Solubility measurement and solid-liquid equilibrium model for the ternary system MgBr2 + MgSO4 + H2O at 288.15 K

THERMODYNAMICS

Solubility measurement and solid-liquid equilibrium model for the ternary system MgBr₂ + MgSO₄ + H₂O at 288.15 K

Dan Li^I,*; Bo Huang^II; Lingzong Meng^III,IV and Qinhong Xu^III

^ISchool of Media Communications, Phone/Fax: [phone], Linyi University, Linyi 276000, P. R. China. E-mail: [e-mail]

^IILinyi Institute of Product Quality Supervision, Inspection and Testing, Linyi, 276000, P. R. China

^IIISchool of Chemistry and Chemical Engineering, Linyi University, Linyi, 276000, P. R. China

^IVTianjin Key Laboratory of Marine Resources and Chemistry, Tianjin University of Science and Technology, Tianjin, 300457, P. R. China

ABSTRACT

The solubility of magnesium minerals and the refractive index of the ternary system MgBr₂ + MgSO₄ + H₂O at 288.15 K were investigated using an isothermal dissolution method. It was found that there are two invariant points in the phase diagram and the solubility isotherm of this ternary system consists of three branches, corresponding to equilibrium crystallization of Epsomite (MgSO₄·7H₂O, Eps), hexahydrite (MgSO₄·6H₂O, Hex) and magnesium bromide hexahydrate (MgBr₂·6H₂O, Mb). Neither solid solutions nor double salts were found. The refractive indices calculated from empirical equation are in good agreement with the experimental data. Combining the results from solubility measurements with the single-salt parameters for MgBr₂ and MgSO₄, and the mixed ion-interaction parameter θ, Br,S0₄ the parameter ψ Mg,Br,S0₄ at 288.15 K was fitted using the Pitzer theory and Harvie-Weare (HW) approach. In addition, the average equilibrium constants of the stable equilibrium solids at 288.15 K were obtained by a method using the activity product constant. A chemical model, which combined the Pitzer parameters and the average equilibrium constants, was constructed to calculate the solid + liquid equilibria in the ternary system MgBr₂ + MgSO₄ + H₂O at 288.15 K. The model agreed well with the equilibrium solubility data for the magnesium salts.

Keywords: Phase equilibrium; Phase diagram; Magnesium bromide; Solubility; Pitzer model.

INTRODUCTION

Bromine-containing brine is widely distributed in the Qinghai-Tibet Plateau and the Sichuan basin of China (Zheng et al., 1988; Sang et al., 2011). These brines belong mostly to the complex system Li + Na + K + Mg (Ca) + Cl +SO₄ + Br + borate + H₂O. The phase equilibria and phase diagrams are the theoretical foundations for exploiting the brine resources and describing the geochemical behaviour of the brine and mineral systems. Therefore, investigations of the thermodynamics and the phase diagram of brominecontaining systems at different temperatures are valuable, because this investigation provides the theoretical foundation and scientific guidance for the comprehensive and effective exploitation of bromine resources.

The phase equilibria of some three-, four- or fivecomponent bromine-containing systems have been reported (Sang et al., 2011; Cui et al., 2013; Christov, 2012a, 2012b and 2012c; Christov, 2011). The ternary system MgBr₂ + MgSO₄ + H₂O has previously been investigated at 273.15, 298.15 and 308.15 K since the 1960s, but the solubility data and the reports of the corresponding equilibrium solid phases are not complete. In the literature (Howard and Silcock, 1979), both MgSO₄·7H₂O and MgSO₄·6H₂O occur at 273.15 K, but no invariant points saturated with MgSO₄·7H₂O + MgSO₄·6H₂O have been reported yet. More complicatedly, at 298.15 K, there are five crystallisation fields, corresponding to MgSO₄·7H₂O, MgSO₄·6H₂O, MgSO₄·5H₂O, MgSO₄·H₂O and MgBr₂·6H₂O, but there is only one invariant point saturated with MgBr₂·6H₂O + MgSO₄·H₂O. At 308.15 K, there are only two crystallisation fields (MgBr₂·6H₂O and MgSO₄·7H₂O). All the data for the system MgBr₂ + MgSO₄ + H₂O system at 273.15, 298.15 and 308.15 K need to be investigated again. Recently, we reported a detailed study on the system at 323.15 K (Meng et al., 2013). It was found that there are four crystallisation fields MgSO₄·6H₂O, MgSO₄·4H₂O, MgSO₄·H₂O and MgBr₂·6H₂O. As it is known, the temperature in the Qinghai-Tibet Plateau in summer is nearly 288.15 K, but the ternary system at 288.15 K has not been reported in the literature to date.

