Journal of Chemistry

Volume 2014 (2014), Article ID 654168, 11 pages

http://dx.doi.org/10.1155/2014/654168

Research Article

Dissolution and Solubility of the ()HAsO₄·H₂O Solid Solution in Aqueous Solution at 25°C and pH 2

Xuehong Zhang,¹ Yinian Zhu,¹ Caichun Wei,1,2 Zongqiang Zhu,¹ and Zongning Li¹

¹College of Environmental Science and Engineering, Guilin University of Technology, Guilin 541004, China

²College of Light Industry and Food Engineering, Guangxi University, Nanning 530004, China

Received 2 October 2013; Accepted 27 January 2014; Published 17 March 2014

Academic Editor: Stefan Tsakovski

Copyright © 2014 Xuehong Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Six different members of the ()HAsO₄·H₂O solid solution were prepared and characterized, and then dissolution of the synthetic solids was studied at 25°C and pH 2 in a series of batch experiments for 4320 h. With the increase in the Ba/() mole fraction of the solids, the aqueous pH decreased and the aqueous barium concentration increased. The aqueous strontium and arsenic concentrations had the highest values at . The solubility products for BaHAsO₄·H₂O and SrHAsO₄·H₂O were calculated to be and , respectively. The corresponding free energies of formation were determined to be − kJ/mol and − kJ/mol. The solid solution had a minimum solubility product of at . The Guggenheim coefficients were determined to be and . The Lippmann diagram was a typical Lippmann diagram for a nonideal solid solution with a negative enthalpy of mixing. The system shows an “alyotropic” minimum at the aqueous activity fraction of 0.87 where the solutus and solidus curves meet. At the end of the dissolution experiment, the dissolution followed the saturation curve for the pure endmember BaHAsO₄·H₂O and approached the intersection with the minimum stoichiometric saturation curve on the Lippmann diagram.

1. Introduction

Arsenic in natural waters is a worldwide problem. Arsenic has been known from antiquity to be highly toxic for animals and the majority of plants [1, 2]. Although arsenic has been classified at the top of the priority list of the most hazardous substances [3, 4], the crystal structures and the solubility as well as the thermodynamic properties of numerous arsenates remain poorly determined. This is an important handicap because an in-depth study of the arsenate behaviour in soils, sediments, and natural waters that have been subjected to pollution requires a precise knowledge of the possible precipitating phases, their crystal chemistry, and their thermodynamic properties. Furthermore, in multicomponent aqueous systems, the precipitation of solid solutions is always a possibility such that the study of arsenate solid solutions involving substitution between atoms of similar size and character is worthwhile [5, 6]. Previous studies indicate that, at high concentrations, compounds in this series could be a limiting phase for arsenic in natural aqueous environments [7, 8]. In solution, Ba tends to associate with As at pH 7.47–7.66, forming BaHAsO₄·H₂O and Ba₃(AsO₄)₂ [9]. This chemical interaction is used to remove As from aqueous solutions, but its efficiency depends on the solubility of both elements, which is altered by the physicochemical conditions of water [10, 11]. Tiruta-Barna et al. [12] also found that the leaching behaviour of arsenic from a compacted coal fly ash was controlled by the weak soluble phase BaHAsO₄·H₂O. The only available data on this series correspond to the strontium endmember, whose space group (Pbca), cell parameters, and atomic positions of Sr and As were determined by Binas and Boll-Dornberger [13]. From powder diffraction data, Martin et al. [14] determine the same space group for the barium endmember and suggest that SrHAsO₄·H₂O and BaHAsO₄·H₂O are isomorphous and therefore good candidates to form solid solutions. The previous data indicate that SrHAsO₄·H₂O and BaHAsO₄·H₂O form a complete solid solution where Sr²⁺ ions substitute for Ba²⁺. Both endmembers crystallize in the same orthorhombic Pbca space group, with lattice parameters that vary significantly with composition [4].

The determination of the equilibrium behaviour in SS-AS systems requires knowledge of both the endmember solubility products and the degree of nonideality of the solid solution [5]. Unfortunately, the lack of thermodynamic data for arsenates is even greater than the lack of crystal-chemical data. The value for BaHAsO₄·H₂O was determined to be 10−4.70 by Robins [10], 10−24.64 by Essington [15], 10−5.31 by Itoh and Tozawa [16], 10−0.8 by Orellana et al. [17], 10−5.51 by Davis [18], and 10−5.60 by Zhu et al. [9], which showed a great inconsistency of the currently accepted solubility data. Moreover, the solubility of the strontium endmember as well as the thermodynamic properties of the solid solution is unknown [4]. The fact that there is a significant preferential partitioning of barium toward the solid phase seems to indicate a lesser solubility (≈ one order of magnitude) for the strontium endmember. A thermodynamic character of these compounds needs to be confirmed [4].

