Solid–Liquid Phase Equilibria of the Aqueous Ternary System

Article pubs.acs.org/jced

Solid−Liquid Phase Equilibria of the Aqueous Ternary System (MgSO4 + Mg2B6O11 + H2O) at (288.15, 298.15, and 308.15) K Huan Wang,† Long Li,† Mengxue Wang,† Xuanpeng Lei,† Yafei Guo,*,†,‡ and Tianlong Deng† †

Tianjin Key Laboratory of Marine Resources and Chemistry, College of Chemical Engineering and Materials Science, Tianjin University of Science and Technology, Tianjin 300457, P. R. China ‡ College of Chemistry and Materials Science, Northwest University, Xi’an 710127, P. R. China ABSTRACT: Solubilities, densities, refractive indices, and pH values for the ternary system (MgSO4 + Mg2B6O11 + H2O) at (288.15, 298.15, and 308.15) K and 0.1 MPa, obtained using the method of isothermal dissolution equilibrium, are reported for the first time. On the basis of the experimental data, the phase diagrams and the physicochemical properties of density, refractive index, and pH versus concentration of magnesium sulfate were plotted. It was found that there are one invariant point, two univariant curves, and two crystallization regions corresponding to inderite (Mg2B6O11·15H2O, Inde) and epsomite (MgSO4·7H2O, Eps). The crystallized area of inderite is larger than that of epsomite at three temperatures, indicating that the solubility of inderite is lower than that of epsomite. Comparison of the phase diagrams at (288.15, 298.15, and 308.15) K shows that the areas of Inde and Eps increase with increasing temperature. There are no solid solutions and double salts at these three temperatures in this system. The density and refractive index of this ternary system at the three temperatures change regularly with the changing concentration of magnesium sulfate. Empirical equations for the density and refractive index were further used to correlate the data, and the calculated results agree well with the experimental values at the three temperatures.

1. INTRODUCTION The salt lake brine resources with high concentrations of magnesium and boron are widely distributed in western China.1 To exploit the surface brine and the solid-mixture minerals of epsomite (MgSO4·7H2O) and inderite (Mg2B6O11·15H2O) deposited in salt lakes, the phase diagrams of the solid−liquid ternary system (MgSO4 + Mg2B6O11 + H2O) are essential. It should be pointed out that the literature has reported that the structures of the boron ions of inderite, hungchaoite (MgB4O7·9H2O), and mcallisterite (MgB6O10·7.5H2O) are B6O7(OH)62−, B4O5(OH)42−, and B3O3(OH)52−, but B6O114−, B4O72−, and B6O102−, respectively, are used in this paper for subsequent description convenience.2 To date, there have been a number of literature reports on the stable phase equilibria of the system (Mg2+//Cl−, SO42−, B4O72−−H2O),3,4 the quaternary interaction system (Li+, Mg2+//B4O72−, SO42−−H2O),5,6 and its

subsystem (Mg2+//SO42−, B4O72−−H2O).7 Although the metastable equilibrium data on the quaternary system (MgCl2 + MgSO4 + MgB6O10 + H2O) at 323.15 K were reported previously,8 there are no phase equilibrium data concerning inderite in the

Table 1. Reagents Used in This Study

Figure 1. X-ray diffraction pattern of inderite (Mg2B6O11·15H2O).

initial mass fraction purity

purification method

final mass fraction purity

Inde

b

A.R.

0.99

recrystallization

0.998

Epsc

A.R.d

0.99

recrystallization

0.998

chemical name source a

analysis method

literature. In this work, the solubilities and relevant physicochemical properties, including density, refractive index, and pH, for the ternary system (MgSO4 + Mg2B6O11 + H2O) were measured at (288.15, 298.15, and 308.15) K using the classical isothermal dissolution method.9

gravimetric method for B6O114− gravimetric method for SO42−

Inde = inderite, Mg2B6O11·15H2O. bSynthesized in our laboratory. Eps = epsomite, MgSO4·7H2O. dFrom the Sinopharm Chemical Reagent Co. Ltd.