Computer models, which can predict the behaviour of solutions and solid + liquid equilibria with close to experimental accuracy, have wide applicability. The current theory for aqueous solutions of electrolytes is reliable for calculating the solubilities of a salt-water system. There are also studies that embrace currently available theories of electrolyte solution chemistry to simulate the physicochemical processes of solutes, and these studies are able to predict thermodynamic behaviour. These widely used models are important for studying the geochemistry of natural waters and mineral deposits, as well as for solving environmental problems and optimising industrial processes (Christov, 2012a). Pitzer and co-workers developed an ion-interaction model and published a series of papers (Pitzer 1973; Pitzer 1992), which gave a set of expressions for the osmotic coefficients of a solution and the mean activity coefficients of electrolytes in solution. Single ion activity coefficients, which are more convenient to use in solubility calculations, are given in the Harvie and Weare modelling approach (Harvie and Weare, 1980; Harvie et al, 1984). On the basis of the Pitzer approach and its extension the Harvie-Weare (HW) model (denoted hereafter as the Pitzer and HW model), the solubilities of the systems containing bromine were predicted (Meng, 2013; Christov, 2012a, 2012b and 2012c; Christov, 2011), and these predictions demonstrated that the Pitzer and HW model could be expanded to calculate the solubility of bromine minerals in complex brines accurately. However, studies modelling the ternary system MgBr₂ + MgSO₄ + H₂O at 288.15 K are still lacking in the literature.

In this study, the solubilities and the relevant refractive indices of the ternary system MgBr₂ + MgSO₄ + H₂O at 288.15 K were determined. Additionally, a chemical model incorporating Pitzer theory and the HW approach was constructed to calculate the solid + liquid equilibrium in the ternary system.

EXPERIMENTAL SECTION

Apparatus and Reagents

A thermostatic shaker (model THZ-82, Jintan Yitong Electronics Co., Ltd., China) was used to prepare the solution in its equilibrium state. The temperature in the thermostatic bath was maintained at a constant temperature of (288.15 ± 0.1) K, and the detailed experimental procedures were described previously (Meng et al., 2011). The solid phase minerals were determined using Schreinemaker's method (Song, 1991) and an X-ray diffractometer (D8 Advance, Bruker Ltd., Germany). All the analytical grade chemicals, which were obtained from the Chengdu Aike Chemical Reagent Plant or the Shanghai Xinbao Fine Chemical Plant, were recrystallised before use, including magnesium bromide hexahydrate (MgBr₂·6H₂O, with mass fraction 0.98) and epsomite (MgSO₄·7H₂O, 0.99). Doubly deionised water (DDW) with a conductivity of less than 1.2×10^-4 S·m^-1 at 298.15 K was used to prepare the series of artificial, synthesised brines and for the chemical analysis.

Experimental Methods

The isothermal dissolution method was used in this study. A series of artificially synthesised brines were mixed from the appropriate quantities of salts and DDW, which were calculated according to the composition at phase equilibrium, and then were loaded into clean polyethylene bottles and capped tightly. The bottles were placed in a thermostatic rotary shaker, which was maintained at a constant temperature of (288.15 ± 0.1) K and a rotation speed of 120 rpm to accelerate equilibration of the complexes.