In the present study, a series of the ()HAsO₄·H₂O solid solution with different Ba/(Ba + Sr) atomic ratios was prepared by a precipitation method. The resulting solid solution particles were characterized by various techniques. This paper reports the results of a study that monitors the dissolution and release of constituent elements from synthetic ()HAsO₄·H₂O solid solutions using batch dissolution experiments. The solid solution aqueous solution reaction paths are also discussed using the Lippmann diagram to evaluate the potential impact of such solid solutions on the mobility of arsenic in the environment.

2. Experimental Methods

2.1. Solid Preparation and Characterization

The experimental details for the preparation of the samples by precipitation were based on the following equation: + HA + H₂O = HAsO₄·H₂O, where = Ba²⁺ or Sr²⁺. The ()HAsO₄·H₂O solid solutions were synthesized by controlled mixing of a solution of 100 mL 0.5 M Na₃AsO₄ and a solution of 100 mL 0.5 M Ba(ClO₄)₂ and Sr(ClO₄)₂, so that the (Ba + Sr)/As molar ratio in the mixed solution was 1.00. The amounts of Ba(ClO₄)₂ and Sr(ClO₄)₂ were varied in individual syntheses to obtain synthetic solids with different mole fractions of Ba/(Ba + Sr) (Table 1). Reagent grade chemicals and ultrapure water were used for the synthesis and all experiments. The initial solutions were slowly mixed in a covered beaker in a course of 10 minutes at room temperature (°C). The resulting solutions were kept at 70°C and stirred at a moderate rate (100 rpm) using a stir bar. After one week to crystallize, the precipitates were allowed to settle. The resultant precipitates were then washed thoroughly with ultrapure water and dried for 24 h at <110°C to avoid decomposition of the solid samples obtained.

Table 1: Summary of synthesis and composition of the ()HAsO₄·H₂O solid solution.

Volumes of the precursors (mL)
Solid solution

Ba(ClO₄)₂
Sr(ClO₄)₂
Na₃AsO₄
Molecular formula

0.5 mol/L
0.5 mol/L
0.5 mol/L

0
100
100
SrHAsO₄·H₂O
0.00

20
80
100
(Ba0.21Sr0.79)HAsO₄·H₂O
0.21

40
60
100
(Ba0.42Sr0.58)HAsO₄·H₂O
0.42

60
40
100
(Ba0.61Sr0.39)HAsO₄·H₂O
0.61

80
20
100
(Ba0.82Sr0.18)HAsO₄·H₂O
0.82

100
0
100
BaHAsO₄·H₂O
1.00

The composition of the solid sample was determined. 50 mg of sample was digested in 10 mL of 2 M HNO₃ solution and then diluted to 50 mL with 2% HNO₃ solution. It was analysed for Ba, Sr, and As using an inductively coupled plasma atomic emission spectrometer (ICP-OES, Perkin Elmer Optima 7000DV). The synthetic solids were also characterised by powder X-ray diffraction (XRD) with an X’Pert PRO diffractometer using Cu Kα radiation (40 kV and 40 mA). Crystallographic identification of the synthesised solids was accomplished by comparing the experimental XRD pattern to standard compiled by the International Centre for Diffraction Data (ICDD), which were card 00-023-0823 for BaHAsO₄·H₂O and card 01-074-1622 for SrHAsO₄·H₂O. The morphology was analysed by scanning electron microscopy (SEM, Joel JSM-6380LV). Infrared transmission spectra (KBr) were recorded over the range of 4000–400 cm⁻¹ using a Fourier transformed infrared spectrophotometer (FT-IR, Nicolet Nexus 470 FT-IR).

2.2. Dissolution Experiments

1.5 g of the synthetic ()HAsO₄·H₂O solid was placed in 250 mL polypropylene bottle. 150 mL of 0.01 M HNO₃ (initial pH 2) was added to each bottle. The bottles were capped and placed in a temperature-controlled water bath (°C). Water samples (3 mL) were taken from each bottle on 18 occasions (1 h, 3 h, 6 h, 12 h, 1 d, 2 d, 3 d, 5 d, 10 d, 20 d, 30 d, 40 d, 50 d, 60 d, 75 d, 90 d, 120 d, and 180 d). After each sampling, the sample volume was replaced with an equivalent amount of ultrapure water. The samples were filtered using 0.20 μm pore diameter membrane filters and stabilised with 0.2% HNO₃ in 25 mL volumetric flask. Ba, Sr, and As were analysed by using an ICP-OES. After 180 d of dissolution, the solid samples were taken from each bottle, washed, dried, and characterised using XRD, FT-IR, and SEM in the same manner as described above.

