, it has been used as a backfill material for geological repositories for nuclear waste [15], and as an adsorbent in engineered barriers for environmental restoration [16]. It was also reported that phosphates with an amorphous structure are more efficient adsorbents of lead, uranium, and plutonium [17].Although several adsorbents have been developed, and the retention of the metals hasbeen extensively studied, the sorption mechanisms are still rather difficult to identify. This could be because several phenomena, such as iso-morphous substitutions, surface complexation, and dissolution–precipitation, can occur simultaneously during the sorption process [18,19,20,21]. In addition, there is a lack of data on the adsorption of many metals on amorphous or poorly-crystallized phosphates.Published studies show that the uptake of hexavalent chromium by calcium phosphate, exhibits typical anionic (such as HCrO4− and CrO42−) sorption behavior, and that the adsorption decreases by increasing the pH [22]. They also show that Cr (VI) adsorption is favored on phosphate that ispositively charged, at a low to neutral pH level (i.e., high point of zero charge (PZC)) [23]. The findings suggest that the retention of Cr (VI) by phosphates occurs through an electrostatic attraction and via binding to the surface functional groups OH2+ and OH−. In other studies, it was found that hydroxapatite (HAp) and tricalcium phosphate (TCP) composite are able to adsorb a significant amount of chromium (VI), at a pH level of about 5. So, the composites showed a lower PZC than HAp (6.2–8.5) [22,23,24].Moreover, there is no systematic understanding of the mechanism of chromium immobilization that involves the protonation/deprotonation of surface hydroxyl groups, and their interaction with the metal oxyanion. The combined effect of both pH and contact time on the adsorption mechanism requires more investigation (Figure 1).Taking these considerations into account, the present study aims to investigate the complexation of hexavalent chromium with low-crystallized octacalcium phosphate (OCP). To achieve the aim of this study, the removal of Cr (VI) from aqueous solution was studied through batch experiments, as a function of contact time, the amount of adsorbent, and the equilibrium pH of chromate (10−4 M) solution. The ion exchange method, which has already been successfully implemented, especially in solvent extraction, has been chosen by the authors, in order to study the behavior of chromium (VI) on the surface of OCP. Another aim of this work is to investigate the surface complexation of OCP. 2. Experiment 2.1. Materials and MethodsOctacalcium phosphate (OCP) was synthesized in our laboratory. Phosphoric acid (99%), Chromium (VI), Calcium hydroxide (99%), Potassium hydroxide (KOH) (99%), and Nitric acid (HNO3) (99%), were purchased from Sigma Aldrich, and were used in the same form as they were received. High-purity distilled water was used for all of the experiments. 2.2. Synthesis and Characterization of OCPCalcium phosphate was synthesized using the microwave-hydrothermal method. In this method, phosphoric acid (0.3 M) and calcium hydroxide solution (0.5 M) are used as the starting materials. The preparation method has been described in [22]. The obtained mixture was heated at 150 °C for 1 h, and then irradiated in a microwave oven (800 w) for 5 min. The resulting gel was filtered off and dried overnight in an air oven, at 80 °C. The obtained solid was repeatedly washed with hot distilled water, and was identified as OCP by the associated XRD patterns and FT-IR. The characteristics of the diffraction line observed in the XRD patterns at 2θ = 4.7°, is evidence for the formation of OCP [22].This result was confirmed by the FTIR characteristic peaks of OCP at 1089 and 1033, and by the Ca/P ratio of 1.34, which was close to the theoretical OCP ratio of 1.33 [25,26]. 