Solubility Isotherm of the System Li2SO4–K2SO4–MgSO4–H2O at

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Solubility Isotherm of the System Li2SO4−K2SO4−MgSO4−H2O at 273.15 K Hongyan Zhou,† Dewen Zeng,*,†,‡ Haijun Han,† Ouyang Dong,† Dongdong Li,† and Yan Yao† †

Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining, 810008, P.R. China College of Chemistry and Chemical Engineering, Central South University, Changsha, 410083, P.R. China

‡

S Supporting Information *

ABSTRACT: The solubility isotherms for the ternary system Li2SO4−MgSO4− H2O and the quaternary system Li2SO4−K2SO4−MgSO4−H2O at T = 273.15 K were determined by the isothermal equilibrium method. A Pitzer−Simonson− Clegg (PSC) model was used to simulate the properties of the binary and ternary systems of the quaternary title system. The binary model parameters were fitted against selected reliable experimental data of water activity. The mixture model parameters were obtained by fitting them to the ternary solubility isotherms taken from the literature and determined in this work. The solubility isotherms of the quaternary title system were predicted by the PSC model and compared with the experimental results in this work. The excellent agreement between the predicted and experimental results indicates that the experimental results obtained in this work are reliable.

1. INTRODUCTION The extraction of valuable resources from salt lakes requires consulting hundreds of solubility phase diagrams for the ions Na+, K+, Mg2+, Li+, Cl−, SO42−, B4O72−, CO32−, and H2O over a wide temperature range. Although numerous studies on the solubility isotherms of salt lake systems have been reported over the past several decades, some of these systems have not yet been described at a given temperature. To close these gaps, we planned to carry out a series of experimental measurements and necessary computational simulations. Among the salt lake systems are the systems Li2SO4−MgSO4−H2O and Li2SO4− K2SO4−MgSO4−H2O, which have been widely studied over a wide temperature range (25 °C to 100 °C).1−10 However, their solubility isotherms at 273 K are even more important for a solar pond technique in winter and have been unknown so far. In this paper, phase equilibrium data for the ternary system Li2SO4−MgSO4−H2O and the quaternary system Li2SO4− K2SO4−MgSO4−H2O were elaborately determined at T = 273.15 K, and a thermodynamic model was chosen to simulate and predict the solubility isotherms.

before use. The main impurity elements in the prepared reagents were analyzed by inductively coupled plasma emission spectrometer (ICP, Thermo Electron Corporation, ICAP 6500 DUO), and the results are shown in Table 1. It can be conservatively evaluated that the purities of all the prepared reagents in this work are above 99.95 %. Throughout the experimental process, doubly distilled water with a conductance of 1.4·10−4 S·m−1 was used. 2.2. Experimental Apparatus. A thermostat (LAUDA E219, Germany) with a temperature stability of ± 0.01 K was used for the solubility measurements. The temperature was calibrated by a glass thermometer with an accuracy of ± 0.01 K. An analytical electronic balance (Sartorius, CPA225D, ± 0.1 mg) was used for weighing. 2.3. Experimental Procedure. Solid−liquid equilibrium was achieved in a 150 cm3 ground flask immersed in a glycol− water bath at 273.15 K. The samples were stirred with a magnetic stirrer placed outside of the bath. Solution compositions were analyzed for the system MgSO4−H2O after 5 days and 6 days; the maximal relative deviation between two samples is 0.09 %. Thus, the equilibration time for the ternary system was taken to be 7 to 10 days. The equilibrium experiments for the quaternary system Li2SO4−K2SO4− MgSO4−H2O were initiated by adding the third salt to the saturated solution in equilibrium with two solid phases. Solution analysis was made after 10 days and 14 days; the maximal relative deviation between two samples is 0.15 %.

2. EXPERIMENTAL SECTION 2.1. Chemical Materials. The lithium sulfate used in this work was prepared by neutralizing lithium carbonate (purity > 0.999 in mass fraction, Shanghai China-Lithium Industry Co. Ltd.) with sulfuric acid (GR, Tianjin Hengxing Chemical Preparation Co. Ltd.), followed by double crystallization with 50 % salt recovery each time. Magnesium sulfate and potassium sulfate (AR, Tianjin Kermel Chemical Reagent Ltd.; purities: w(MgSO4·7H2O) > 99.5 %, w(K2SO4) > 99.0 %) were purified by double crystallization with 50 % salt recovery each time © 2013 American Chemical Society

Received: February 1, 2013 Accepted: April 22, 2013 Published: May 6, 2013 1692

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Table 1. Impurity Contents for the Reagents Prepared in this Work impurity contents (100w)a

a

reagents

Ca

K

Li

Na

Mg

Fe

Li2SO4·H2O MgSO4·7H2O K2SO4

0.00058 − 0.0047

0.0045 0.00007 /

/ 0.00015 −

0.0018 0.000068 0.0067

− / 0.0004

0.000032 − /

Notation: /, undetected; −, undetectable.