The rotary system rested for 2 h before sampling, and a 1.0 mL sample of the clarified solution was taken from each polyethylene bottle with a pipette at regular intervals and then used for a refractive index measurement. If the difference between two refractive index measurements was within ± 0.0002, then the equilibrium state was achieved. Otherwise, the solution was rotated continually until the equilibrium state was achieved. Generally, it took approximately 20 days to reach the equilibrium state. Twice, at different times, a sample of approximately 5.0 mL was taken, weighed and diluted to a final volume of 250 mL using a volumetric flask filled with DDW. Then, a quantitative analysis was performed. If the difference between the concentrations of the two liquid phases was within ± 0.3% in mass fraction, then the solubility of this equilibrium point, which was the average of the experimental data, was obtained. Meanwhile, some of the wet residue was separated from the solution, and one portion of the wet residue was weighed and dissolved to a final volume of 250 mL using a volumetric flask filled with DDW for chemical analysis by Schreinemaker's wet residue method (Song, 1991) (i.e., the solid phase mineral point lies on the extension of the line on the phase diagram through the composition points of the liquid phase and the wet residue). Another portion was dried, ground into powder and analysed by X-ray diffraction. The solid phase could then be identified.

Analytical Methods

The concentrations of the liquid phases and the wet residues were analysed with chemical analytical methods. The concentration of Mg²⁺ was determined with a precision of within ± 0.3% in mass fraction by titration with an EDTA standard solution in the presence of the indicator Eriochrome Black-T. The Brconcentration was measured by titration with a standard solution of Hg(NO3)2 using a mixed indicator of diphenylcarbazone and bromophenol blue (precision: ± 0.3%) (Zhai et al., 1988). The SO₄^2- concentration was calculated by subtraction via charge balance. An Abbe refractometer (model WZS-1) was used to measure the refractive index (nD) with an uncertainty of ± 0.0001. Through control with a thermostat, all measurements were conducted at the desired temperature of (288.15 ± 0.1) K.

RESULTS AND DISCUSSION

Solubility and Refractive Index Data

The solubility and the refractive index data of the system MgBr₂ + MgSO₄ + H₂O at 288.15 K are presented in Tables 1 and 2. The mineral concentrations in the stable equilibrium solutions and the wet residue are expressed as mass percentage. Based on the experimental data (Table 1), the stable phase diagram of the system at 288.15 K was plotted, as shown in Figure 1.

The stable phase diagram of the system at 288.15 K consists of three stable crystallisation fields corresponding to Epsomite (MgSO₄·7H₂O, Eps), hexahydrite (MgSO₄·6H₂O, Hex) and magnesium bromide hexahydrate (MgBr₂·6H₂O, Mb). Points E and F are the invariant points, which are saturated with Eps + Hex and Hex + Mb. Curves AE, EF and FB are the univariant curves, which are saturated with a single salt (Eps, Hex or, Mb). The Eps crystallisation area is relatively large; whereas, the Hex crystallisation area is relatively small. The smallest crystallisation area is that of Mb. These results indicate that magnesium sulphate is relatively easy to saturate and that magnesium bromide has a high solubility. Neither solid solutions nor double salts were found. Because it is known that the phase diagram of the MgCl2 + MgSO₄ + H₂O system at 288.15 K (Howard and Silcock, 1979) also consists of crystallisation fields corresponding to Eps, Hex and MgCl2·6H₂O (Bis), it is shown that magnesium bromide reacts with magnesium sulphate in solution similarly to magnesium chloride.

Using the refractive index data shown in Table 2, the relationships of the solutions' refractive index to the concentration of magnesium bromide were plotted in Figure 2. It is seen that the refractive indices of the solutions increase with the increase in magnesium bromide concentration, reach their maximum values at invariant point F (Hex + Mb), and then decrease. Using the diagram (Figure 2), the refractive index could be used to roughly estimate the magnesium bromide concentration in the ternary system.

