Dissolution and Solubility Product of Cd-Fluorapatite [ Cd 5 ( PO 4 ) 3 F ] at pH of 2 – 9 and 25 – 45 ° C

Dissolution of the synthetic cadmium fluorapatite [Cd5(PO4)3F] at 25°C, 35°C, and 45°C was experimentally examined in HNO3 solution, pure water, and NaOH solution. ,e characterization results confirmed that the cadmium fluorapatite nanorods used in the experiments showed no obvious variation after dissolution. During the dissolution of Cd5(PO4)3F in HNO3 solution (pH� 2) at 25°C, the fluoride, phosphate, and cadmium ions were rapidly released from solid to solution, and their aqueous concentrations had reached the highest values after dissolution for<1h, 1440h, and 2880h, respectively. After that, the total dissolution rates declined slowly though the solution Cd/P molar ratios increased incessantly from 1.55∼1.67 to 3.18∼3.22. ,e solubility product for Cd5(PO4)3F (Ksp) was determined to be 10 (10∼10) at 25°C, 10 (10∼10) at 35°C, and 10 (10∼10) at 45°C. Based on the logKsp values obtained at an initial pH of 2 and 25°C, the Gibbs free energy of formation for Cd5(PO4)3F (ΔGf) was calculated to be −4065.76 kJ/mol (−4064.11∼4068.23 kJ/mol). ,e thermodynamic parameters for the dissolution process were computed to be 342515.78 J/K·mol, −85088.80 J/mol, −1434.91 J/K·mol, and 2339.50 J/K·mol for ΔG0, ΔH0, ΔS0, and ΔCp 0, correspondingly.


Introduction
Apatite [Ca 5 (PO 4 ) 3 (F,OH)] forms a large family of minerals due to many isomorphous substitutions, which play a very important role in numerous industrial, medical, and environmental processes [1][2][3].Apatite minerals are the raw materials to produce phosphatic fertilizers and usually contain many harmful minor elements.Among them, cadmium is one of the most toxic heavy elements in natural environment and can cause animal osteoporosis and osteomalacia due to its possible concentration in mammal's hard tissues through food chains [4][5][6].Cd 2+ (0.095 nm radius) and F − have the probability of substitution for Ca 2+ (0.100 nm radius) and OH − in the vertebral animals' bones and teeth that are principally composed of calcium hydroxyapatite.Additionally, the ion exchangeability of apatite offers a possibility for the remediation of heavy metalcontaminated soils and the removal of hazardous heavy metals from industrial wastewaters.Apatite minerals have been applied to stabilize many heavy metals including cadmium [7][8][9][10].
e substitution of Cd 2+ for Ca 2+ in the apatite results in the formation of its isomorph, cadmium fluorapatite (Cd-FAP) [11].erefore, it is essential to understand its fundamental physicochemical properties, predominantly the solubility of cadmium apatite and its dissolution mechanism.Although many experimental works on the dissolution mechanism and kinetics of apatites in aqueous solution had already been executed [7,[12][13][14][15][16], much of them only concentrated on calcium hydroxyapatite and fluorapatite.Unfortunately, the thermodynamic data and dissolution kinetics for cadmium fluorapatite in aqueous solution under different conditions are now deficient, even though its dissolution and following release of cadmium, phosphate, and fluoride ions into water play an important role in cycling of these components.
No researches have been done on the dissolution and solubility of cadmium fluorapatite [Cd-FAP, Cd 5 (PO 4 ) 3 F], for which no thermodynamic data could be obtained in literatures to evaluate the environmental risk of Cd in relation with fluorapatite.In the present work, cadmium fluorapatite was synthesized by the precipitation method and characterized with different instruments.e dissolution mechanism of the synthetic cadmium fluorapatite was examined at different initial pHs and temperatures.As comparison, a similar test was also performed using the pure synthetic calcium fluorapatite (Ca-FAP).Furthermore, the aqueous concentrations of cadmium, calcium, phosphate, and fluoride ions from the experiment were used to estimate the solubility products and Gibbs free energies of formation.