a

Received: April 22, 2017 Accepted: August 17, 2017 Published: September 6, 2017

c

© 2017 American Chemical Society

3334

DOI: 10.1021/acs.jced.7b00378 J. Chem. Eng. Data 2017, 62, 3334−3340

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2. EXPERIMENTAL SECTION

Table 2. Solubility, Density, and Refractive Index of the Binary System (MgSO4 + H2O) at (288.15, 298.15, and 308.15) K and p = 0.1 MPaa T/K

solubility in water (100wb)

nD

ρ/(g·cm−3)

ref

24.62 24.44 24.74 24.59 27.18 27.25 26.89 27.18 29.55 29.82 29.82 29.74

− − − 1.3840 − − 1.3883 1.3895 − − − 1.3902

1.2691 − − 1.27447 − − 1.3022 1.30241 − − 1.3353 1.32591

13 14 15 this work 15 15 16 this work 14 17 18 this work

288.15

298.15

308.15

a b

c

Apparatus. A magnetic stirring thermostatic water bath (HXC-500-6A, Beijing Fortune Joy Science Technology Co. Ltd., China) was used to control the temperature with an uncertainty of ±0.01 K. The densities (ρ) of solutions were measured with an digital U-tube densimeter (DMA 4500, Anton Paar, Austria) with a precision of 1.0 × 10−5 g·cm−3 and an uncertainty of ±0.5 mg·cm−3. An Abbe refractometer (WAY-2S, Shanghai Yuguang Instrument Co. Ltd., China) was used to measure the refractive indices (nD) with an uncertainty of ±0.0001 at the 0.68 level of confidence. The pH values were measured using a high-precision pH meter (PH-7310, WTW Co. Ltd., Germany) with a standard uncertainty of ±0.001 at the 0.68 level of confidence. All of the measurements were controlled to within ±0.01 K at the desired temperature (T = 288.15 K, 298.15 K, or 308.15 K) by a circulating water bath (K20-cc-NR, Huber, Germany).

The standard uncertainties u are u(T) = 0.1 K and u(p) = 0.005 MPa. w is the mass fraction. cNot measured.

Table 3. Solubilities, Experimental and Calculated Values of Refractive Index and Density, and pH Values for the Ternary System (MgSO4 + Mg2B6O11 + H2O) at (288.15, 298.15, and 308.15) Ka physicochemical properties composition of liquid phase (100wb)

ρ/g·cm−3

no.

MgSO4

Mg2B6O11

exptl

calcd

1, A1 2 3 4 5 6 7, E1 8 9 10 11, B1

0.00 4.72 8.85 12.97 16.99 21.22 24.41 24.52 24.30 24.25 24.59

0.23 0.28 0.34 0.40 0.45 0.49 0.51 0.46 0.24 0.15 0.00

1.00246 1.05034 1.09475 1.14260 1.18991 1.24161 1.28206 1.28129 1.27839 1.27717 1.27447

1.00085 1.04995 1.09502 1.14191 1.18952 1.24164 1.28235 1.28329 1.27831 1.27679 1.27329

1, A2 2 3 4 5 6 7, E2 8 9 10 11, B2

0.00 3.22 5.67 11.00 22.11 25.69 27.38 27.48 27.48 27.62 27.18

0.27 0.33 0.38 0.46 0.62 0.65 0.67 0.49 0.28 0.08 0.00

0.99956 1.03214 1.06049 1.11519 1.24030 1.28197 1.30990 1.30814 1.30520 1.30463 1.30241

0.99950 1.03167 1.05679 1.11356 1.24164 1.28570 1.30708 1.30631 1.30377 1.30319 1.30285