Comparison of the Ternary System at Different Temperatures

The comparison of the solubility data for the ternary system MgBr₂ + MgSO₄ + H₂O at 273.15, 298.15, 308.15 K (Howard and Silcock, 1979), 323.15 K (Meng et al., 2013) and 288.15 K (this study) is shown in Figure 3. The patterns for the solubility curves at different temperatures are similar. The areas of the crystallised regions of magnesium bromide and magnesium sulphate decrease as the temperature increases, and these decreases indicate that the solubilities are positively correlated with temperature. The crystallisation zone for hydrated magnesium bromide was considerably smaller than that for hydrated magnesium sulphate. With this information, the mixture of magnesium bromide and magnesium sulphate salts can be separated and purified. There is one crystallisation field for hydrated magnesium bromide; whereas, there are many crystallisation fields for hydrated magnesium sulphate. Moreover, it is worthwhile to note that the crystallisation fields corresponding to hydrated magnesium sulphate differ greatly with temperature. Hydrated magnesium sulphate MgSO₄·7H₂O occurs when the temperatures are in the lower range (273.15, 288.15, 298.15 and 308.15 K); MgSO₄·6H₂O occurs at all five temperatures; whereas MgSO₄·4H₂O and MgSO₄·H₂O occur at relatively higher temperatures (308.15, 323.15 K). The crystallisation water for the hydrated magnesium sulphate decreases as the temperature increases. It shows that the water sorption decreases as the temperature increases and the stability field of different hydrates depends on temperature. This crystallisation information for the various minerals at different temperatures is important for the recovery of hydrated magnesium sulphate. Because of the lack of invariant points and of some crystallisation fields in the system at 273.15, 298.15 and 308.15 K, the differences between the diagrams at the five temperatures were not developed further.

Empirical Equation for the Refractive Index

Song and Du (Song and Du, 1986) have given an expression, which has been widely used in brine systems, for the refractive index and solubility data. The following empirical equation was used to calculate the refractive index:

where n₀ = 1.333390, the refractive index of water at 288.15 K. B_i is the coefficients of each possible component i in the system. W_i is the salt of i in the solution in mass fraction. For the calculation of the refractive index of MgBr₂ and MgSO₄, coefficients B_i were set to be 0.001725, 0.001328, respectively. The calculated results and experimental values are presented for comparison in Table 2, and the maximum relative deviations for all of the calculated results are less than 0.28%. The reasons for the relative errors in the data in Table 2 are multifarious and include the error in the solubility data caused by temperature deviations, the uncertainty in the concentration, and the uncertainty in the measurements of refractive index. The calculated values agree well with the experimental data, and this agreement shows that the coefficients B_i obtained in this work are reliable and can be used for more complicated systems containing MgBr₂ and MgSO₄ at 288.15 K.

SOLUBILITY PREDICTION

Ion-Interaction Model

The Pitzer theory and HW approach, which incorporate concentration dependent equations showing the specific interactions of the solutes (Pitzer 1973; Pitzer 1992; Harvie and Weare, 1980; Harvie et al, 1984), were used for the aqueous solutions in this study. Additional work has centred on developing variable temperature models below 298.15 K, which have increased applicability to a number of diverse geochemical systems (Spencer et al., 1990; Marion and Farren, 1999). The following equations, which are described in the literature (Pitzer 1992), are the main expressions related to the solubility calculation of this model.

In expressions (2) to (4), M, C and C' represent cations, X, A and A' represent anions, and N_C and N_Arefer to the number of cations and anions, respectively. Additionally, m_iand γ_i represent the concentration (mol·kg^-1) and the activity coefficient of the ions, respectively, Z_irefers to the valence of the ions, and ø refers to the permeability coefficient. The other symbols in Eqs. (3) to (5), for example, F, C, Z, A^Ø, Ψ, Φ, B^Ø , and B, are all described in the references (Harvie and Weare, 1980; Harvie et al, 1984).

For a hydrated salt, M X· H₂O, the solubility equilibrium constant (K_sp) for the dissolution reaction at a definite temperature and pressure is expressed as follows:

The activity of water is related to the osmotic coefficient ø, by the equation

where M_w is the molar mass of water (kg·mol^-1), and the sum covers all the solute species. The activity coefficients γ_i, and the osmotic coefficients ø can be calculated using the Pitzer and HW model.

The mean activity coeff icients γ_±, which are a function of the activity coefficients γ_M and γ_X in Equation (8), can also be calculated using the Pitzer theory and HW approach.