2.3. Surface Properties and Adsorption ExperimentsThe adsorption experiments were carried out by a batch method. A stock solution of Cr (VI) (10−4 M) was prepared from potassium dichromate. The pH level of the solution was measured using a Hanna combined electrode (Hanna pH 210). Nitric acid and KOH were used to adjust the starting acidity of the aqueous solutions of Cr (VI), with a concentration of 10−4 M in all cases. Sorption experiments were conducted at room temperature, as a function of the pH, contact time, and amount of adsorbent (m). The supernatants (5.0 mL) were filtered and analyzed for aqueous chromium using the 1,5-diphenylcarbazide (EPA 7196A) spectrophotometry method. The adsorbed chromium was calculated from the difference between the concentrations before and after equilibrium with calcium phosphate. The ratio of Cr (VI) concentrations in solid and aqueous phases led to the distribution coefficient D. 3. Results and Discussion 3.1. Effect of pH on Chromium AdsorptionThe logarithmic variation of D with pH at different contact times, for 0.5, 1.0, and 1.5 g/L of calcium phosphate solutions, is plotted in Figure 1.As shown in Figure 1, all cases exhibit similar behavior; log D increased by increasing the pH, to reach the maximum at pHmax of 4.0 to 5.0, before decreasing as the pH continued to increase. The maximum adsorption efficiencies were found to increase with the amount of adsorbent (m). The results also show that the pHmax is dependent on the contact time; when the contact time increased from 5 to 150 min, the pHmax rose from about 4 to 5.The variation in the extraction efficiency with the solution’s pH could be related to the protonation/deprotonating of both surface groups, and to the acidity of H2CrO4 (pKa1 = 0.2 and pKa2 = 6.5) [27,28,29]. According to the chromium speciation pH-diagram, the chromium (VI) was adsorbed as hydrogen chromate (HCrO4−) at pH ≤ 5.0 (≥95%), as chromate (CrO42−) at pH ≥ 7.6 (≥95%), and as a mixture of these species between pH 5.0 and 7.6. In this case, both electrostatic and chemical sorption mechanisms could occur, and generally, it is not possible to distinguish between these two mechanisms [30]. It was assumed that the maximum adsorption occurred when the combination of a high positive surface charge and a high concentration of anionic chromium species, are achieved. Thus, the uptake of weak acid was maximal at a pH value around its dissociation constant, or near the PZC of surface sorbent materials [31]. In general, anion adsorption is strongly dependent on the pH of the medium, exhibiting the greatest removal in acidic to neutral solution. As has been demonstrated in previous studies, optimal Cr (VI) adsorption occurs at a pH lower than 4 for various sorbents, such as some metallic (oxy)hydroxides [32,33,34] and natural bio-sorbents, for example, larch bark [35], cooked tea dust [36], papaya seeds [37], raw Bagasse [38], and activated carbon [39]. In the case where iron and aluminum oxides are used as adsorbents, an adsorption efficiency of higher than 80% was reached at a pH of 4 to 6. The adsorption was seen to be highly dependent on the pH of the medium; the Cr (VI) uptake increased by increasing the pH values from 1.0 to 7.0, after which the uptake decreased.Similar results were reported for the variation of hexavalent chromium adsorption with pH solution, with other adsorbents such as clay minerals [40], oxide-coated sand [40], aluminosilicate [41], zeolite [42], chitosan [43], and hydroxyapatite [44], which all exhibited a maximum uptake at a pH of 5 to 7. It has been suggested that, at a low pH, the adsorption is also low, due to the competition between the metal ions and protons for the adsorption sites. In these cases, the uptake of Cr (VI) followed the ion exchange mechanism. From these results, it could be concluded that, at a pH higher than pHmax, Cr (VI) exhibited typical anionic sorption behavior, with adsorption decreasing when the pH was increased. Similar results were reported for the retention of similar anions on oxide surfaces [45,46]. This adsorption pattern is the result of the protonation of surface hydroxyl sites and of Cr (VI) hydrolysis [47]. Thus, at a pH higher than pHmax, the retention of Cr (VI) was due to the interaction of HCrO4− and/or CrO42− with OH surface groups, rather than with OH2+ groups, which were predominant at a pH lower than pHmax [44]. The significant influence on the adsorption of CrO42− was found at the slope of the pH adsorption edges. Distinct pH regions with different slopes characterized the various adsorbed species. This result reflected the change in the sorption mechanism [48]. 