2.3. Thermodynamic Calculations

Associated with each dissolution is an assemblage of solid phases, a solution phase containing dissolved calcium, phosphate, arsenate, and a pH value. Assuming equilibrium has been reached, the thermodynamic data can be calculated using established theoretical principles. In this study, the simulations were performed using PHREEQC (Version 3.1.1) together with the most complete literature database minteq.v4.dat, which bases on the ion dissociation theory. The input is free format and uses order-independent keyword data blocks that facilitate the building of models that can simulate a wide variety of aqueous-based scenarios [19]. The aqueous species considered in the calculations were Ba²⁺, BaOH⁺, BaAs, BaHAsO₄, BaH₂As, Sr²⁺, SrOH⁺, SrAs, SrHAsO₄, SrH₂As, H₃AsO₄, H₂As, HAs, and As. The activities of Ba²⁺(aq), Sr²⁺(aq), and HAs(aq) were firstly calculated by using PHREEQC, and then the ion activity products (IAPs) for ()HAsO₄·H₂O, BaHAsO₄·H₂O, and SrHAsO₄·H₂O were determined according to the mass-action expressions by using Microsoft Excel.

3. Results and Discussion

3.1. Solid Characterizations

The composition of the synthetic solid depends on the initial Ba : Sr : As mole ratio in the starting solution. To ensure that the ()HAsO₄·H₂O solid solution was formed, the precipitation was conducted by mixing barium solution, strontium solution, and arsenate solution at low rate. Results suggest that the crystal was the intended composition of ()HAsO₄·H₂O. The atomic (Ba + Sr)/As ratios were 1.00 which is a stoichiometric ratio of ()HAsO₄·H₂O. The atomic Ba/(Ba + Sr) ratios were almost the same as those of the precursor solutions . No Na⁺ and were detected in the prepared solid (Table 1).

XRD, FT-IR, and SEM analyses were performed on the solid samples of ()HAsO₄·H₂O before and after dissolution (Figures 1, 2, and 3). As illustrated in the figures, the results of the analyses on materials before the dissolution were almost indistinguishable from the following reaction. No evidence of secondary mineral precipitation was observed in the dissolution experiment.

Figure 1: XRD patterns of the (BaxSr1 − x )HAsO₄·H₂O solid solution before (A) and after (B) dissolution.

Figure 2: FT-IR patterns of the (BaxSr1 − x )HAsO₄·H₂O solid solution before (A) and after (B) dissolution.

(a)

(b)

Figure 3: SEM images of the (BaxSr1 − x )HAsO₄·H₂O solid solution before (A) and after (B) dissolution.

The XRD patterns of the obtained solids indicated the formation of the ()HAsO₄·H₂O solid solution, which has the same type structure as BaHAsO₄·H₂O (ICDD PDF 00-023-0823) and SrHAsO₄·H₂O (ICDD PDF 01-074-1622) (Figure 1). The patterns correspond exactly with the database patterns and no impurities are observed. The solid solution is complete, with the space group Pbca (orthorhombic) being retained throughout. BaHAsO₄·H₂O and SrHAsO₄·H₂O are the two endmembers of a structural family series. When subjected to XRD, they produce the same reflections; but the reflections exist at different two-theta values; that is, the reflective planes are the same but “” spacings are different. All the compounds have indicated the formation of a solid phase differing only in reflection location, reflection width, and absolute intensity of the diffraction patterns. The reflection peaks of BaHAsO₄·H₂O and SrHAsO₄·H₂O were slightly different from each other. The reflections of the ()HAsO₄·H₂O solid solutions shifted gradually to a lower-angle direction when the mole fraction of the solids increased (Figure 1).