1, A3 2 3 4 5 6, E3 7 8 9 10, B3

0.00 6.10 15.23 18.18 19.38 29.50 29.46 29.54 29.58 29.74

0.32 0.51 0.68 0.72 0.74 0.89 0.88 0.56 0.28 0.00

0.99748 1.05839 1.15910 1.19252 1.20747 1.33424 1.33018 1.33237 1.32940 1.32591

0.99755 1.06036 1.16056 1.19474 1.20901 1.33554 1.33479 1.33124 1.32752 1.32553

nD relative error/%

exptl

calcd

T = 288.15 K and p = 0.1 MPa 0.16 1.3350 1.3338 0.04 1.3430 1.3438 −0.02 1.3521 1.3525 0.06 1.3611 1.3613 0.03 1.3702 1.3700 0.00 1.3795 1.3791 −0.02 1.3860 1.3860 −0.16 1.3860 1.3861 0.01 1.3852 1.3851 0.03 1.3852 1.3848 0.09 1.3840 1.3841 T = 298.15 K and p = 0.1 MPa 0.01 1.3335 1.3326 0.05 1.3395 1.3392 0.35 1.3444 1.3441 0.15 1.3553 1.3551 −0.11 1.3776 1.3781 −0.29 1.3846 1.3856 0.22 1.3901 1.3891 0.14 1.3894 1.3892 0.11 1.3883 1.3891 0.11 1.3881 1.3893 −0.03 1.3895 1.3893 T = 308.15 K and p = 0.1 MPa −0.01 1.3322 1.3320 −0.19 1.3439 1.3444 −0.13 1.3626 1.3631 −0.19 1.3686 1.3691 −0.13 1.3712 1.3716 −0.10 1.3926 1.3926 −0.35 1.3924 1.3925 0.08 1.3916 1.3919 0.14 1.3910 1.3913 0.03 1.3902 1.3910 3335

relative error/%

pH

equilibrium solid phasec

0.08 −0.06 −0.04 −0.02 0.01 0.03 0.00 −0.01 0.00 0.02 −0.01

9.675 8.936 8.729 8.535 8.296 8.114 7.750 7.736 7.722 7.699 7.242

Inde Inde Inde Inde Inde Inde Inde+Eps Eps Eps Eps Eps

0.07 0.03 0.02 0.01 −0.04 −0.07 0.07 0.01 −0.06 −0.08 0.01

9.316 8.660 8.538 8.227 7.915 7.917 7.518 7.440 7.405 7.233 6.628

Inde Inde Inde Inde Inde Inde Inde+Eps Eps Eps Eps Eps

0.01 −0.04 −0.04 −0.04 −0.03 0 0 −0.02 −0.02 −0.05

9.137 8.156 7.781 7.701 7.638 7.212 7.358 7.201 7.196 6.055

Inde Inde Inde Inde Inde Inde+Eps Eps Eps Eps Eps

DOI: 10.1021/acs.jced.7b00378 J. Chem. Eng. Data 2017, 62, 3334−3340

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Table 3. continued a

The standard uncertainties u are u(T) = 0.1 K and u(p) = 0.005 MPa. u(w) for MgSO4 and Mg2B6O11 are 0.00063 and 0.00060 in mass fraction, respectively. u(x) for ρ, nD, and pH are 0.5 mg·cm−3, 0.001, and 0.01, respectively. bw is the mass fraction cInde, Mg2B6O11·15H2O; Eps, MgSO4·7H2O.

Figure 4. Stable phase diagram of the ternary system (MgSO4 + Mg2B6O11 + H2O) at 308.15 K: △, experimental points at 308.15 K; , solubility curve at 308.15 K; Inde denotes inderite, Mg2B6O11· 15H2O; Eps denotes epsomite, MgSO4·7H2O.

Figure 2. Stable phase diagram of the ternary system (MgSO4 + Mg2B6O11 + H2O) at 288.15 K: ●, experimental points at 288.15 K; , solubility curve at 288.15 K; Inde denotes inderite, Mg2B6O11· 15H2O; Eps denotes epsomite, MgSO4·7H2O.

ternary system were loaded into bottles, which were then capped and placed in the magnetic stirring thermostatic water bath and stirred at 120 rpm to reach equilibrium. At regular intervals, a proper amount of clarified supernatant was taken out for chemical analysis of the liquid phase. When the composition in each bottle was constant, the equilibrium was achieved. Generally, about 90 days was needed for the boratecontaining system to reach equilibrium. After the system reached equilibrium, the magnetic stirring was stopped, and then the supernatant liquids were taken out for quantitative chemical analysis and measurements of the physicochemical properties (density, refractive index, and pH). The solid phase was identified by X-ray diffraction (XD-3 diffractometer, Beijing Purk. Instrument Co. Ltd., China) and digital polarizing microscopy (BX51 microscope, Olympus, Japan). Analytical Method. The concentration of Mg2+ was determined using the EDTA complexometric titration method with an uncertainty of ±0.003 in mass fraction.11 The SO42− concentration was analyzed by the gravimetric method using barium chloride as the precipitator with an uncertainty of ±0.0005. The concentration of B6O114− was evaluated by the gravimetric method using mannitol with an uncertainty of ±0.0005 in mass fraction.12 According to the analytical data on the concentrations of SO42− and B6O114− in solution, the MgSO4 and Mg2B6O11 contents were calculated with uncertainties of ±0.00063 and ±0.00060 in mass fraction, respectively.