3.2. Effect of Contact TimeThe effect of contact time on the adsorption efficiency was examined, and the results are shown in Figure 2. At a pH lower than pHmax, a distinct difference was observed for adsorption envelopes in relation to the sorbent dose, or sorbet/sorbent ratio (surface coverage). At a sorbent dose of 0.5 and 1.0 g/L, the pH adsorption edges followed a similar trend for t ≥ 15 min. At a pH of 50% of adsorption (pH50), a negligible variation occurred at pH 3.9–4.1. When the sorbent dose was1.5 g/L, the adsorption process was dependent on the hydration time. Therefore, the adsorption envelopes shifted to higher pH values, resulting in an increase in pH50 from 2.9 to 3.9, as the time increased from 0 to 150 min. The mechanism for the oxyanion adsorption was dependent on the surface coverage and hydration of the surface sites, involving the formation of distinct surface complexes. This was in agreement with the spectroscopic study results, which indicated that chromium (VI) resulted in the formation of both monodentate and bidentate surface complexes on iron oxides [49,50]. The proportion of these species was dependent on the metallic ion concentration. Recently, through the use of a spectroscopic study, it has been shown that the monodentate chromate complexes on ferrihydrite were predominant at a low surface coverage and a pH ≥ 6.5. In contrast, bidentate surface complexes were formed at a high surface coverage and pH ≤ 6 [51].Taking into account the previous results, it could be deduced that, at a low adsorbent dose, monodentate surface complexes prevailed for all of the examined experimental conditions. In contrast, at a higher adsorbent dose, the bidentate surface complexes became predominant at a low hydration level of sorbent materials at pH ≤ pHmax, and were subsequently converted to monodentate species, when hydration equilibrium was reached.At a pH higher than pHmax, adsorption envelopes become more alkaline. The shift to this alkalinity increased by increasing the hydration time. Due to electrostatic repulsion with the negative surface charges, the chromium uptake initially involved the adsorption of a HCrO4− anion, which was followed by the subsequent slower, and less important, uptake of CrO42− in the alkaline region. These electrostatic factors could influence both the kinetics and equilibrium of chromate ions, as observed for the adsorption of a similar oxyanion on ferrihydrite [52]. When the contact time increased, the adsorption of the chromate anion also increased, and the Log(D) = f(pH) curves show a pronounced difference in the slopes at t = 150 min. As previously discussed, this phenomenon could be due to a change in the adsorbed fraction of the Cr (VI)-predominant surface complexes. 3.3. Chromium (VI) Adsorption Reactions and Stability ConstantsThe acid-based properties of calcium phosphate were described by the protonation and deprotonation reactions of the phosphate surface functional groups, as shown in Equations (1) and (2), > SOH ¯ [53,54]: > SOH ¯ + H + ↔ > S ( OH 2 ) + ¯ K + (1) > SOH ¯ ↔ > SO − ¯ + H + K − (2) K+ and K− were the surface stability constants, and the on lined species referred to the solid phase.The adsorption reaction of chromium (VI) on calcium phosphate can be expressed as follows: ( > SOH ) l ( H i Cr O 4 ) H − n ¯ + n H + ; l = 1 ; 2 , i = 1 ; 2 (3) where n is the number of protons, which