According to the Pitzer theory and HW approach, the activity and osmotic coefficients are parametric functions of β⁽⁰⁾, β⁽¹⁾, β⁽²⁾, C^Ø, θ_cc' and ψ;_cc'a; β⁽⁰⁾, β⁽¹⁾, β⁽²⁾, and C^Ø are the parameters of a single salt; θ_cc' represents the interaction between the two ions with the same sign, and ψ;_cc'a represents the interactions among the three ions, in which the sign of the third ion is different from the first two ions. By combining the Pitzer parameters and the equilibrium constants of single salts, a chemical model could be constructed to calculate the solid + liquid equilibrium in the ternary MgBr₂ + MgSO₄ + H₂O system at 288.15 K from Eqs. (2)-(8).

Model Parameterization

The Debye-Hückel parameter A^ø = 0.385646 at 288.15 K was obtained from the literature (Spencer et al., 1990). The Pitzer binary parameters for MgBr₂, and the mixing parameters θ were calculated from the temperature-dependent equations presented in the literature (Christov, 2011; Christov, 2012b). The Pitzer binary parameters for MgSO₄ can be gotten from the literature (Spencer et al., 1990; Marion and Farren, 1999), but the parameter β⁽²⁾ for MgSO₄ is not mentioned in the literature (Spencer et al., 1990). Therefore, the parameters for MgSO₄ used in this study were calculated using the literature (Marion and Farren, 1999). The solubility data for the ternary system MgBr₂ + MgSO₄ + H₂O in this study were used to fit the mixing parameters Ψ, via a multiple linear regression procedure. All the parameters used in the prediction are presented in Table 3. According to the parameters and the measured solubilities of the ternary system in this work, the equilibrium constants of the minerals in the ternary system at 288.15 K were fitted for each stable solution by a method using the activity product constant. For MgBr₂·6H₂O at 288.15 K, the lnKsp is 11.6742, which is very close to the data in the literature (Christov, 2011; Meng, 2013). For MgSO₄·7H₂O, the lnKsp calculated using the pure electrolyte parameters and the solubility data in our study is -4.7194, which is very close to the data in the literature (Marion and Farren, 1999), but the lnKsp for magnesium sulfate hydrate at the other points in the solubility isotherm are very different. The main reason may be that the parameters for MgBr₂ and MgSO₄ do not match. Another reason may be the deviation caused by the parameter fitting. Therefore, the average equilibrium constants (lnK_aver) of equilibrium solid salts were used to calculate the solubilities in this study. These average equilibrium constants (lnK_aver) and uncertainties for the equilibrium solid salts of MgSO₄·7H₂O, MgSO₄·6H₂O are presented in Table 4.

Validation and Application of the Model

In Figure 4, we calculated the mean activity coefficients of magnesium bromide and magnesium sulphate in the solutions (γ± vs. molality) up to the saturation molality at 288.15 K using Equation (8). In Figure 4(a), the mean activity coefficients of magnesium bromide increase with increasing concentrations of magnesium bromide. The γ± values first decrease with concentration to a wide minimum at low to moderate concentration, and an additional increase in molality leads to a sharp increase up to the equilibrium precipitation of the corresponding solids. The trend for the curve at 288.15 K is similar to that for the curve at 323.15 K, but the activity coefficients in bromide electrolyte systems at 288.15 K are smaller than those for systems at 323.15 K (Meng et al., 2013). This result represents another step that validates the present parameters for the bromide systems presented in Table 3. Compared with the curve in Figure 4(a), the curve in Figure 4(b) shows the opposite trend. The γ± values of magnesium sulphate first decrease sharply with concentration and then change relatively smoothly with concentration. The solubilities for the ternary system at 288.15 K were also calculated using Eqs. (2)-(7) to validate the accuracy of the model. It should be noted that solutes below their saturation molalities were fixed at their experimental values and the saturated solubilities were calculated. The comparison of the calculated and the experimental phase diagrams of the ternary system is shown in Figure 5. The calculated phase diagram and the experimental phase diagram are found to be in good agreement. These results indicate that the model obtained in this work that combines the Pitzer parameters and the equilibrium constants is reliable and is capable of predicting equilibrium in the system studied.