Thus, the equilibration time for the quaternary system was set to be 10 days to 14 days. When equilibration was reached, the solid in the solution was allowed to settle for at least 10 h. The compositions of the liquids and their corresponding wet solid phases were analyzed. A certain amount of clear solution was removed by a pipet covered with glass cloth as a filter and transferred to a weighed 25 cm3 bottle with a weight of about 12 g to 15 g and then closed with a glass stopper at once. The compositions were determined by analyzing the concentrations of Mg2+ and SO42− for the ternary system Li2SO4−MgSO4−H2O and Mg2+, K+, and SO42− for the quaternary system Li2SO4−K2SO4−MgSO4− H2O. The Mg2+ concentration was determined by titration with EDTA using Erio T as an indicator. The interference of the Li+ ions was eliminated by adding different amounts of an nbutanol−ethanol mixture, as described in the literature.11 The K+ concentration was analyzed by gravimetric methods using sodium tetraphenyl borate. The SO42− concentration was analyzed gravimetrically by precipitating with barium chloride solution (wBaCl2 = 0.05), as described in the literature.12 The average of three parallel determinations for a sample was taken as the final results. The analysis error for Mg2+ can be controlled to within 0.3 % in most cases, and that for K+ can be controlled to within 0.16 %. Duplicate analyses of the SO42− concentration yielded the maximum relative deviations of w(SO42−) = ± 0.1 %. Overall, the uncertainty of the experimental solubility results in this work can be reasonably evaluated to be less than 0.4 % for the ternary systems and 0.6 % for the quaternary system.

Table 2. Experimental Solubility Data for the Ternary System Li2SO4−MgSO4−H2O at 273.15 K composition of the solution (100w)

composition of the wet solid phase (100w)

Li2SO4

MgSO4

H2O

Li2SO4

MgSO4

H2O

solid phasea

0 3.45 6.15 9.01 10.81 16.7 18.25 19.31 19.16 20.4 22.17 23.23 24.6 26.59

21.03 18.93 17.57 16.04 15.21 12.17 11.38 10.98 10.82 9.52 6.76 4.83 2.82 0

78.97 77.62 76.28 74.95 73.98 71.13 70.37 69.71 70.02 70.08 71.07 71.94 72.58 73.41

− 1.83 2.72 4.05 6.09 6.81 13.85 15.2 21.24 27.52 42.87 36.75 36.37 −

− 34.98 36.1 35.26 29.94 34.42 20.84 24.04 17.16 8.45 4.6 4.38 2.24 −

− 63.19 61.18 60.69 63.97 58.77 65.31 60.76 61.6 64.03 52.53 58.87 61.39 −

A A A A A A A A+B A+B B B B B B

a

A, MgSO4·7H2O; B, Li2SO4·H2O.

Table 3. Experimental Solubility Data for the Quaternary System Li2SO4−K2SO4−MgSO4−H2O at 273.15 K

3. RESULTS For the ternary system Li2SO4−MgSO4−H2O, the measured solubility results at T = 273.15 K are presented in Table 2. The solid phases in equilibrium with the saturated solution were determined by Schreinemaker’s method and powder X-ray diffraction. The identified solid phases in equilibrium with the saturated solution are MgSO4·7H2O and Li2SO4·H2O. For the quaternary system Li2SO4−K2SO4−MgSO4−H2O, the measured solubility results at 273.15 K are presented in Table 3. The solid phases in equilibrium with the saturated solution were determined by powder X−ray diffraction exclusively. The phase diagram of this system at 273.15 K consists of five crystallization fields corresponding to K2 SO 4 , LiKSO4 , Li2SO4·H2O, K2SO4·MgSO4·6H2O, and MgSO4·7H2O. The crystallization field of the salt K2SO4 is the largest, whereas that of Li2SO4·H2O is the smallest. These results indicate that the solid phase K2SO4 is easiest to crystallize from the solution at 273.15 K.