ranges from −1 to +1.The initial ionization of H2CrO4 is relatively strong, so HCrO−4 was the main species found at pH > 5, and i = 1 at equilibrium (Equation (3)), under these conditions.The symbol H−n, stands for both hydrogen atoms (n < 0) and for OH groups (n > 0). Taking into account that H2O ≡ H−l + Hl, the surface complexes > ( SOH ) l ( H i CrO 4 ) H − n ¯ noted thereafter Cln, represented a general formulation of species, differentiated by water composition. So > ( SOH ) l ( H 2 CrO 4 ) H − n ¯ could be > ( SOH ) l ( HCrO 4 ) H − n + 1 ¯ + H2O or > ( SOH ) l ( CrO 4 ) H 2 − n ¯ + 2H2O, and even > ( S ) l ( H 2 CrO 4 ) H − n − l ¯ or > ( S ) l ( HCrO 4 ) H − n − l + 1 + H2O or > ( S ) l ( H 2 CrO 4 ) H − n − l + 2 + 2H2O.The surface complexation constant for the relationship (3) is: K ln = [ ( > SOH ) l ( H i _ Cr O 4 ) H − n ¯ ] [ H + ] n [ > SOH ¯ ] l [ H i Cr O 4 ( i − 2 ) + ] (4) The distribution coefficient being: D = [ ( > SOH ) l ( H i C r O 4 ) H − n ¯ ] [ H i C r O 4 ( i − 2 ) + ] (5) where [HiCrO4(i-2)+] represents the equilibrium concentration of Cr (VI) in solution, it was obtained that: log D = log K ln + log m + npH (6) where > SOH ¯ = m, was the concentration of sorbent used in g/L.Assuming that the first approximation is the essential formation of mononuclear (l = 1), the surface complexes of Equation (6) become: log D = log K 1n + log m + npH (7) The variation of the distribution coefficient with pH allowed us to define the nature of the C1n-adsorbed species. The values of (l,n) were obtained according to: ( δ logD δ pH ) m = n (8) So, the surface complexes of Cr (VI) with calcium phosphate could be well described from the experimental data logD = f(pH), shown in Figure 1. The analysis of the obtained results showed that the plots of logD = f(pH) were linear at various pH ranges. The straight lines of the slope correspond to the mean values of n, and varied between −1 and 1. The value of the surface complexes (1,n), involved in this case were (l,0), (l,1), (l,2), and (l,−1). In this case, the co-precipitation/adsorption process of chromium (VI), and the species distribution diagram as a function of pH, are needed. It is worth noting that the interaction of Cr (VI) with the OCP surface could be described as an n = f(pH) variation. For this purpose, fitting of the data into a polynomial equation was carried out for the three pH regions. The obtained results show that, when in acidic solution (pH < 5), a second-degree equation fitted (R2 > 99%) the ascendant curve, whereas in low acidic to alkaline media, a cubic polynomial fitted (R2 > 99%) two distinct segments of the descendant curve, at pH regions of about 4 to 6 and 6 to 10. 3.3.1. Surface Complexes and Effect of pH and Contact Time on H3O+/OH− ExchangeThe variations of n = f(pH) are illustrated in Figure 2. As shown in Figure 2, the protonation/deprotonating reaction followed a similar trend, with respect to the pH value. In all cases, the maximum H3O+ and OH− exchange of |n| = 0.8 occurred at a pH range of 4.0–6.0. When considering the obtained results, it becomes evident that the H3O+/OH− stoichiometry was not an integer, as might be expected from the theoretical single reaction. Similar results were observed for other adsorbed elements on iron (oxy) hydroxides [55,56].It was assumed that the chromium adsorption occurred by different reactions, and consequently, resulted in a combination of at least two predominant surface complexes. In the case l = 1, the predominant complexes would be different for the sorbent amounts of 0.5 and 1.0 g/L, while a different adsorption behavior was observed for 1.50 g/L. Indeed, a low value of around 0.5 was found at low pH and at t < 150 min, indicating that C10 is not the predominant species under these conditions.Taking into account these considerations, the uptake of Cr (VI), characterized by n = 0.5, and the general adsorption reaction, can be expressed by: > SOH ¯ + 2 H 2 C r O 4 ↔ > S ( O H 2 ) + ( H C r