Figure 3. Stable phase diagram of the ternary system (MgSO4 + Mg2B6O11 + H2O) at 298.15 K: ▲, experimental points at 298.15 K; , solubility curve at 298.15 K; Inde denotes inderite, Mg2B6O11· 15H2O; Eps denotes epsomite, MgSO4·7H2O.

Reagents. The reagents were recrystallized before use and are listed in Table 1. Inderite (Mg2B6O11·15H2O) was synthesized in our laboratory,10 and Figure 1 shows its characterization by XRD analysis. Doubly deionized water (pH 6.60, κ < 1 × 10−4 S·m−1 at 298.15 K) was used in the whole work. Experimental Method. The classical method of isothermal dissolution equilibrium was used.9 A series of samples for the

3. RESULTS AND DISCUSSION Although no data have been reported for the binary subsystem (Mg2B6O11 + H2O), the solubility data for the binary subsystem (MgSO4 + H2O) at three temperatures are reported in the literature and are shown in Table 2.13−18 A comparison shows that the solubilities of magnesium sulfate at (288.15, 298.15, and 3336

DOI: 10.1021/acs.jced.7b00378 J. Chem. Eng. Data 2017, 62, 3334−3340

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Figure 6. Comparison of the stable phase diagrams of the ternary system (MgSO4 + Mg2B6O11 + H2O) at (288.15, 298.15, and 308.15) K: ●, experimental points at 288.15 K; ▲, experimental points at 298.15 K; △, experimental points at 308.15 K; ·-·-·-, solubility curve at 288.15 K; , solubility curve at 298.15 K; - - -, solubility curve at 308.15 K; Inde denotes inderite, Mg2B6O11·15H2O; Eps denotes epsomite, MgSO4·7H2O. Figure 5. X-ray diffraction patterns of (a) epsomite (MgSO4·7H2O) and (b) (Mg2B6O11·15H2O + MgSO4·7H2O) at the invariant points at the three temperatures.

100w(Mg2B6O11) = 0.89 and 100w(MgSO4) = 29.50). The corresponding X-ray diffraction patterns are drawn in Figure 5, which shows that salts Mg2B6O11·15H2O and MgSO4·7H2O coexist at the invariant points E1, E2, and E3. The crystallized area of Inde is much larger than that of Eps at the three temperatures. The reason is that Mg2B6O11 has low solubility in water. Before the invariant point is reached, the solubility of Mg2B6O11 is increasing with increasing MgSO4 content, which indicates that MgSO4 has a solubilizing effect on Mg2B6O11. Neither solid solutions nor double salts in this ternary system were formed at these three temperatures. Figure 6 shows a comparison of the phase diagrams for the ternary system at the three temperatures (dot-dashed line for 288.15 K, solid line for 298.15 K, and dashed line for 308.15 K). Those results indicate that the system at these three temperatures belongs to hydrate type I. The single solubilities of MgSO4 and Mg2B6O11 in mass fraction (100w) in each boundary subsystems at (288.15, 298.15, and 308.15) K are 24.59, 27.18, and 29.74 and 0.23, 0.27, and 0.32, respectively. In other words, the solubilities of Mg2B6O11 and MgSO4 are positively correlated with temperature, i.e., the solubilities of the single salts in the two boundary subsystems (Mg2B6O11 + H2O) and (MgSO4 + H2O) increase with increasing temperature. At each temperature, the crystallized area of inderite is larger than that of epsomite, indicating that the solubility of inderite is lower than that of epsomite. A comparison of the phase diagrams at (288.15, 298.15, and 308.15) K in Figure 6 shows that the areas of Inde and Eps increase with increasing temperature. The Pitzer model and its extend version have been widely used to predict the solubility of salt/water systems.19 Although there are the model single-salt parameters for epsomite (MgSO4· 7H2O), the single-salt parameters for Mg2B6O11·15H2O and the mixing ion-interaction parameters ΘSO4,B6O11 and φMg,SO4,B6O11 are too scarce. Thus, more studies of the thermodynamics data such as osmotic coefficient, dilution heat, dissolution heat, and