The FT-IR spectra of the ()HAsO₄·H₂O solid solutions are shown in Figure 2. The spectra may be divided into three sections: (a) hydroxyl-stretching region, (b) water HOH bending region, and (c) arsenate As–O stretching and OAsO bending region [9]. The free arsenate ion, As, belongs to the point group . The normal modes of the tetrahedral arsenate ion are , symmetric As–O stretching; , OAsO bending; , As–O stretching; and , OAsO bending. In the undistorted state, only the absorptions corresponding to and vibrations are observed. The two remaining fundamentals and become infrared active when the configuration of the As ions is reduced to some lower symmetry [9]. The degenerate modes are split by distortion of the arsenate groups through lack of symmetry in the lattice sites. As shown in Figure 2, the bands of As appeared around 815.74, 814.92, and 693.82 cm⁻¹ () and 1747.66, 1662.27, 1620.03, and 1442.49 cm⁻¹ () for the endmember BaHAsO₄·H₂O and around 854.23, 814.92, 704.10 cm⁻¹ (), and 1465.20 cm⁻¹ () for the endmember SrHAsO₄·H₂O. For the ()HAsO₄·H₂O solid solutions, the and bands shifted slightly to a smaller wavenumber when the mole fraction of the solids increased.

Well-crystallized solids formed (Figure 3). The cell parameters and and volume increased and decreased in a nonlinear way with . The flaky appearance increased; that is, the morphology of the ()HAsO₄·H₂O solid solutions changed from short prismatic or granular crystals () to platy or blades crystals ().

3.2. Evolution of Aqueous Composition

The solution pH and element concentrations during the dissolution experiments at 25°C and initial pH 2 as a function of time are shown in Figure 4 for the ()HAsO₄·H₂O solid solution. The experimental results indicated that the dissolution could be stoichiometrical only at the very beginning of the process, and then dissolution became nonstoichiometrical and the system underwent a dissolution-recrystallization process that affects the ratio of the substituting ions in both the solid and the aqueous solution.

(a)

(b)

(c)

(d)

Figure 4: Change of the aqueous pH and component concentrations with dissolution time.

When dissolution progressed at the initial pH 2, the aqueous pHs increased rapidly from 2.00 to 5.51–7.71 within the first hour of the experiment. For the dissolution of the ()HAsO₄·H₂O solid solution with = 0.00, 0.21, 0.42, and 0.61, the solution pHs increased gradually from 1 h to 120 h and after that decreased gradually until they reached the steady state after 2160 h. For the dissolution of the solids with = 0.82 and 1.00, the aqueous pHs varied only slightly after 1 h and reached the steady state after 2160 h. The aqueous pHs decreased with the increasing of the ()HAsO₄·H₂O solid solution.

For the dissolution of the solids with = 0.21, 0.42, and 0.61, the aqueous Ba concentrations increased rapidly and reached the peak values within the first hour and then decreased gradually and reached the lowest peak values in 240 h. After that, they increased gradually and reached the steady state after 2160 h. For the dissolution of the solids with = 0.82 and 1.00, the aqueous Ba concentrations increased rapidly within the first six hours and then increased gradually in 6–480 h. After that, they decreased gradually and reached the steady state after 2160 h. The aqueous Ba concentrations increased with the increasing of the ()HAsO₄·H₂O solid solution.

When dissolution progressed at the initial pH 2, the aqueous Sr concentrations increased rapidly and reached the peak values within 120–480 h and then decreased gradually until they reached the steady state after 2880 h. The aqueous Sr concentrations increased with the increasing of the ()HAsO₄·H₂O solid solution with (or ) and decreased with the increasing of the solids with (or ); that is, the aqueous Sr concentrations had the highest value for the dissolution of (Ba0.21Sr0.79)HAsO₄·H₂O.

The aqueous As(V) concentrations increased rapidly and reached the peak values within the first hour and then decreased gradually and reached the lowest peak values in 48 h. After that, they increased gradually and reached the second peak values in 120–720 h. And then they decreased gradually and reached the steady state after 2880 h. The aqueous As(V) concentrations had the highest value for the dissolution of (Ba0.21Sr0.79)HAsO₄·H₂O.

3.3. Determination of Solubility and Free Energies of Formation

For the stoichiometric dissolution of the ()HAsO₄·H₂O solid solution according to

a stoichiometric ion activity product, IAP, can be written as

The activities of Ba²⁺(aq), Sr²⁺(aq), and HAs(aq) were firstly calculated by using PHREEQC [19], and then the IAP values for ()HAsO₄·H₂O, BaHAsO₄·H₂O, and SrHAsO₄·H₂O were determined according to the mass-action expression (2). The aqueous pH, Ba, Sr, and As concentrations had reached stable values after 2880 h dissolution and the IAP values of 2880 h, 3600 h, and 4320 h were considered as of the solids (Figure 4 and Table 2).

Table 2: Analytical data and solubility determination of the ()HAsO₄·H₂O solid solution.