O 4 ) 2 H − n ¯ + 1 H + ; l = 1 n = 2 (9) > S O H ¯ + 2 H 2 C r O 4 ↔ > S H ( H C r O 4 ) 2 H − n ¯ + H 2 O + n H + ; l = 1 n = 2 (10) The adsorption constant K10.5 for equilibrium (10) was given by: K 1n ′ = [ > S H ( H C r O 4 ) 2 H − n ¯ ] [ H + ] n [ > S O H ¯ ] [ H 2 C r O 4 ] 2 = D [ H + ] n [ > S O H ¯ ] [ H 2 C r O 4 ] (11) Based on this adsorption mechanism, the following relationship could be obtained: log ( D ( D + 1 ) ) = log K 1n ′ + log m + log [ C r ] 0 + n p H (12) For [Cr]0 = 10−4 M, which was the chromium analytical concentration used, the equation becomes: log ( D ( D + 1 ) ) = log K 1n ′ + log m − 4 + n p H (13) At a pH range of 2.5 to 5.0, the relation log(D(D + 1)) = f(pH) exhibited a linear variation, with slopes increasing from 0.5 to 1.0, as the time increased from 0 to 150 min.Accordingly, C11, C10.5 and C10 were the predominant surface species in the case of l = 1. A non-protonated C11 ( > SOH ( H 2 CrO 4 ) H − 1 ¯ ≡ > S ( HCrO 4 ) H − 1 ¯ ≡ > SCrO 4 ¯ ) complex was always formed at low acidity (pH ~ 4.4), combined with the protonated C10 ( > SOH ( H 2 CrO 4 ) H 0 ¯ ≡ > S ( HCrO 4 ) H 0 ¯ ≡ > SHCrO 4 ¯ ), complex during hydration equilibrium conditions. Nevertheless, when this equilibrium was not reached at the 1.5 g/L sorbent amount, the C10 complex was not favored, and disappeared, to the benefit of the bidentate: C10.5 ( > SOH ( H 2 CrO 4 ) 2 H − 1 ¯ ≡ > SH ( HCrO 4 ) 2 H − 1 ¯ ≡ > S ( HCrO 4 ) 2 ¯ ) species. As a result, in this condition, C10.5 and C11 were the prevailing complexes. The C10.5 surface complex can also be formulated as the > S ( H 2 Cr 2 O 7 ) ¯ species. However, the bichromate surface complexes were not found at 0.5 and 1.0 g/L sorbent doses and were neglected, as previously reported [57].The results show that, as the sorbent amount increased, the number of surface sites also increased. At high-hydration equilibrium, the hydrogen chromate anions (HCrO4−) and water molecules were competing for the active surface sites. At a low-hydration level of the sorbent material’s surface site, the HCrO4− ions displaced the H2O molecules, in the hydration sphere of the C11 complex. Bidentate surface species were then formed at a high sorbent dose and short contact time. These results were in accordance with previous studies, suggesting that high-chemisorbed water molecules prevented the bidentate complexes from forming, as noted for the complexation of chromium with ferrihydrite [48]. A similar substitution of water molecules by HCrO4− anions could take place at a higher chromium concentration, even at hydration equilibrium, explaining the formation of bidentate surface species when there is a high surface coverage, observed for the adsorption of Cr (VI) or a similar anion on ferrihydrite [29].It should be noted that the C10 ≡ > S ( HCrO 4 ) H 0 ¯ complex could also be expressed as an outer-sphere > SOH 2 + − HCrO 4 − ¯ species, since we could not distinguish between the different complexes’ formulations or structures, based on one H2O molecule. Generally, when at a low pH value, the formation of such outer-sphere Cr (VI) surface complexes is favored, similar to that previously obtained on amorphous aluminum oxides [58], and supported by the formation of SOH2+ in acidic media, as was indicated in a titration experiment [59].At a pH higher than 4.5, n varied between −1 and 0, in all investigated conditions. The predominant surface species formed in these conditions, were C10 and C1-1. Thus, Cr (VI) was adsorbed via the formation of > S ( OH ) ( HCrO 4 ) H 0 ¯ (C10) and > S ( OH ) ( HCrO 4 ) H 1 ¯ (C1-1) complexes, that could be expressed as > SCrO 4 ¯ and > SHCrO 4 ¯ , respectively. As the contact time increased, the optimal pH formation of protonated C1-1 ≡ > SHCrO 4 ¯ ≡ > S ( OH 2 + ) ( HCrO 4 − ) ¯ and the un-protonated C10 ≡ > SCrO 4 ¯ ≡ > S ( OH ) ( HCrO 4 ) ¯ species, shifted from 5 to 6 and 7 to 8, respectively. The adsorption of Cr (VI) increased with t, and at a higher hydration