composition of the solution (100w)

composition of the wet solid phase (100w)

Li2SO4

K2SO4

MgSO4

Li2SO4

K2SO4

MgSO4

solid phasea

18.73 19.31 0 17.86 3.47 26.10 12.84 3.60 21.50 12.12 5.62 4.40 23.42 11.50 22.32 7.38 6.97 10.70 0 12.04 11.30

1.61 0 7.76 1.62 7.80 1.75 7.85 4.57 2.50 7.70 7.77 3.49 1.75 7.78 1.64 7.88 3.43 7.72 3.45 3.24 6.23

11.05 10.98 8.64 11.43 7.72 0 0 15.03 2.20 2.12 7.14 18.18 4.04 4.00 5.84 6.69 16.66 5.75 20.92 14.03 7.65

12.03 15.20 0 12.17 2.39 − 18.37 2.60 27.03 17.77 4.19 3.40 26.97 13.04 24.46 6.65 4.78 10.54 0 7.48 −

1.30 0 3.98 6.27 30.56 − 28.36 18.34 19.93 18.10 28.05 13.11 14.27 25.82 8.10 17.10 14.85 16.01 10.79 15.79 −

28.72 24.04 10.03 24.69 10.20 − 0 20.33 1.51 1.63 9.55 22.52 3.15 3.01 5.13 7.24 21.69 7.12 25.89 22.27 −

LiS+Eps+Db4 Eps+LiS Ar+Pic Eps+Db4 Ar+Pic LiS+Db4 Db4+Ar Pic Db4 Db4+Ar Ar+Pic Eps+Pic LiS+Db4 Db4+Ar LiS+Db4 Ar+Pic Eps+Pic Db4+Pic+Ar Eps+Pic Eps+Pic+Db4 Pic+Db4

Eps, MgSO4·7H2O; LiS, Li2SO4·H2O; Ar, K2SO4; Db4, LiKSO4; Pic, K2SO4·MgSO4·6H2O. a

4. MODELING To verify the reliability of the experimental results and to obtain more information on the solid−liquid equilibria, a thermodynamic model is necessary to represent the properties of these

systems. For the consistency of model representation, the chosen model should be able to represent the properties of the 1693

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Table 4. Binary Pitzer−Simonson−Clegg Model Parameters

a

solute

α

Bmx

α1

B1mx

Wmx

Umx

Vmx

SDa

source of osmotic coefficients for the parametrization

Li2SO4 K2SO4 MgSO4

13 13 7

46.418 −39.769 135.134

0 0 95

0 0 −45466.73

−11.829 −2.122 −47.896

−13.832 −2.843 −52.027

3.273 0 0

0.0007 0.0002 0.0005

17 19 20

Standard deviation, SD:

SD =

2 (a w (expt) − a w (calcd)) n

systems of the moderately soluble salts MgSO4, K2SO4, and Li2SO4 as well as the highly soluble salts, such as LiCl and MgCl2, which coexist in salt lakes. The Pitzer−Simonson− Clegg model,13,14 a mole-fraction-based ion interaction model, has been proven to meet the requirements15,16 and was chosen to represent the properties of these systems. The activity of water and activities of the ions as functions of salt concentration in the framework of the model were described in our previous work15,16 and are introduced again in the Supporting Information of this work. 4.1. Binary Parameter Determination. For the model parametrization, the water activity or osmotic coefficient data were needed. The experimental values of the osmotic coefficients for the Li2SO4−H2O system at 273.15 K were reported uniquely by Li and Yao,17 and these data could be evaluated as reliable because the osmotic coefficient data for the same system at 323.15 K determined by the same authors agree with those measured by Rard et al.18 very well. For the K2SO4(aq) solution, no experimental water activity data at 273.15 K are available at present; however, Holmes and Mesmer19 have reported their extrapolated results using reliable model parameters. The osmotic coefficients for the MgSO4(aq) solution at 273.15 K were reported by Platford20 with an uncertainty of not more than ± 0.004. Before the model parametrization, the binary model parameters α and α1 were taken to be 13.0 and 0, respectively, for Li2SO4(aq) and K2SO4(aq). As recommended by Clegg et al.,14 the parameters α and α1 for the 2−2 electrolyte MgSO4(aq) are 7 and 95, respectively. The other binary model parameters B, B1, W, U, and V were determined by fitting them to the water activity data mentioned above.17,19,20 For the Li2SO4−H2O system, the parameter B1 in the long-range terms was omitted, as its solubility limit is within 3.5 mol·kg−1 at 273.15 K. The parameters B, W, and U were found to be sufficient for the K2SO4−H2O system with a solubility of 0.43 mol·kg−1. The fitted parameters for these three binary systems and their standard deviations are listed in Table 4. The calculated water activities agree well with the experimental values, as shown in Figure 1. 4.2. Ternary Parameter Determination. To calculate the ternary and quaternary phase diagrams, the solubility product based on the mole fraction for each solid phase should be determined in advance. The solubility products were obtained by calculating the activities of ions and water at the solubility points in each binary system according to eq 1, using the parameters in Table 4.