308.15) K in mass fraction are 100w(MgSO4) = 24.60 ± 0.12, 27.12 ± 0.16, 29.73 ± 0.13 at the 95% level of confidence. Those results indicate that our experimental procedure and analysis are reliable. Solubility and Physicochemical Property Data on the Ternary System. The experimental data on the solubilities and physicochemical properties, including density, refractive index and pH, for the ternary system (MgSO4 + Mg2B6O11 + H2O) at (288.15, 298.15, and 308.15) K are presented in Table 3. The composition of the liquid phase is expressed in mass fraction. According to the experimental data, the phase diagrams at the three temperatures are drawn in Figures 2, 3, and 4, respectively. In the solid−liquid phase diagrams of the ternary system at (288.15, 298.15, and 308.15) K in Figures 2, 3, and 4, there are two crystallization regions corresponding to inderite (Mg2B6O11· 15H2O, Inde) and epsomite (MgSO4·7H2O, Eps), one invariant point E1, E2, or E3 for (Inde + Eps), and two univariant curves A1E1 and B1E1 at 288.15 K, A2E2 and B2E2 at 298.15 K, or A3E3 and B3E3 at 308.15 K. Points A1 and B1 in Figure 2, A2 and B2 in Figure 3, and A3 and B3 in Figure 4 represent the solubilities of the two boundary subsystems (Mg2B6O11 + H2O) and (MgSO4 + H2O) in mass fraction with 100w(Mg2B6O11) = 0.23 and 100w(MgSO4) = 24.59 at 288.15 K, 100w(Mg2B6O11) = 0.27 and 100w(MgSO4) = 27.18 at 298.15 K, and 100w(Mg2B6O11) = 0.32 and 100w(MgSO4) = 29.74 at 308.15 K. Points E1, E2, and E3 in Figures 2, 3, and 4, respectively, represent the invariant cosaturation solid phases of (Inde + Eps) with the compositions in mass fraction 100w(Mg2B6O11) = 0.51 and 100w(MgSO4) = 24.41 at 288.15 K, 100w(Mg2B6O11) = 0.67 and 100w(MgSO4) = 27.38 at 298.15 K, and 3337

DOI: 10.1021/acs.jced.7b00378 J. Chem. Eng. Data 2017, 62, 3334−3340

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Figure 7. Plots of (a) density, (b) refractive index, and (c) pH as functions of the concentration of magnesium sulfate for the ternary system: ●, experimental points at 288.15 K; ▲, experimental points at 298.15 K; △, experimental points at 308.15 K; ···, solubility curve at 288.15 K; , solubility curve at 298.15 K; - - -, solubility curve at 308.15 K.

are 9.675 and 7.242 at 288.15 K, 9.316 and 6.628 at 298.15 K, and 9.137 and 6.055 at 308.15 K, respectively. Those results indicate that the pH of the cosaturated solution of Mg2B6O11 is the highest and the pH of the cosaturated solution of MgSO4 is the lowest at each temperature. The pH values in the ternary system decrease gradually with increasing magnesium sulfate concentration and obtain the singular values of 7.750 at 288.15 K, 7.518 at 298.15 K, and 7.212 at 308.15 K at the invariant points E1, E2, and E3, respectively. Density and Refractive Index Calculations. Empirical equations for the density and refractive index were adopted to correlate the experimental results:20

mixing heat for this ternary system at (288.15, 298.15, and 308.15) K are needed to fit those mixing ion-interaction parameters. On the basis of the physicochemical property data (densities, refractive indices, and pH values) in Table 3, the physicochemical properties as functions of magnesium sulfate concentration for the ternary system at three temperatures are shown in Figure 7. The physicochemical properties change regularly with increasing magnesium sulfate concentration. Figure 7a,b shows that both the density (ρ) and the refractive index (nD) increase at the beginning, reach maximum values of 1.28206 g·cm−3 and 1.3860 at 288.15 K, 1.30990 g·cm−3 and 1.390126 at 298.15 K, and 1.33424 g·cm−3 and 1.392682 at 308.15 K, respectively, at the invariant points (E1, E2, and E3), and then decrease with increasing magnesium sulfate concentration. Figure 7c shows the pH variation curves versus the magnesium sulfate concentration. The pH values of the two boundary subsystems (Mg2B6O11 + H2O) and (MgSO4 + H2O)

ln

ln 3338

ρ = ρ0

∑ Aiwi

nD = n D0

i

∑ Bi wi i

(1)

