Phase Equilibria and Phase Diagrams for the Aqueous Ternary

Aug 19, 2013 - ... a combined BX51 digital polarizing microscope (Olympus, Japan) and ..... The density values at point E2 at 288 K and point F3 at 30...
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Phase Equilibria and Phase Diagrams for the Aqueous Ternary System (Na2SO4 + Li2SO4 + H2O) at (288 and 308) K Yafei Guo, Yuanhui Liu, Qin Wang, Chenxiao Lin, Shiqiang Wang, and Tianlong Deng* Tianjin Key Laboratory of Marine Resources and Chemistry, College of Marine Science and Engineering, Tianjin University of Science and Technology, Tianjin 300457, P.R. China ABSTRACT: The solubility and density of the thermodynamic phase equilibria ternary system (Na2SO4 + Li2SO4 + H2O) at (288 and 308) K were determined using the isothermal dissolution method. According to the experimental results of the ternary system at (288 and 308) K, the phase diagrams and the diagrams of density versus composition were plotted. In the ternary system at 308 K, four crystallization regions corresponding to thenardite (Na2SO4, Th), two congruent double salts of Li2SO4· 3Na2SO4·12H2O (Db1) and Li2SO4·Na2SO4 (Db2), and lithium sulfate monohydrate (Li2SO4·H2O, Ls) were found, whereas only three crystallization regions corresponding to Ls, one incongruent double salt of Db1, and mirabilite (Na2SO4·10H2O, Mir) were found in the system at 288 K. No solid solution was found at either temperature. When the experimental phase diagram at 308 K was compared with that at 288 K, it shows that (1) a new phase region of double salt Db2 was formed and the mineral of Mir transformed into Th with the increase of temperature from (288 to 308) K and (2) the area of the crystallization region of sodium sulfate was decreased sharply and those of the crystallized regions of Li2SO4·H2O and double salt Db1 increased obviously. The solution densities of the ternary system both at (288 and 308) K change regularly with increasing lithium sulfate concentration in solution. Based on the Pitzer model and its extended Harvie-Weare (HW) model, the mixing triple interaction parameter of ΨLi,Na,SO4 at (288 and 308) K and the solubility equilibrium constants Ksp of solid phases Ls, Db1, Db2, Th, and Mir at (288 and 308) K, which are not reported in the literature, were acquired by fitting the experimental solubility data of the ternary system (Li2SO4 + Na2SO4 + H2O) by the lease-square method. A comparison between the calculated and experimental results at (288 and 308) K for the ternary system shows that the predicted solubilities obtained with the extended HW model agree well with experimental data.

1. INTRODUCTION A number of salt lakes with abundant lithium resources are widely distributed in the Qaidam Basin of the Qinghai-Tibet Plateau, China.1,2 Salt-water phase equilibrium and phase diagram are important predicting tools to use for exploiting the brine resources and describing the geochemical behavior of brine-mineral. Therefore, experimental studies on phase equilibria and phase diagrams are essential to describe the phase equilibrium behaviors of brines in order to separate the lithium-containing mixture salts effectively.3 According to the statistical data from 1971 to 2000, the temperature of the brine in the Qaidam Basin in a year was between (285 and 292) K during March and May and (298 and 313) K during June and October, with the average temperature being (288 and 308) K, respectively. Although the phase equilibria for the systems (Na2SO4 + Li2SO4 + H2O) at (273 and 298) K have been reported,4,5 that of the same ternary system at (288 and 308) K has not yet been reported in the literature. Therefore, the solubilities and the solution densities in the ternary system (Na2SO4 + Li2SO4 + H2O) at (288 and 308) K are presented together in this study with the predictive solubilities on the basis of the Pitzer ion-interaction model and its extended HW model after acquiring the lacking Pitzer mixing triple parameters ΨLi,Na,SO4 and the solubility equilibrium © XXXX American Chemical Society

constants Ksp of solid phases existing in the ternary system at (288 and 308) K through fitting using the experimental solubility data of the ternary system at the two temperatures.