Solid Preparation.
e pure cadmium fluorapatite [Cd-FAP, Cd 5 (PO 4 ) 3 F] was synthesized in the similar method as that used in our previous research [11].e synthetic detail for the Cd-FAP preparation was dependent on the following precipitation: 5Cd 2+ + 3PO 4 3− + F − � Cd 5 (PO 4 ) 3 F.In an 1 L polypropylene bottle, cadmium nitrate [Cd(NO 3 ) 2 •4H 2 O] was firstly dissolved in ultrapure water to prepare 0.5 L of 0.2 mol/L Cd 2+ solution.0.1 L of 0.2 mol/L NaF solution and 0.3 L of 0.2 mol/L (NH 4 ) 2 HPO 4 solution were then rapidly mixed with the cadmium solution in the bottle to form white suspension.e pH of the resulting mixed solution with a Cd : P : F molar ratio of 5 : 3 : 1 was adjusted to 9.00 by using NH 4 OH solution, which was then stirred for 10 min at room temperature and aged at 100 °C for 48 h.Finally, the white solid of cadmium fluorapatite obtained was carefully washed using ultrapure water and dried at 70 °C for 48 h.

Characterization.
A quantity of 0.01 g of the synthetic cadmium fluorapatite (Cd-FAP) was dissolved in 0.025 L of 1 M HNO 3 solution and diluted to 0.1 L in a volumetric flask with ultrapure water.e total cadmium, phosphor, and fluor contents were analyzed by a PerkinElmer inductively coupled plasma optical emission spectrometer (ICP-OES, Optima 7000DV) or a Dionex ion chromatography system (IC, ICS-2100).An X'Pert PRO diffractometer with Cu Kα radiation (40 kV and 40 mA) was applied to record the powder X-ray diffraction (XRD) pattern of Cd-FAP.Owing to no ICDD reference code for cadmium fluorapatite exist, the mineral phase was identified by comparing with the ICDD reference code for cadmium hydroxyapatite (00-014-0302).
e obtained Cd-FAP nanorods were morphologically observed using a Hitachi field emission scanning electron microscope (FE-SEM, S-4800) and characterized using a Nicolet Nexus Fourier transform infrared spectrophotometer (FT-IR, 470) in a KBr pellet within 4000-400 cm −1 .
e total cadmium, phosphor, and fluor contents were analyzed by a Dionex IC system (ICS-2100) and a PerkinElmer ICP-OES instrument (Optima 7000DV).After 7200 h dissolution, the Cd-FAP solids were taken out, rinsed with ultrapure water, dried, and analyzed with different instruments as described above.

2.3.
ermodynamic Calculations.All calculations were executed by the computer program PHREEQC using the minteq.v4.dat database (Version 3.1.2)[17].e PHREEQC input files use order-independent keyword data blocks and are of free-format, which ease the model constructing to simulate numerous aqueous-based scenarios.e aqueous Cd 2+ , PO 4 3− , and F − activities were first computed using PHREEQC, and then, the ion activity product (IAP) for cadmium fluorapatite [Cd 5 (PO 4 ) 3 F] was calculated after the mass-action expression.e aqueous species Cd 2+ , CdOH + , Cd(OH) 2 0 , Cd(OH)