(2) DOI: 10.1021/acs.jced.7b00378 J. Chem. Eng. Data 2017, 62, 3334−3340

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where ρ and ρ0 are the densities and nD and nD0 the refractive indices of the solution and pure water, respectively, at the same temperature, wi is the mass fraction of the ith component in the electrolyte solution in the system, and Ai and Bi are the constants for the ith component in the aqueous system. The ρ0 values at (288.15, 298.15, and 308.15) K are 0.99910, 0.99704, and 0.99403 g·cm−3, respectively, and the nD0 values at 288.15, 298.15, and 308.15 K are 1.33339, 1.33250, and 1.33131, respectively.21 The values of Ai and Bi are shown in Table 4.

Funding

The authors gratefully acknowledge partial financial support from the National Natural Science Foundation of China (U1607123 and U1407113), the Yangtze Scholars and Innovative Research Team in Chinese University (IRT_17R81), and the Postdoctoral Science Foundation of China (2016M592827).

■

(1) Gao, S. Y.; Song, P. S.; Zheng, M. P.; Xia, S. P. Salt Lake Chemicals; Science Press: Beijing, 2007. (2) Li, J.; Gao, S. Y.; Xia, S. P.; Li, B.; Hu, R. Z. Thermochemistry of hydrated magnesium borates. J. Chem. Thermodyn. 1997, 29, 491−497. (3) Meng, L. Z.; Deng, T. L. Solubility prediction for the system of MgCl2 − MgSO4 − MgB4O7 − H2O at 298.15 K using the ioninteraction model. Russ. J. Inorg. Chem. 2011, 56, 1335−1338. (4) Du, X. H.; Song, P. S.; Zhang, J. T. Phase equilibrium in the quaternary system MgB4O7 − MgSO4 − MgCl2 − H2O at 25°C. J. Wuhan Inst. Chem. Technol. 2000, 22, 9−15. (5) Song, P. S.; Fu, H. A. Solubilities and properties of solution in the reciprocal system Li+, Mg2+/B4O72−, SO42− − H2O at 25°C. Chin. J. Inorg. Chem. 1991, 7, 344−347. (6) Sang, S. H.; Li, M.; Li, H.; Sun, M. L. A study on phase equilibria of the quaternary system (Li+, Mg2+//SO42−, B4O72− − H2O) at 288 K. Acta Geol. Sin. 2010, 84, 1704−1707. (7) Song, P. S.; Du, X. H.; Sun, B. Study on the ternary system (MgB4O7 − MgSO4 − H2O) at 25°C. Chin. Sci. Bull. 1988, 33, 1492− 1495. (8) Meng, L. Z.; Li, D.; Guo, Y. F.; Deng, T. L. Stable phase equilibrium of the aqueous quaternary system (MgCl2 + MgSO4 + MgB6O10 + H2O) at 323.15 K. J. Chem. Eng. Data 2011, 56, 5060− 5065. (9) Deng, T. L.; Zhou, H.; Chen, X. Salt−Water System Phase Diagrams and Applications; Chinese Chemical Industry Press: Beijing, 2013. (10) Li, F.; Zhang, S. S.; Guo, Y. F.; Wang, S. Q.; Deng, T. L. A rapid synthetic method for inderite. Acta Geol. Sin. 2014, 88, 343−344. (11) Wang, S. Q.; Du, X. M.; Jing, Y.; Guo, Y. F.; Deng, T. L. Solid− liquid phase equilibrium in the ternary systems (Li2B4O7 + MgB4O7 + H2O) and (Na2B4O7 + MgB4O7 + H2O) at 298.15 K. J. Chem. Eng. Data 2017, 62, 253−258. (12) Li, L.; Guo, Y. F.; Zhang, S. S.; Shen, M. M.; Deng, T. L. Phase equilibria in the aqueous ternary systems (LiCl + LiBO2 + H2O) and (Li2SO4 + LiBO2 + H2O) at 323.15 K and 0.1 MPa. Fluid Phase Equilib. 2017, 436, 13−19. (13) Wang, S. Q.; Guo, Y. F.; Li, D. C.; Zhao, F. M.; Qiao, W.; Deng, T. L. Solid-liquid phase equilibria in the ternary systems (LiCl + MgCl2 + H2O) and (Li2SO4 + MgSO4 + H2O) at 288.15 K. J. Chem. Eng. Data 2015, 60, 821−827. (14) Deng, T. L.; Yu, X.; Li, D. C. Metastable phase equilibrium in the aqueous ternary system K2SO4 + MgSO4 + H2O at (288.15 and 308.15) K. J. Solution Chem. 2009, 38, 27−34. (15) Silcock, H. L. Solubilities of Inorganic and Organic Compounds; Pergamon Press: Oxford, U.K., 1979. (16) Li, B.; Fang, C. H.; Wang, Q. Z.; Li, J.; Song, P. S. A study on the phase diagram and solution properties of ternary system Li+, Mg2+/SO42− at 25°C. J. Salt Lake Res. 1993, 1, 1−5. (17) Gao, J.; Deng, T. L. Metastable phase equilibrium in the aqueous ternary system (MgCl2 + MgSO4 + H2O) at 308.15 K. J. Chem. Eng. Data 2011, 56, 1847−1851. (18) Wang, S. Q.; Deng, T. L. Solid + liquid) isothermal evaporation phase equilibria in the aqueous ternary system (Li2SO4 + MgSO4 + H2O) at T = 308.15 K. J. Chem. Thermodyn. 2008, 40, 1007−1011. (19) Felmy, A. R.; Weare, J. H. The Prediction of Borate Mineral Equilibria in Natural Waters: Application to Searles Lake, California. Geochim. Cosmochim. Acta 1986, 50, 2771−2783. (20) Bu, B. H.; Li, L.; Zhang, N.; Guo, Y. F.; Wang, S. Q.; Sun, L. Y.; Deng, T. L. Solid−liquid metastable phase equilibria for the ternary