2. EXPERIMENTAL SECTION 2.1. Apparatus and Reagents. A thermostatic rotary shaker (HXC-500-12A, Beijing Fortunejoy Sci. Technol. Co. Ltd.) with a precision of 0.1 K was used. The equilibrium solid phase minerals were identified with a combined BX51 digital polarizing microscope (Olympus, Japan) and an XD-2800 Xray diffractometer with the LTK-450 accessory of transition temperature ranging from (80 to 72)3 K (Dandong Haoyuan Instrument Co. Ltd., China). The chemicals of analytical grade were obtained from either the Tianjin Kermel Chemical Reagent Ltd. or the ShanghaiLithium Industrial Co. Ltd.: sodium sulfate (Na2SO4, 0.99 in mass fraction) and lithium sulfate monohydrate (Li2SO4·H2O, 0.99) were recrystallized with doubly deionized water (DDW) before use. DDW with the conductivity less than 1·10−4 S·m−1 Received: April 29, 2013 Accepted: July 31, 2013

A

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at 298 K was used to prepare the series of artificial synthesized complexes and for chemical analysis.2,3 2.2. Experimental Methods. The isothermal dissolution method was used in this study, and more details of the experimental method are available in our previously works.6,7 In briefly, the series of artificial synthesized complexes were loaded in the cleaned polyethylene bottles and capped tightly, and then the bottles were placed in the thermostatic rotary shaker. When the compositions of the liquid phase in the bottle became constant, it indicated that the equilibrium had been achieved. Generally, it took about (3 to 5) days to be at equilibrium. After equilibrium was achieved, the rotary system was paused for 1 h in order to separate the solid phase from the liquid phase before sampling. Some clarified liquid phases were taken out for quantitative analysis, and some other solutions were used to measure the density. The solid phase minerals were evaluated with combined chemical analysis and observed with a BX51 digital polarizing microscope and XD-2800 X-ray diffraction.8 2.3. Analytical Methods. The concentration of SO42‑ was obtained by the gravimetric method of barium chloride; the uncertainty for the analytical results in triplicate was within ± 0.0005 in mass fraction.9 The concentration of Li+ was measured in triplicate with inductively coupled plasma optical emission spectroscopy (ICP-OES, Prodigy, Leeman Laboratories), and the uncertainty was within ± 0.005 in mass fraction. The Na+ concentration was evaluated using molar balance of ions and combined with ICP-OES measurement.10 The densities (ρ) were measured in triplicate using an automatic oscillating U-tube densimeter (DMA 4500, Anton Paar, Austria) with an uncertainty of ± 1.0·10−5 g·cm−3. Dry air and freshly double distilled water were used as standards for calibration of the apparatus before each series of measurements. Temperature oscillations were kept within 0.01 K, and an external bath circulator (K20-cc-NR, Huber, Germany) was used to maintain it at the desired temperature ± 0.01 K.11,12

Table 1. Solubility and Density Data of the Ternary System (Na2SO4 + Li2SO4 + H2O) at T = 288 K and Pressure p = 0.1 MPaa composition of liquid phase, 100wb

density, ρ

no.

Li2SO4

Na2SO4

H2O

g·cm−3

equilibrium solid phased

1, A 2 3 4 5 6, E1 7 8 9 10 11 12, E2 13 14 15 16 17 18 19, B

0.00 3.37 5.99 7.61 11.20 13.20 20.06 19.58 19.85 20.89 22.00 22.21 22.24 22.50 22.62 23.41 23.83 26.35 26.01

11.74 15.77 16.56 14.09 15.22 15.33 10.21 10.39 11.66 10.04 9.59 8.66 9.47 8.60 7.82 5.42 4.38 0.53 0.00

88.26 80.86 77.45 78.30 73.58 71.47 69.73 70.03 68.49 69.07 68.41 69.13 68.29 68.90 69.56 71.17 71.79 73.12 73.99

1.0049 1.0059 c 1.1980 1.2654 1.2744 1.2877 1.2854

Mir Mir Mir Mir Mir Mir+Db1 Db1 Db1 Db1 Db1 Db1 Ls+Db1 Ls Ls Ls Ls Ls Ls Ls

1.2914 1.2966 1.2918 1.2922 1.2718 1.2593 1.2370 1.2364

a

Standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, ur(Li2SO4) = 0.003, ur(Na2SO4) = 0.003, and ur(ρ) = 0.01 mg·cm−3. bw = mass fraction. cNot determined. dMir, Na2SO4·10H2O; Db1, Li2SO4· 3Na2SO4·12H2O; Ls, Li2SO4·H2O.