Sample
Dissolution time (h)
pH
Concentration (mmol/L)

Average
(kJ/mol)

Ba
Sr
As

SrHAsO₄·H₂O
2880
7.96
0.00
9.08
12.88
−4.62
−4.62
−1537.94

3600
7.90
0.00
9.12
12.83
−4.62

4320
7.95
0.00
9.16
12.53
−4.62

(Ba0.21Sr0.79)HAsO₄·H₂O
2880
7.77
0.91
13.34
15.38
−4.70
−4.69
−1538.54

3600
7.77
0.98
13.32
15.54
−4.69

4320
7.74
0.94
13.32
15.53
−4.69

(Ba0.42Sr0.58)HAsO₄·H₂O
2880
6.86
1.63
8.73
11.68
−5.11
−5.13
−1541.25

3600
6.85
1.56
8.82
11.07
−5.13

4320
6.83
1.54
8.69
10.81
−5.15

(Ba0.61Sr0.39)HAsO₄·H₂O
2880
6.18
3.92
5.18
10.15
−5.45
−5.49
−1543.50

3600
6.10
3.91
5.17
10.17
−5.51

4320
6.06
3.93
5.20
10.24
−5.53

(Ba0.82Sr0.18)HAsO₄·H₂O
2880
5.72
9.45
1.55
11.58
−5.57
−5.61
−1544.24

3600
5.67
9.51
1.56
11.16
−5.63

4320
5.68
9.57
1.57
11.07
−5.62

BaHAsO₄·H₂O
2880
5.61
10.53
0.00
11.42
−5.49
−5.52
−1543.99

3600
5.56
10.56
0.00
11.25
−5.53

4320
5.57
10.69
0.00
10.94
−5.53

For (1),

Rearranging,

The standard free energy of reaction (), in kJ/mol, is related to at standard temperature (298.15 K) and pressure (0.101 MPa) by

The solution chemistry representing equilibrium involving the solution phase and ()HAsO₄·H₂O, along with the calculated log using PHREEQC, is shown in Table 2. Based on the obtained literature data,  kJ/mol,  kJ/mol,  kJ/mol,  kJ/mol, and the free energies of formation, [()HAsO₄·H₂O], were also calculated (Table 2).

The mean values were calculated for BaHAsO₄·H₂O of 10−5.52 (10−5.49–10−5.53) at 25°C, for SrHAsO₄·H₂O of 10−4.62 at 25°C. The corresponding free energies of formation () were determined to be − kJ/mol and  kJ/mol. The value of 10−5.52 for BaHAsO₄·H₂O is approximately 19.12log units higher than 10−24.64 reported by Essington [15] and approximately 4.72log units lower than 10−0.8 reported by Orellana et al. [17], but in accordance with those of Robins [10], Davis [18], and Zhu et al. [9] (10−4.70, 10−5.51, and 10−5.60, resp.). Essington [15] determined the solubility of BaHAsO₄·H₂O(c) based not on his own experimental measurement, but on the data of Chukhlantsev [20] for Ba₃(AsO₄)₂(c). He took the Ba₃(AsO₄)₂ solid used by Chukhlantsev [20] for BaHAsO₄·H₂O(c) and recalculated the original analytical data. Orellana et al. [17] determined the solubility product only from precipitation experiments. The aqueous solution in his experiment might not reach equilibrium and was still supersaturated with regard to the solid. Based on our experimental results and those available in the literature, the solubility product for BaHAsO₄·H₂O should be around 10−5.50.

BaHAsO₄·H₂O is less soluble than SrHAsO₄·H₂O. For the ()HAsO₄·H₂O solid solution, the solubility decreased as increased when and increased as increased when . The (BaxSr1 − x )HAsO₄·H₂O solid solution had a minimum solubility product of 10−5.61 at . This variation tendency is in accordance with the change of the unit cell parameters [4].

3.4. Saturation Index for BaHAsO₄·H₂O and SrHAsO₄·H₂O

The values of 10−5.52 for BaHAsO₄·H₂O and 10−4.62 for SrHAsO₄·H₂O were used in the calculation using the program PHREEQC in the present study. The calculated saturation indices for BaHAsO₄·H₂O show a trend of increasing values as the composition of the solid phases approaches that of the pure-phase endmember, BaHAsO₄·H₂O (Figure 5). At the beginning of the dissolution of the ()HAsO₄·H₂O solid solution, the BaHAsO₄·H₂O saturated index (SI) values increased with time until the aqueous solution was oversaturated with respect to BaHAsO₄·H₂O, and then the SI values decreased slowly. At the end of the dissolution experiment (2880–4320 h), the aqueous solution was saturated with respect to BaHAsO₄·H₂O for the ()HAsO₄·H₂O solid solution with SI = −0.06~0.10.