CONCLUSIONS

The stable equilibria of the aqueous ternary system MgBr₂ + MgSO₄ + H₂O were investigated at 288.15 K. The phase diagram and diagram of the variation in the refractive indices with composition were plotted for this system at 288.15 K. It was found that there are two three-salt cosaturated invariant points, three univariant solubility isotherms, and three stable crystallisation fields in the ternary system. Neither solid solutions nor double salts are found. The refractive indices of the solution are positively correlated with the concentration of magnesium bromide, with the maximum value occurring at point F (Hex + Mb). No significant differences are found among the diagrams of the ternary system at different temperatures; however, the crystallisation fields are very different, especially the fields for hydrated magnesium sulphate. The empirical equations were used to calculate the refractive indices; the coefficients have been fitted, and the calculated values for the refractive index are in good agreement with the experimental data.

The parameter ψ

at 288.15 K was fitted using the measured solubility data in this study, and the average equilibrium constants for stable equilibrium solids at 288.15 K were obtained with a method using the activity product constant. Based on Pitzer theory and the HW approach, a new chemical model, including the Pitzer parameters and the equilibrium constants, was constructed for the ternary system at 288.15 K. The model gave very good agreement with the equilibrium solubility data of the magnesium salts.

ACKNOWLEDGEMENTS

Financial support from the Foundation of Tianjin Key Laboratory of Marine Resources and Chemistry at Tianjin University of Science & Technology (Gant. 201101) and the Science Foundation of Linyi University (Grant. BS201005) are greatly acknowledged. We also thank Prof. P.S. Song from the Qinghai Institute of Salt Lakes for his kind help.

NOMENCLATURE

A ^Ø Debye-Hückel parameter B ^Ø parametric functions of Pitzer parameter B parametric functions of Pitzer parameter B' parametric functions of Pitzer parameter C ^Ø

single-salt Pitzer parameter

C

parametric functions of Pitzer parameter

f ^γ parametric functions of Pitzer parameter g(x), g'(x)

parametric functions of Pitzer parameter

I ionic strength mol/kg Ksp

solubility equilibrium constant

m molality mol/kg M,C cation n neutral molecules X, A anion z

valence of ions

Z parametric functions of the molality of species i Greek Letters α_w water activity β⁽⁰⁾ single-salt Pitzer parameter β⁽¹⁾ single-salt Pitzer parameter β⁽²⁾ single-salt Pitzer parameter υ number of ions in the molecule γ activity coefficient of the ions ø

osmotic coefficients

θ mixing ion interaction Pitzer parameter Ψ mixing ion interaction Pitzer parameter

(Submitted: July 12, 2013; Revised: August 28, 2013; Accepted: September 23, 2013)