solubility curves corresponding to curves A′E1′, E1′E2′, E2′E3′, and E3′B′. Points C and D are the solubilities of the single salts of Na2SO4 and Li2SO4 at 308 K corresponding to 33.06 and 25.37 in mass fraction (100w). The double salts of Li2SO4· 3Na2SO4·H2O and Li2SO4·Na2SO4 belong to the congruent double salt at 308 K. A comparison of the equilibria phase diagrams for the ternary system at (288 and 308) K is shown in Figure 3. It was found that (1) a new phase region of double salt Db2 was formed at 308 K; (2) the mineral mirabilite (Na2SO4·10H2O) transformed into the thenardite (Na2SO4) and the area of the crystallized region of anhydrate sodium sulfate decreased sharply with the increase of temperature; and (3) the area of the crystallized region of Db1 increased obviously and the area of the crystallized region of Ls increased significantly, which implies that it is suitable to use the temperature variation effects of the lithium sulfate and sodium sulfate to separate the sulfates of lithium-containing mixture salts. On the basis of density data given in Tables 1 and 2, the relationship between density and composition of lithium sulfate in the ternary system (Na2SO4 + Li2SO4 + H2O) at (288 and 308) K was plotted in Figure 4. It was found that the solution densities in the ternary system at the two temperatures changed regularly with an increase in the mass fraction of lithium sulfate. The solution densities from point A to point E1 in the phase region of Mir of the ternary system at 288 K increased sharply with the increasing concentration of lithium sulfate, and the solution densities from point C to points F1, F2, and F3 in the each phase region of Th, Db1, and Db2 in the ternary system at 308 K decreased slowly with the increasing concentration of lithium sulfate.

3. RESULTS AND DISCUSSION The experimental data on the solubilities and densities of the ternary system (Li2SO4 + MgSO4 + H2O) at (288 and 308) K are listed in Tables 1 and 2, respectively. The compositions of the equilibrium liquid phase were expressed in mass fraction. According to the experimental data of Tables 1 and 2, the phase diagrams of the ternary system at (288 and 308) K were plotted in Figures 1 and 2, respectively. In Figure 1, the equilibrium phase diagram of the ternary system at 288 K consists of three crystallization regions corresponding to lithium sulfate monohydrate (Li2SO4·H2O, Ls), double salt 1 (Li2SO4·3Na2SO4·H2O, Db1), and mirabilite (Na2SO4·10H2O, Mir); two invariant points corresponding to E1 (Mir + Db1) and E2 (Db1 + Ls); and three univariant isothermal curves corresponding to curves A1E1, E1E2, and E2B1. Points A and B represent the solubilities of the single salts of Na2SO4 and Li2SO4 at 288 K corresponding to 11.74 and 26.01 in mass fraction (100w), respectively. The double salt 1 belongs to the incongruent double salt, and no solid solution was found. In Figure 2, the equilibrium phase diagram of the ternary system at 308 K consists of four crystallization regions corresponding to lithium sulfate monohydrate (Li2SO4·H2O, Ls), double salt 1 (Li2SO4·3Na2SO4·H2O, Db1), double salt 2 (Li2SO4·Na2SO4, Db2), and thenardite (Na2SO4, Th); three invariant points corresponding to F1 (Th + Db1), F2 (Db1 + Db2), and F3 (Db2 + Ls); and four univariant isothermal B

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Table 2. Solubility and Density Data of the Ternary System (Na2SO4 + Li2SO4 + H2O) at T = 308 K and Pressure p = 0.1 MPaa composition of liquid phase, 100wb

density, ρ

no.

Li2SO4

Na2SO4

H2O

g·cm−3

equilibrium solid phased

1, C 2 3 4, F1 5 6 7 8 9 10 11 12 13, F2 14 15 16 17, F3 18 19 20 21 22 23 24 25, D

0.00 3.00 3.86 3.97 3.92 5.06 8.05 4.03 4.69 4.59 6.12 6.77 13.99 18.46 20.43 20.06 20.64 20.29 21.83 22.09 22.50 22.74 23.25 23.85 25.37

33.06 29.33 29.48 30.10 30.05 28.15 23.92 29.63 28.63 28.91 26.59 25.50 19.21 14.69 12.50 12.95 12.37 12.27 8.45 7.71 6.4 5.52 2.91 2.47 0.00