(a)

(b)

Figure 5: Saturation indices for BaHAsO₄·H₂O and SrHAsO₄·H₂O.

The calculated saturation indices for SrHAsO₄·H₂O show a distinctly different trend than those for BaHAsO₄·H₂O (Figure 5). For the ()HAsO₄·H₂O solid solution with , the SrHAsO₄·H₂O saturated index (SI) values decreased as the SrHAsO₄·H₂O mole fraction decreased or the BaHAsO₄·H₂O mole fraction increased for the ()HAsO₄·H₂O solid solution with . The SrHAsO₄·H₂O saturated index (SI) values increased with time for the ()HAsO₄·H₂O solid solution with . For the ()HAsO₄·H₂O solid solution with , the SrHAsO₄·H₂O saturated index (SI) values increased as the SrHAsO₄·H₂O mole fraction increased or the BaHAsO₄·H₂O mole fraction decreased for the ()HAsO₄·H₂O solid solution with . At the beginning of the dissolution, the SrHAsO₄·H₂O saturated index (SI) values increased with time until the aqueous solution was oversaturated with respect to SrHAsO₄·H₂O, and then the SI values decreased slowly. At the end of the dissolution experiment (4320 h), the aqueous solution was saturated with respect to SrHAsO₄·H₂O for the ()HAsO₄·H₂O solid solution with , while the aqueous solution was undersaturated with respect to SrHAsO₄·H₂O for the ()HAsO₄·H₂O solid solution with .

3.5. Lippmann Diagram

3.5.1. Construction of Lippmann Diagram

Understanding solid solution aqueous solution (SSAS) processes is of fundamental importance. However, in spite of the numerous studies, the availability of thermodynamic data for SSAS systems is still scarce [6]. Lippmann extended the solubility product concept to solid solutions by developing the concept of “total solubility product ,” which is defined as the sum of the partial activity products contributed by the individual endmembers of the solid solution [5, 6]. At thermodynamic equilibrium, the total activity product , expressed as a function of the solid composition, yields Lippmann’s “solidus ” relationship. In the same way, the “solutus ” relationship expresses as a function of the aqueous solution composition. The graphical representation of “solidus ” and “solutus ” yields a phase diagram, usually known as a Lippmann diagram [5, 6]. A comprehensive methodology for describing reaction paths and equilibrium end points in solid solution aqueous solution systems had been presented and discussed in literatures [5, 6, 21–23].

In the case of the ()HAsO₄·H₂O solid solution, the term “total solubility product ” is defined as the ({Ba²⁺} + {Sr²⁺}){HAs at equilibrium and can be expressed by

where designate aqueous activity. and , and , and and are the thermodynamic solubility products, the mole fractions , and the activity coefficients of the BaHAsO₄·H₂O and SrHAsO₄·H₂O components in the ()HAsO₄·H₂O solid solution, respectively. This relationship, called the solidus, defines all possible thermodynamic saturation states for the two-component solid solution series in terms of the solid phase composition.

The term “total solubility product ” can also be expressed by

where and are the activity fractions of the aqueous Ba and Sr components. This relationship, called the solutus, defines all possible thermodynamic saturation states for the two-component solid solution series in terms of the aqueous phase composition.

For a solid solution with fixed composition , a series of minimum stoichiometric saturation scenarios as a function of the aqueous activity fraction of the substituting ions in the aqueous solution can be described by

For the endmembers BaHAsO₄·H₂O and BaHAsO₄·H₂O and and , the endmember saturation equations can be written as

A Lippmann phase diagram for the ()HAsO₄·H₂O solid solution is a plot of the solidus and solutus as on the ordinate versus two superimposed aqueous and solid phase mole fraction scales on the abscissa.

3.5.2. Lippmann Diagram for the Ideal Solid Solution

In the ()HAsO₄·H₂O system, the endmember solubility products are −5.52 for BaHAsO₄·H₂O and −4.62 for SrHAsO₄·H₂O; that is, they differ by about 0.9 log units. The (BaxSr1 − x )HAsO₄·H₂O solid solutions are assumed ideal. In this case, the pure-phase solubility curves for BaHAsO₄·H₂O and SrHAsO₄·H₂O are quite distinct from the solutus, and the solution compositions along the solutus are clearly undersaturated with respect to both pure BaHAsO₄·H₂O and SrHAsO₄·H₂O solids. The dotted horizontal tie lines indicate the relation between the solid mole fractions and the aqueous activity fractions at thermodynamic equilibrium (points T2 and T1) or at primary saturation (points P2 and P1) with respect to a (Ba0.61Sr0.39)HAsO₄·H₂O solid. The dashed curve gives the series of possible () aqueous compositions that satisfy the condition of stoichiometric saturation with respect to a (Ba0.61Sr0.39)HAsO₄·H₂O solid. Point M1 is the “minimum stoichiometric saturation” point for a (Ba0.61Sr0.39)HAsO₄·H₂O solid.