Solid Characterization.
e component of the synthesized cadmium fluorapatite [Cd-FAP, Cd 5 (PO 4 ) 3 F] is dependent on the initial Cd : P : F ratio molar ratio in the precursor solution.e crystal nanorods were confirmed to be the aimed composition of Cd 5 (PO 4 ) 3 F. e atomic Cd : P : F ratio was 5 : 3 :1 that is the stoichiometric ratio of Cd 5 (PO 4 ) 3 F.No other components were detected in the white solid precipitate.
e Cd-FAP nanorods before and after dissolution were characterized using XRD, FT-IR, and FE-SEM.As showed in Figures 1-3, the synthetic Cd-FAP solids before and after dissolution were not distinguishable.No secondary minerals were evidenced after dissolution.e XRD patterns of the prepared solids are presented in Figure 1. e X-ray diffraction showed that all the solid samples were pure apatite with crystallizing in the hexagonal system P6 3 /m, which was confirmed by comparing with the JCPDS reference for cadmium hydroxyapatite (00-014-0302) (Figure 1).e Cd-FAP solids were highly crystallized and showed the formation of apatite nanorods with the lattice parameters of a � 9.3284 and c � 6.6378.e regular mode of the tetrahedral PO 4 3− ions includes v 4 (the O-P-O bending), v 3 (the P-O stretching), v 2 (the O-P-O bending), and v 1 (the symmetric P-O stretching).Only the absorptions of the v 4 and v 3 vibrations can be observed in the undistorted situation.e v 2 and v 1 vibrations are infrared inactive as the symmetry of the tetrahedral PO 4 3− is reduced [18,19].e FT-IR spectra of the Cd-FAP solids before and after dissolution are plotted together in Figure 2. e regular mode of the tetrahedral PO 3−  4 ions in the prepared cadmium fluorapatite could be observed in the region around 949 cm −1 (] 2 ), 1019 and 1100 cm −1 (] 3 ), and 561 and 590 cm −1 (] 4 ).e 712.60 cm −1 bands and the 3533∼3537 cm −1 bands were assigned to the vibrational motion of OH − ions and the stretching vibration of the bulk OH − ions, respectively [4,20].
e symmetric P-O stretching vibration (] 1 ) was not visible.e bands at 871 cm −1 , which were related to HPO 4 2− ions presenting in cation-deficient apatite, had not been detected [4].
e bands at 3650∼3680 cm −1 representing the P-OH groups [4] and the bands at 1455 cm −1 representing the CO 3 2− vibration [21] were also not observed in the FT-IR spectra.
As shown in Figure 3, the FE-SEM examination indicated that all the synthesized cadmium fluorapatite nanorods were the typical hexagonal crystals that elongated along the c axis (diameter <50 nm) and with or without pinacoids as terminations.No obvious morphological variation was found after dissolution for 7200 h.e early dissolution of the cadmium fluorapatite in water was nearly stoichiometric and then nonstoichiometric.During the Cd-FAP dissolution at an initial pH of 2 and 25 °C (Figure 4(a)), the solution pHs increased from 2.00 to 3.80 within 1 h and after that, varied between 3.72 and 3.95.e release rates of cadmium and phosphate increased quickly until the highest cadmium and phosphate concentrations appeared after 480 h and 1080 h, respectively.ereafter, the total dissolution rate of Cd-FAP slowly declined while the solution Cd : P molar ratios increased continually from 1.55∼1.67,which are near to the stoichiometric Cd : P molar ratio for Cd-FAP, to 3.18∼3.22(Figure 4(f )).Generally, the aqueous fluoride concentrations reached the highest value in 1 h and decreased rapidly from 1 h to 2160 h, and then, it increased slowly and attained a steady state after 5760 h.For the Cd-FAP dissolution at different temperatures, the solution pHs and aqueous Cd 2+ , PO 4 3− , and F − concentrations became constant after 5760 h indicating an achievement of a steady state between the solid and the solution (Figures 4(a  e transient peak values in the aqueous component concentrations during the apatite dissolution were also reported in some earlier works [13], which were probably due to the grain size distribution.e smaller the apatite grains, the greater the dissolution rate of apatite, and the larger the apatite solubility.Hence, the peak values may be a consequence of the fast dissolution of the smaller grains, followed by reprecipitation to larger grains, which resulted in the achievement of the asymptotic solubility [13].