Table 4. Constants for the Calculation of Densities and Refractive Indices of Saturated Solutions in the Ternary System (MgSO4 + Mg2B6O11 + H2O) at (288.15, 298.15, and 308.15) K and p = 0.1 MPa T/K

constant

MgSO4

Mg2B6O11

288.15

Ai Bi Ai Bi Ai Bi

0.00759528 0.00163529 0.00966945 0.00149172 0.00972094 0.00146593

0.01006648 0.00155165 0.00997887 0.00117824 0.00788465 0.00170055

298.15 308.15

Comparisons of the calculated values and experimental results for the densities and refractive indices at (288.15, 298.15, and 308.15) K are presented in Table 3. The maximum relative error for the densities and refractive indices was no more than 0.35%. The calculated results agreed well with the experimental results, demonstrating that the empirical equations are suitable for this ternary system.

4. CONCLUSION The solubilities and physicochemical properties, including density, refractive index, and pH, for the ternary system (MgSO4 + Mg2B6O11 + H2O) at (288.15, 298.15, and 308.15) K were investigated using the method of isothermal dissolution equilibrium. At each temperature there are one invariant point, two univariant curves, and two crystallization regions corresponding to epsomite and inderite. Neither solid solutions nor double salts in this ternary system were formed at these three temperatures. Comparison of the phase diagrams at the three temperatures shows that the crystallized areas of inderite and epsomite increase with increasing temperature. The physicochemical properties changed regularly with increasing magnesium sulfate concentration, and the densities and refractive indices calculated using the empirical equations agree well with the experimental results. Since the Pitzer singlesalt parameters for Mg2B6O11·15H2O and the mixing ioninteraction parameters of ΘSO4,B6O11 and φMg,SO4,B6O11 are too scarce, more studies of thermodynamic properties such as heat capacity, osmotic coefficient, dilution heat, dissolution heat, and mixing heat for this ternary system are needed as the next step.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel. and Fax: +86 22 60601156. ORCID

Yafei Guo: 0000-0003-0698-3565 Tianlong Deng: 0000-0002-1728-2943 Notes

The authors declare no competing financial interest. 3339

DOI: 10.1021/acs.jced.7b00378 J. Chem. Eng. Data 2017, 62, 3334−3340

Journal of Chemical & Engineering Data

Article

system (Li2SO4 + K2SO4 + H2O) at 288.15 and 323.15 K, p = 0.1 MPa. Fluid Phase Equilib. 2015, 402, 78−82. (21) Speight, J. G. Lange’s Handbook of Chemistry; McGraw-Hill: New York, 2005.

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DOI: 10.1021/acs.jced.7b00378 J. Chem. Eng. Data 2017, 62, 3334−3340