66.94 67.67 66.66 65.93 66.03 66.79 68.03 66.34 66.68 66.50 67.29 67.73 66.80 66.85 67.07 66.99 66.99 67.44 69.75 70.20 71.10 71.74 73.84 73.68 74.63

1.3287 c

Th Th Th Th+Db1 Db1 Db1 Db1 Db1 Db1 Db1 Db1 Db1 Db1+Db2 Db2 Db2 Db2 Db2+Ls Ls Ls Ls Ls Ls Ls Ls Ls

1.3102

1.3092

1.3067 1.3127

1.3107 1.3058 1.2797 1.2755 1.2578 1.2527 1.2369 1.2262

Figure 2. Equilibrium phase diagram of the ternary system (Na2SO4 + Li2SO4 + H2O) at 308 K. ○, Experimental point; , isotherm curve; Th, Na2SO4; Db1, Li2SO4·3Na2SO4·12H2O; Db2, Li2SO4·Na2SO4; Ls, Li2SO4·H2O.

a

Standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, ur(Li2SO4) = 0.003, ur(Na2SO4) = 0.003, and ur(ρ) = 0.01 mg·cm−3. bw = mass fraction. cNot determined. dTh, Na2SO4; Db1, Li2SO4·3Na2SO4· 12H2O; Db2, Li2SO4·Na2SO4; Ls, Li2SO4·H2O.

Figure 3. Comparison of the experimental phase diagram of the ternary system (Na2SO4 + Li2SO4 + H2O). ●, experimental point at 288 K; -●-, isotherm curve at 288 K; ○, experimental point at 308 K; ·○·, isotherm curve at 308 K; Mir, Na2SO4·10H2O; Th, Na2SO4; Db1, Li2SO4·3Na2SO4·12H2O; Db2, Li2SO4·Na2SO4; Ls, Li2SO4·H2O.

remarkable singular points where the pure minerals of lithium sulfate monohydrate started to seed out.

4. SOLUBILITY PREDICTION 4.1. Ion-Interaction Model. The Pitzer ion-interaction model and its extended Harvie−Weare (HW) model have been successfully used in calculating thermodynamic properties and the solubilities of electrolytes.13−16 Using the Pitzer’s single salt parameters, the mixing ion-interaction parameters and the solubility products of the solid−liquid phase equilibria allowed us to identify the coexisting solid phases and their compositions at equilibrium.2,17,18 4.2. Model Parameterizations. Pitzer’s single salt parameters β(0), β(1), and C(Φ) of Li2SO4 and Na2SO4 and the mixing binary interaction parameter of θLi,Na at (288 and 308) K were obtained from the literature and are shown in Tables 3 and 4.19−21 The mixing triple interaction parameters of ΨLi,Na,SO4 at (288 and 308) K, which have not been reported

Figure 1. Equilibrium phase diagram of the ternary system (Na2SO4 + Li2SO4 + H2O) at 288 K. ●, Experimental point; , isotherm curve; Mir, Na2SO4·10H2O; Db1, Li2SO4·3Na2SO4·12H2O; Ls, Li2SO4·H2O.

However, in the phase region of Ls both at (288 and 308) K in the ternary system, the density of solution sharply decreased with the increasing lithium sulfate concentration. The density values at point E2 at 288 K and point F3 at 308 K were the most C

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basis of the calculated solubilities, a comparison between the experimental and calculated phase diagrams of the ternary system at (288 and 308) K was drawn in Figures 5 and 6,

Figure 4. Relationship between the density of solid−liquid equilibrium solution and composition of lithium sulfate in the system (Na2SO4 + Li2SO4 + H2O). ▲, at 288 K; Δ, at 308 K.

Table 3. Pitzer Single Salt Parameters of Electrolyte in the System (Na2SO4 + Li2SO4 + H2O) at T = 288 and 308 K electrolyte

T/K

β(0)

β(1)

C(Φ)

ref

Li2SO4 Na2SO4 Li2SO4 Na2SO4

288 288 308 308

0.125762 −0.00877615 0.134997 0.0393867

1.26521 1.03286 1.30785 1.15325

−0.000504599 0.0124223 −0.00472651 0.00142264

11 11 11 11

Figure 5. Comparison of the experimental and calculated phase diagram of the ternary system (Na2SO4 + Li2SO4 + H2O) at 288 K. ●, experimental points; -●-, experimental isotherm curve; ○, calculated points; ·○·, calculated isotherm curve; Th, Na2SO4; Db1, Li2SO4· 3Na2SO4·12H2O; Db2, Li2SO4·Na2SO4; Ls, Li2SO4·H2O.