e decrease in solution pH indicated that protons were consumed during the Cd-FAP dissolution, that is, the negatively charged O ions of surface PO 4 3− groups adsorbed protons from solution and transformed into HPO 4 2− , which accelerated the Cd-FAP dissolution.Additionally, the   stoichiometric ion exchange of 2H + from solution for Cd 2+ on the Cd-FAP surface and some other reactions also consumed protons [14,21].Besides, the dissolution mechanism of apatite is strongly dependent on the experimental condition such as temperature, solution composition, solid component, solid/solution ratio, and agitation [14].Diverse models for the apatite dissolution have been proposed, but most of them take only some specific dissolution aspects into account and cannot describe the general dissolution mechanism of apatite [14].
Based on our experimental results and the data obtained for the apatite dissolution by different researchers, the cadmium fluorapatite (Cd-FAP) dissolution in the aqueous media is proposed to comprise the following simultaneous processes: groups on the Cd-FAP surface [22], which resulted in an increase in the solution pHs from 2.00 to 3.80 in 1 h of dissolution.In comparison with the negative charged O ions of PO 4 3− groups on the Cd-FAP surface, H + ions should be adsorbed preferentially to the F − ions owing to their higher electronegativity [14].Meanwhile, the surface PO 4 3− groups were transformed into HPO 4 2− , which would catalyze the apatite dissolution [23].
Apatites are complex minerals, and when investigating their dissolution, several possible reactions must be considered [3].e dissolution of Cd-FAP according to reaction (1) is strongly dependent on the solution pH and coupled with protonation and complexation reactions (2)-( 4), which could result in an increase in the aqueous pHs for the Cd-FAP dissolution in the acidic solution or a decrease in the aqueous pHs for the dissolution in the alkali solution: e speciation calculation using PHREEQC indicated that, for the Cd-FAP dissolution at 25 °C and initial pH 2, the solution Cd species presented in the order of Cd 2+ > CdF + , CdNO 3 2− ; the solution phosphate species presented in the order of H 2 PO 4 − > H 3 PO 4 > HPO 4 2− > PO 4 3− ; and the solution fluoride species presented in the order of F − > HF > CdF + ≫ HF 2 − .In processes (iv) and (v), cadmium, phosphate, and fluoride ions were released from the Cd-FAP solid into solution nonstoichiometrically with the solution Cd : P molar ratios >1.67 and the solution Cd : F molar ratios >5.00, which might result in the formation of a surface layer with a component different from the bulk solid [14].Some amount of cadmium, phosphate, and fluoride were adsorbed from the solution back onto the Cd-FAP surface after an initial portion of Cd-FAP had dissolved, the solution F concentrations had started to decrease gradually within 1 h of dissolution in the present experiment, the solution phosphate concentrations began to decrease gradually after 1440 h of dissolution, and the solution Cd concentrations began to decrease gradually after 2880 h of dissolution at 25 °C and initial pH 2.
Fluorapatite dissolution might be started through a relatively fast and complete dissociation of F − ions from the solid surface [14,21].In processes (iii)∼(v), F − ions were dissociated faster than cadmium and phosphate ions, and then the dissolved F − ions were quickly adsorbed back to the Cd-FAP surface.As a result, the solution Cd : F ratio and P : F ratio became noticeably higher than the stoichiometric ratio of 5.00 and 3.00, respectively.e detachment of cadmium and phosphate ions followed the dissociation of F − ions from the Cd-FAP surface.e F − release was coupled to a quick hydrolysis of phosphate ions [21].O ions of PO 4 3− groups cover 80∼90% of the apatite surface [14].≡CdOH 2 + and ≡PO − are thought to be the two distinct groups on the surface.According to the surface protonation model, the FAP surface protonation in the solution of pH 5∼7 happened through the formation of ≡POH groups [24].In the early dissolution of apatite (1-6 h), the solution Cd : P ratios (1.55∼1.65)were a little smaller than its stoichiometric Cd : P ratio of 1.67, suggesting that PO 4 3− ions could be preferentially dissociated from the FAP surface in comparison to Cd 2+ ions.e corners and edges of the apatite crystal were predominantly occupied by PO 4 3− ions, and the apatite dissolution could start through the complexation of H + ions from solution with these weakly bounded PO 4 3− groups on the solid surface [14].Finally, the desorption-adsorption processes of cadmium, phosphate, and fluoride ions attained a steady state; that is, the solution cadmium, phosphate, and fluoride concentrations were constant for the Cd-FAP dissolution in the solution of pH 2 at 25 °C from 5760 h to the end of experiment (7200 h).