• Christov, C., Study of bromide salts solubility in the (m₁KBr + m₂CaBr₂)(aq) system at T = 323.15 K. Thermodynamic model of solution behaviour and (solid + liquid) equilibria in the ternaries (m₁KBr + m₂CaBr₂) (aq), and (m₁MgBr₂ + m₂CaBr₂)(aq), and in the quinary (Na + K + Mg + Ca + Br + H₂O) systems to high concentration and temperature. J. Chem. Thermodyn., 55,7-22 (2012).
• Christov, C., Temperature variable chemical model of bromide-sulfate solution interaction parameters and solid-liquid equilibria in the Na-K-Ca-Br- SO₄-H₂O system. CALPHAD, 36,71-81 (2012).
• Christov, C., Study of bromide salts solubility in the (m₁NaBr + m₂MgBr₂)(aq) system at T = 323.15 K. Thermodynamic model of solution behavior and (solid + liquid) equilibria in the (Na + K + Mg + Br + H₂O) system to high concentration and temperature. J. Chem. Thermodyn., 47,335-340 (2012).
• Christov, C., Isopiestic investigation of the osmotic coefficients of MgBr₂(aq) and study of bromide salts solubility in the (m₁KBr + m₂MgBr₂)(aq) system at T = 323.15 K. Thermodynamic model of solution behaviour and (solid + liquid) equilibria in the MgBr₂(aq), and (m₁KBr + m₂MgBr₂) (aq) systems to high concentration and temperature. J. Chem. Thermodyn., 43, 344-353 (2011).
• Cui, R. Z., Sang, S. H., and Hu, Y. X., Solid-liquid equilibria in the quaternary systems KCl-KBr- K2B4O7-H₂O and KCl-KBr-K2SO₄-H₂O at 373 K. J. Chem. Eng. Data, 58,477-481 (2013).
• Harvie, C. E., Møller, N. and Weare, J. H., The prediction of mineral solubilities in nature waters: The Na-K-Mg- Ca-H-SO₄-OH-HCO3-CO3-H₂O system to high ionic strengths at 25 şC. Geochim. Cosmochim. Acta, 48,723-751 (1984).
• Harvie, C. E., and Weare, J. H., The prediction of mineral solubilties in nature waters: The Na-K-Mg- Cl-SO₄-H₂O system from zero to high concentration at 25 şC. Geochim. Cosmochim. Acta, 44,981-997 (1980).
• Howard, D. and Silcock, L., Solubilities of Inorganic and Organic Compounds. Pergamon Press, New York (1979).
• Marion, G. M. and Farren, R. E., Mineral solubilities in the Na-K Mg-Ca-Cl-SO₄-H₂O system: A reevaluation of the sulfate chemistry in the Spencer-Moller-Weare model. Geochim. Cosmochim. Acta, 63,1305-1318 (1999).
• Meng, L. Z., Deng, T. L., Guo, Y. F., Li, D. and Yang, L., Measurement and thermodynamic model study on solid + liquid equilibria and physicochemical properties of the ternary system MgBr₂ + MgSO₄ + H₂O at 323.15 K. Fluid Phase Equilib., 342,8894 (2013).
• Meng, L. Z., Li, D., Guo, Y. F. and Deng, T. L., Stable phase equilibrium of the aqueous quaternary system (MgCl2 + MgSO₄ + MgB₆O₁₀ + H₂O) at 323.15 K. J. Chem. Eng. Data, 56,5060-5065 (2011).
• Pitzer, K. S., Thermodynamics of electrolytes I: Theoretical general equation. J. Phys. Chem., 77,268-277 (1973).
• Pitzer, K. S., Activity coefficients in electrolyte solutions. 2nd Ed., CRC Press, London (1992).
• Sang, S. H., Sun, M. L., Li, H., Zhang, X. and Zhang, K. J., A study on equilibria of the quaternary system Na⁺,K⁺//Br^-,SO₄^2--H₂O at 323 K. Chin. J. Inorg. Chem., 27, 845-849 (2011).
• Song, P. S., Studies on the application of the wet residues method in phase equilibrium for the saltwater systems. J. Salt Lake Res., (China), 1, 4246 (1991).
• Song, P. S., and Du, X. H., Phase equilibrium and properties of the saturated solution in the quaternary system Li2B4O7-Li2SO₄-LiCl-H₂O at 25 şC. Chin. Sci. Bull., (China), 3,209-213 (1986).
• Spencer, R. J., Moller, N., and Weare, J. H., The prediction of mineral solubilities in natural water: A chemical equilibrium model for the Na-K-Ca-Mg- Cl-SO₄-H₂O system at temperature below 25 şC. Geochim. Cosmochim. Acta, 54,575-590 (1990).
• Zhai, Z. X., Cheng, Z. B., Hu, F., Wu, G. L., Xiao, Y. K. and Liu, F. M., Analytical Methods of Brines and Salts. 2nd Ed., Qinghai Institute of Salt Lakes, Chinese Academy of Science. Chin. Sci., Press, Beijing (1988)
• Zheng, X. Y., Tang, Y. and Xu, C., Tibet Saline Lake. Science Press, Beijing, China (1988).

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To whom correspondence should be addressed

Publication Dates

• Publication in this collection
  07 July 2014
• Date of issue
  June 2014

History

• Accepted
  23 Sept 2013
• Reviewed
  28 Aug 2013
• Received
  12 July 2013