As with all the “minimum stoichiometric saturation” curves, the “pure endmember saturation” curves plot above the solutus for all aqueous activity fractions, concurring with the solutus only for or equal to one. This can be seen in Figure 6, in which the curves and have been represented for the same solid solution as in Figure 6. Note that the two curves intersect at the point “S.” This point represents an aqueous solution at simultaneous stoichiometric saturation with respect to both endmembers.

Figure 6: Lippmann diagram for the (BaxSr1− x )HAsO₄·H₂O ideal solid solution.

The hypothetical reaction path is also shown in Figure 6, in relation to Lippmann solutus and solidus curves for the (Ba0.61Sr0.39)HAsO₄·H₂O solid solution. The reaction path of a stoichiometrically dissolving solid solution moves vertically from the abscissa of a Lippmann diagram, originating at the mole fraction corresponding to the initial solid solution composition. The pathway shows initial stoichiometric dissolution up to the solutus curve, followed by nonstoichiometric dissolution along the solutus, towards the more soluble endmember.

The difference between the solubility products of the endmembers involves a strong preferential partitioning of the less soluble endmember towards the solid phase. Our dissolution data indicate a final enrichment in the BaHAsO₄·H₂O component in the solid phase and a persistent enrichment in the Sr²⁺ component in the aqueous phase. The possibility of formation of a phase close in composition to pure BaHAsO₄·H₂O seems unavoidable, given the lower solubility of BaHAsO₄·H₂O and the oversaturation with respect to BaHAsO₄·H₂O and the relatively high solubility of SrHAsO₄·H₂O and the undersaturation with respect to SrHAsO₄·H₂O (Figure 5). From the point of view of the crystallization behavior, all data seem to indicate that there is a preferential partitioning of barium into the solid phase [4].

3.5.3. Lippmann Diagram for the Nonideal Solid Solution

Complementary powder XRD measurements indicated that the cell parameters increased in a nonlinear way with indicating the solid solution is complete but could be nonideal [4]. The solid phase activity coefficients of BaHAsO₄·H₂O () and SrHAsO₄·H₂O () as components of the solid solution can be calculated as a function of composition using the Redlich and Kister equations [5, 6], expressed in the form

where and are the mole fractions ( and ) of the BaHAsO₄·H₂O and SrHAsO₄·H₂O components in the (BaxSr1 − x )HAsO₄·H₂O solid solution; the Guggenheim coefficients and can be determined from an expansion of the excess Gibbs free energy of mixing [5, 6].

The excess Gibbs free energy of mixing has not been measured for the (BaxSr1 − x )HAsO₄·H₂O solid solution. Assuming that a stoichiometric saturation state was attained in the dissolution experiments, the Guggenheim coefficients and can be estimated from

Log IAP () values of the samples taken after 2880 h dissolution are shown as a function of in Figure 7. A plot of these log values versus solid mole fraction of BaHAsO₄·H₂O shows that the values are close to and slightly lower than what would be expected for an ideal solid solution. Fitting the values as a function of solid composition to (11) yields a best fit with a two-parameter Guggenheim model of and () (Figure 7).

Figure 7: Estimation of the Guggenheim coefficients for the (BaxSr1−x )HAsO₄·H₂O nonideal solid solution.

The diagram of Figure 8 is a typical Lippmann diagram for a solid solution with a negative enthalpy of mixing. The negative excess free energy of mixing produces a fall of the solutus curve with respect to the position of an equivalent ideal solutus. This means that the solubility of intermediate compositions is significantly smaller than that of an equivalent ideal solid solution. Indeed, for a certain range of solid compositions, the solutus values plot below the solubility product of the less soluble endmember. The system shows an “alyotropic” minimum at where the solutus and solidus curves meet. Such a point represents a thermodynamic equilibrium state in which the mole fraction of the substituting ions in the solid phase equals its activity fraction in the aqueous solution. Obviously, at the alyotropic point, the equilibrium distribution coefficient is equal to unity [5, 6].

Figure 8: Lippmann diagram for the (BaxSr1−x )HAsO₄·H₂O nonideal solid solution.