Table 4. Pitzer Mixing Parameters in the System (Na2SO4 + Li2SO4 + H2O) at T = 288 and 308 K T/K

θLi,Na

ref

ΨLi,Na,SO4

σ

R

ref

288

0.0551530

13

−0.0208797

0.1862

0.7734

308

0.0486550

12

−0.0299950

0.07945

0.9828

this work this work

in the literature, were acquired by fitting the experimental solubility data of the ternary system (Li2SO4 + Na2SO4 + H2O) at (288 and 308) K by the lease-square method. The standard deviation (σ) and related coefficient (R) of the fitting are shown in Table 4. The parameters at (288 and 308) K used to calculate the solubilities of the ternary system are also shown in Table 4. The solubility equilibrium constants Ksp of solid phases Li 2 SO 4 ·H 2 O, Li 2 SO 4 ·3Na 2 SO 4 ·12H 2 O, Li 2 SO 4 ·Na 2 SO 4 , Na2SO4, and Na2SO4·10H2O calculated at (288 and 308) K are listed in Table 5. 4.3. Calculated Solubilities. On the basis of the Pitzer’s and its extended HW model for aqueous electrolytes, the solubilities of the ternary system (Li2SO4 + Na2SO4 + H2O) at (288 and 308) K have been calculated, respectively. On the

Figure 6. Comparison of the experimental and calculated phase diagram of the ternary system (Na2SO4 + Li2SO4 + H2O) at 308 K. ●, experimental points; -●-, experimental isotherm curve; ○, calculated points; ·○·, calculated isotherm curve; Th, Na2SO4; Db1, Li2SO4· 3Na2SO4·12H2O; Db2, Li2SO4·Na2SO4; Ls, Li2SO4·H2O.

respectively. The predicted solubilities both at (288 and 308) K are in good agreement with the experimental phase equilibria, which confirms that the obtained Pitzer mixing triple interaction parameters of Ψ Li,Na,SO 4 and the solubility equilibrium constants parameters of minerals existing in the ternary system at (288 and 308) K are reliable for predicting the solubilities of the system containing the lithium ion.

Table 5. Equilibrium Constants of Solid Phases in the System (Na2SO4 + Li2SO4 + H2O) at T = 288 and 308 K T/K

solid phase

Ksp

288 288 288 308 308 308 308

Li2SO4·H2O Li2SO4·3Na2SO4·12H2O Na2SO4·10H2O Li2SO4·H2O Li2SO4·3Na2SO4·12H2O Li2SO4·Na2SO4 Na2SO4

3.564 3.700·10−4 3.224·10−2 1.619 3.601·10−4 1.068·10−1 4.034·10−1

5. CONCLUSIONS The solubilities and densities of the ternary system (Na2SO4 + Li2SO4 + H2O) were determined using the isothermal dissolution method at (288 and 308) K, respectively. According D