6
Journal of Chemistry

Determination of Solubility.
e aqueous Cd 2+ , PO 4 3− , and F − activities in the final equilibrated solution (5040 h, 5760 h, and 7200 h) were computed with the program PHREEQC to estimate the solubility product of the synthetic cadmium fluorapatite [Cd 5 (PO 4 ) 3 F].
e PHREEQC calculation also indicated that the final equilibrated solution was unsaturated with any possible secondary phases such as Cd 3 (PO 4 ) 2 , Cd(OH) 2 , and monteponite (CdO).
e dissolution reaction of cadmium fluorapatite [Cd 5 (PO 4 ) 3 F] and the dissociation of Cd 2+ , PO 4 3− , and F − are expressed by the dissolution equation (1).Assuming unit activity of Cd 5 (PO 4 ) 3 F: where {} is the thermodynamic activities of the Cd 2+ , PO 4 3− , and F − species and K sp is the solubility product of cadmium fluorapatite [Cd 5 (PO 4 ) 3 F] according to the dissolution equation ( 1).

Determination of ermodynamic Data.
e solubility products (K sp ) for Cd-FAP and Ca-FAP can also be estimated using Equations ( 9)-( 11) [25]: For Cd-FAP, For Ca-FAP, e thermodynamic quantities ΔG 0 , ΔH 0 , ΔS 0 , and ΔC 0 p for the Cd-FAP and Ca-FAP dissolution at an initial pH of 2 are estimated after Equations ( 12)-( 15) [25] and given in Table 2: where A, B, and C are the empirical constants of Equation ( 9). e negative values of ΔH 0 indicated that the Cd-FAP and Ca-FAP dissolution in the aqueous solution was an exothermic reaction, and their solubilities declined with the temperature rising.e larger negative value of ΔS 0 for the Cd-FAP dissolution showed that the order produced by the cadmium cations in the aqueous solution was a little higher than that by calcium cations [25], which was related to the ion size difference between Ca 2+ (0.99 Å) and Cd 2+ (0.97 Å).Generally, the smaller Cd 2+ ions with a high charge can result in a lower entropy in aqueous solution, and consequently, Cd-FAP is less soluble than Ca-HAP.But the very similar ion sizes of Cd 2+ and Ca 2+ resulted in a close solubility product for Cd-FAP and Ca-HAP under the experimental conditions.e values of ΔG 0 , ΔH 0 , and ΔS 0 for the Cd-FAP and Ca-HAP dissolution increased with the increasing temperature and indicated that their dissolution was an energy-consuming process [25].
For the Cd-FAP dissolution at an initial pH of 2 and 25 °C, the dissociation rates of fluoride, phosphate, and cadmium increased quickly until their highest solution concentrations were attained after dissolution for <1 h, 1440 h, and 2880 h, respectively.After that, the Cd-FAP dissolution decreased slowly while the solution Cd/P molar ratios increased steadily from 1.65∼1.67 to 3.18∼3.22.e solution pH increased from 2.00 to 3.80 within 1 h and then varied between 3.72 and 3.95.

Data Availability
e powder XRD data in XML format, the FT-IR data in XLSX format, and all solution analytical data in XLSX format used to support the findings of this study are available from the corresponding author upon request.

3. 2 .
Dissolution Mechanism.e solution Cd 2+ , PO 4 3− , and F − concentrations and pHs during the Cd-FAP dissolution at 25 °C, 35 °C, and 45 °C and different pHs as a function of time are shown in Figures 4(a)-4(f ).
(i) Diffusion of protons from the aqueous solution to the Cd-FAP surface (ii) H + adsorption onto the Cd-FAP surface coupled with protonation and chemical complexation/ transformation on the Cd-FAP surface (iii) Stoichiometric dissolution with Cd 2+ , PO 4 3− , and F − release from the Cd-FAP surface (iv) Nonstoichiometric dissolution with Cd 2+ and PO 4 3− release from the Cd-FAP surface and F − adsorption backwards onto the Cd-FAP surface (v) Nonstoichiometric dissolution with F − release from the Cd-FAP surface and Cd 2+ and PO 4 3− adsorption backwards onto the Cd-FAP surface For the dissolution of the synthetic cadmium fluorapatite at 25 °C and initial pH 2, in process (i) and process (ii), H + ions were adsorbed from the aqueous acidic solution to F − ions as well as to the negative charged O ions of PO 4 3−