3.5.4. Solid Solution Aqueous Solution Reaction Paths

A Lippmann diagram for the (BaxSr1 − x )HAsO₄·H₂O solid solution for the ideal case when is shown in Figure 9. In addition to the solutus and the solidus, the diagrams contain the total solubility product curve at stoichiometric saturation for the (BaxSr1 − x )HAsO₄·H₂O solid solution at = 0.21, 0.42, 0.61, and 0.82. The saturation curves for pure endmembers BaHAsO₄·H₂O () and SrHAsO₄·H₂O () have also been plotted in the chart. Also included are the data from our study, plotted as ({Ba²⁺} + {Sr²⁺}){HAs versus .

Figure 9: Plot of the experimental data on the Lippmann diagram.

In general, the location of data points on a Lippmann diagram will depend on the aqueous speciation, degree to which secondary phases are formed, and the relative rates of dissolution and precipitation. As (BaxSr1 − x )HAsO₄·H₂O dissolves in solution, aqueous Ba²⁺ is converted into Ba²⁺, BaOH⁺, BaAs, BaHAsO4, and BaH₂As, and aqueous Sr²⁺ is converted into Sr²⁺, SrOH⁺, SrAs, SrHAsO4, and SrH₂As; aqueous HAs is converted primarily into As, H₂As, and H₃AsO₄ and only a fraction remains as Ba²⁺, Sr2+, and HAs. The smaller values of the activity fractions are a consequence of the Ba²⁺ and Sr²⁺ speciation. For the plot of the experimental data on the Lippmann diagram, the effect of the aqueous Ba²⁺ and Sr²⁺ speciation was considered by calculating the activity of Ba²⁺ and Sr²⁺ with the program PHREEQC.

The experimental data plotted on Lippmann phase diagrams show that the (Ba0.61Sr0.39)HAsO₄·H₂O precipitate dissolved stoichiometrically at the beginning and approached the Lippmann solutus curve and then overshot the Lippmann solutus curve, the saturation curves for pure endmembers BaHAsO₄·H₂O, and the stoichiometric saturation curve for . After about 1 h dissolution, the aqueous solution was oversaturated with respect to BaHAsO₄·H₂O and the (BaxSr1 − x )HAsO₄·H₂O solid solution. And then, the decreased from 0.61 to 0.21 in 240 h with no obvious change in the log value, indicating the dissolution path for this precipitate may involve stoichiometric dissolution to the Lippmann solutus curve and overshot the Lippmann solutus curve followed by a possible exchange and recrystallization reaction. From 240 to 4320 h, the log value decreased further, but the increased from 0.21 to about 0.43, and the dissolution followed the saturation curve for pure endmembers BaHAsO₄·H₂O and approached the intersection with the minimum stoichiometric saturation curve for .

4. Conclusions

With the increasing , the morphology of the (BaxSr1 − x )HAsO₄·H₂O solid solutions changed from short prismatic or granular crystals () to platy or blades crystals (). The synthetic solids used in the experiments were found to have no obvious variation after dissolution. During the dissolution of the solid solution, the aqueous pH values and component concentrations increased rapidly at the beginning and then varied slowly with time and finally exhibited stable state after 2880 h dissolution. With the increasing , the aqueous pH value decreased and the aqueous Ba concentration increased. At , the aqueous Sr and As concentrations had the highest values. The solubility products () for BaHAsO₄·H₂O and SrHAsO₄·H₂O were calculated to be 10−5.52 and 10−4.62, respectively. The corresponding free energies of formation () were  kJ/mol and  kJ/mol. BaHAsO₄·H₂O is less soluble than SrHAsO₄·H₂O. For the (BaxSr1 − x )HAsO₄·H₂O solid solution, the solubility decreased as increased when and increased as increased when . The (BaxSr1 − x )HAsO₄·H₂O solid solution had a minimum solubility product of 10−5.61 at . The Guggenheim coefficients were determined to be and for the (BaxSr1 − x )HAsO₄·H₂O nonideal solid solution. The constructed Lippmann diagram was a typical Lippmann diagram for a nonideal solid solution with a negative enthalpy of mixing, which produced a fall of the solutus curve with respect to the position of an equivalent ideal solutus, which indicated that the solubility of intermediate compositions is significantly smaller than that of an equivalent ideal solid solution. The system shows an “alyotropic” minimum at . At the end of the experiment, the dissolution followed the saturation curve for the pure endmember BaHAsO₄·H₂O and approached the intersection with the minimum stoichiometric saturation curve on the Lippmann diagram.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

The authors thank the financial supports from the National Natural Science Foundation of China (41263009, 40773059) and the Provincial Natural Science Foundation of Guangxi (2012GXNSFDA053022, 2011GXNSFF018003).

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