time, the adsorption reaction was likely to comply to OH− surface exchange. Thus, for a pH lower than PZC, the negative surface charge of the phosphate material reacts in acidic media to form >S(OH2)+, which adsorbs chromium as HCrO4−. Maximal OH− exchange was observed at a pH range of 5.2–6.0, which approximately coincided with the pH range of zero charge and the iso-electric points of unloaded material. Whilst higher than PZC, the repulsion between chromium anions and negatively sorbent surface charge, increased with pH. The contribution of the columbic effect to the overall uptake of Cr (VI) could be a more important process. Nevertheless, at a pH value around the iso-electric point, the electrostatic repulsion reached a minimum value, and then the intrinsic process (with n = 0) became the major adsorption mechanism. As shown from the obtained results, the pH value became higher with contact time, reaching 8.2 at t ≈ 150 min.Consequently, the overall adsorption equilibrium could be obtained by the intrinsic reaction with 1 mole of H+ (n = −1), or 1 mole of OH− (n = 1) exchange reactions per mole of HCrO4−. 3.3.2. Equilibrium ConstantsIn the Log(D)= f(pH),Figure 1 plots the various contact times and sorbent amounts, and the straight lines show slopes ranging from −0.4 to 0.6. In the cases when the surface complexes are mononuclear (l = 1), apparent equilibrium constants, Kap = K1n or K’1n, were obtained from the origin ordinates A = LogK1n + Log(m) or logK’1n + Log(m) − 4. From the obtained results, it can be that the variations of logK1n = f(n) (Figure 3) and logK’1n = f(n) (not shown), were linear under all experimental conditions.Taking into account that |n| also represented the fraction (x) of the predominant 1H+ or 1OH− exchange reactions contributing to the overall adsorption equilibrium, the apparent constants (Kap) of the overall equilibrium were given by the expressions shown in Equations (14) and (15): K ap = ( K 10 ) ( 1 − | n | ) ( K 1 ± 1 ) | n | (14) logK ap = ( 1 − | n | ) logK 10 + | n | logK 1 ± 1 (15) with K 1 ± 1 = K 11 or K 1 − 1 .As an example, the overall partition equilibrium prevailing for pH > 5.5, and involving successive exchange reactions n = 0 and −1, can be summarized in the following reactions: ( 1 − x ) ( > SOH ¯ + H C r O 4 − ↔ > S ( O H ) ( H C r O 4 ) H 0 ¯ ≡ > S ( C r O 4 ) ¯ + H 2 O ) : ( K 10 ) ( 1 − x ) , n = 0 (16) Overall adsorption reactions are: ( x ) ( > S O H ¯ + H C r O 4 − + H 2 O ↔ ( > S O H ( H C r O 4 ) H 1 ¯ ≡ > S ( H C r O 4 ) ¯ + H 2 O ) + O H − : ( K 1 − 1 ) x , n = − 1 (17) > S O H ¯ + H C r O 4 − + n H 2 O ↔ ( > S O H ( H C r O 4 ) H n ¯ ≡ > S ( H C r O 4 ) ¯ + H 2 O ) + n O H − : ( K 1 n ) , − 1 ≤ n ≤ 0 (18) Where x is the molar fraction of the sorption mechanism with 1 OH− exchange. The apparent constant, Kap = K1n, is then given by: logK1n= (1 − x)logK10 + xlogK11 = (1 − |n|) logK10 + |n| logK10 (19) As shown above, the Kap value could be determined experimentally, and was variable, depending on the surface charge and pH. Therefore, the constants K10 and K1±1 were the intersect and the slope of logKap = f(n), respectively, whereas K1-1 was the opposite of the slope. From this information, the intrinsic constants K10, for H+ (formation of > S ( OH 2 + ) ( HCrO 4 − ) ¯ H 0 ≡ > S ( HCrO 4 ) ¯ ) and OH− (formation of > S ( OH ) ( HCrO 4 ) H 0 ¯ ≡ > S ( CrO 4 ) ¯ ) adsorption reaction exchange, were determined, with corresponding logarithmic values of logK10 = 0.2 and 0.1, respectively. The intrinsic constants (Kint = K10) were obtained in general, by extrapolating the apparent constants to a zero surface charge [57,58].As discussed previously, the variations of logKap= f(n) could be due to the contribution of the electrostatic effect (Kcol), related to Kap [60,61] according to: K int = K ap K col = K ap exp ( − nF Ψ 0 / RT ) (20) K ap = K int ( K col ) − 1 = ( K 10 ) ( 1 − | n | ) ( K 1 ± 1 ) | n | (21) In the particular case of |n| = 1, Equation (22) was obtained: K ap =