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(6) Deng, T. L.; Yin, H. A.; Tang, M. L. Experimental and Predictive Phase Equilibrium of the Li+, Na+/Cl−, CO32‑-H2O System at 298.15 K. J. Chem. Eng. Data 2002, 47, 26−29. (7) Deng, T. L. Phase equilibrium for the aqueous system containing lithium, sodium, potassium, chloride, and borate ions at 298 K. J. Chem. Eng. Data 2004, 49, 1295−1299. (8) Meng, L. Z.; Dan, L.; 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) Gao, J.; Deng, T. L. Metastable Phase Equilibrium in the Aqueous Quaternary System (MgCl2 + MgSO4+ H2O) at 308.15 K. J. Chem. Eng. Data 2011, 56 (5), 1847−1851. (10) Qinghai institute of salt lakes of CAS. Analytical methods of brines and salts, 2nd ed.; Science China Press: Beijing, 1988; pp 39−54. (11) Tara, J.; Fortin, Arno L.; Malte, F.; Stephanie, O. Advanced calibration, adjustment, and operation of a density and sound speed analyzer. J. Chem. Thermodyn. 2013, 57, 276−285. (12) Guo, Y. F.; Yin, H. J.; Wu, X. H.; Deng, T. L. Metastable phase equilibrium in the aqueous quaternary system (NaCl + MgCl2 + Na2SO4 + MgSO4 + H2O) at 323.15 K. J. Chem. Eng. Data 2010, 55, 4216−4220. (13) Pitzer, K. S. Thermodynamics of electrolytes. I Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268−277. (14) Pitzer, K. S. Activity coefficients in electrolyte solutions, 2nd ed., CRC Press: London, 2000. (15) Harvie, C. E.; Moller, N.; Weare, J. H. The prediction of mineral solubilities in natural waters: the Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3CO3-CO2-H2O system to high ionic strengths at 298 K. Geochim. Cosmochim. Acta 1984, 48, 723−751. (16) Harvie, C. E.; Weare, J. H. Mineral equilibrium in a sixcomponent seawater system Na-K-Mg-Ca-SO4-Cl-H2O at 298 K. Geochim. Cosmochim. Acta 1980, 44, 981−997. (17) 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 (1), 27−34. (18) Deng, T.; Yin, H.; Li, D. Metastable Phase Equilibrium in the Aqueous Ternary System (Li2SO4 + MgSO4 + H2O) at 348.15 K. J. Chem. Eng. Data 2009, 54 (2), 498−501. (19) Holmes, H. F.; Mesmer, R. E. Thermodynamics of aqueous solutions of the alkali metal sulfates. J. Solution Chem. 1986, 15 (6), 495−518. (20) Greenberg, J. P.; Moller, N. The prediction of mineral solubilities in natural waters: A chemical equilibrium model for the Na-K-Ca-Cl-SO4-H2O system to high concentration from 0 to 250 °C. Geochim. Cosmochim. Acta 1989, 53, 2503−2518. (21) Lovera, J. A.; Graber, T. A.; Galleguillos, H. R. Correlation of solubilities for the NaCl + LiCl + H2O system with the Pitzer model at 15, 25, 50, and 100 °C. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2009, 33, 388−392.

to our experimental data, the equilibrium phase diagrams and the diagrams of density versus composition of lithium sulfate were plotted. In the same ternary system, it was found that (1) one incongruent double salt of Li2SO4·3Na2SO4·12H2O was formed at 288 K and two congruent double salts of Li2SO4· 3Na2SO4·12H2O and Li2SO4·Na2SO4 existed at 308 K; (2) with the increase of temperature from (288 to 308) K, the area of the crystallization region of sodium sulfate decreased sharply and the areas of the crystallized regions of Li2SO4·H2O and double salt Db1 increased obviously. Therefore, it is suitable to use the temperature variation effects of the lithium sulfate and sodium sulfate to separate the sulfates of lithium-containing mixture salts. The solution densities of the ternary system at both (288 and 308) K changed regularly with increasing lithium sulfate concentration in solution. On basis of the Pitzer model and its extended HW model, the values of the Pitzer mixing triple parameters ΨLi,Na,SO4 and the solubility equilibrium constants Ksp of solid phases existing in the ternary system at (288 and 308) K were fitted using the experimental solubility data of the ternary system (Li2SO4 + Na2SO4 + H2O) by the lease-square method. Comparisons between the calculated and experimental results of the ternary system at (288 and 308) K showed that the predicted solubilities agree well with experimental values, which confirms that the obtained Pitzer mixing triple interaction parameters of ΨLi,Na,SO4 and the solubility equilibrium constants parameters of minerals existing in the ternary system at (288 and 308) K are reliable for predicting the solubilities of the system containing the lithium ion.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel/Fax: +86-22-60602962. Funding

Financial support from the National Natural Science of China (21276194 and 21106103), the Key Pillar Program of Tianjin Municipal Science and Technology (11ZCKGX02800), the Specialized Research Fund for the Doctoral Program of Chinese Higher Education (20101208110003 and 20111208120003), the Senior Professor Program in Tianjin Government for TUST (20100405), and the Tianjin Key Laboratory of Marine Resources and Chemistry in TUST (201201 and 201206) are acknowledged. Notes

The authors declare no competing financial interest.

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REFERENCES

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