Figure 1. Comparisons of calculated osmotic coefficients for the system Li2SO4−H2O, K2SO4−H2O, and MgSO4−H2O with literature data at 273.15 K: ■, Li2SO4(aq);17 □, K2SO4(aq);19 ●, MgSO4(aq);20 , model values.

The binary solubility data for Li2SO4(aq) and MgSO4(aq) were taken from this work, and that for K2SO4(aq) was taken from the literature.21 The obtained ln K values for Li2SO4·H2O, K2SO4 and MgSO4·7H2O are shown in Table 5. Table 5. Solubility Products (ln K) of the Solid Phases in the System Li2SO4−K2SO4−MgSO4−H2O at 273.15 K

+

ln K

source of solubility data for fitting

−10.435 −17.202 −15.002 −15.384 −33.653

this work 21 this work 22 24

Using the binary parameters in Tables 4 and 5, we predicted the solubility isotherms of the three systems and found that the predicted results (dashed lines in Figures 2, 3, and 4) deviate from the experimental values in the literature22−24 and this work remarkably. Thus, the ternary mixing parameters Wmnx, Qmnx, and Umnx must be introduced into the model. Because the water activity data for all three ternary systems at 273.15 K are unavailable, we evaluated their values by fitting them to the experimental solubility isotherms and present them in Table 6. It should be mentioned that the parameter Umnx was set equal to zero in this work as suggested by Clegg et al.14 for reasonably simple systems. Applying the binary and ternary parameters in Tables 4, 5, and 6, we calculated the solubility isotherms of these three ternary systems at 273.15 K. The calculated values (solid lines

M v+X v−·nH 2O(s) = v+ M+(aq) + v− X−(aq) + nH 2O(aq) −

v v n + a − a ln K = ln(a M ) (aq) X (aq) H 2O(aq)

solid phase Li2SO4·H2O K2SO4 MgSO4·7H2O LiKSO4 K2SO4·MgSO4·6H2O

(1) 1694

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Figure 4. Comparison of the calculated (lines) and experimental (symbols) solubility data for the ternary system K2SO4−MgSO4−H2O at 273.15 K: ■, exp. values;23 □, expt values in this work; ○, expt values;24 , model values with binary parameters and mixture parameters; ---, model values with binary parameters only.

Figure 2. Comparisons of calculated (lines) and experimental (symbols) solubility data for the ternary system Li2SO4−MgSO4− H2O at 273.15 K: ■, expt values in this work; , model values with binary parameters and mixture parameters; ---, model values with binary parameters only.

Table 6. Mixture Pitzer−Simonson−Clegg Model Parameters system

Wmnx

Qmnx

source of solubility data for parametrization

Li2SO4−MgSO4−H2O Li2SO4−K2SO4−H2O K2SO4−MgSO4−H2O

−18.85 −10.4 −40.4

2.55 3.2 7.8

this work 22 24

Figure 3. Comparisons of calculated (lines) and experimental (symbols) solubility data for the ternary system Li2SO4−K2SO4− H2O at 273.15 K: ■, expt values;22 , model values with binary parameters and mixture parameters; ---, model values with binary parameters only.

in Figures 2, 3, and 4) agree satisfactorily with the experimental points. 4.3. Solubility Prediction of the Quaternary System Li2SO4−K2SO4−MgSO4−H2O. Furthermore, we predicted the solubility isotherms of the quaternary title system at 273.15 K and compared them with our experimental data, as shown in Figure 5. The two sets of results agree with one another very well. This agreement could be interpreted as indicating that both the measured and predicted solubility results in this work are reliable. On the basis of the model calculation, more information could be obtained concerning the title system. For example, we calculated a series of equal-scale lines of water content (the ratio of water to total salt amounts in mass equals to a certain value) and presented them in Figure 6. With the help of the equal-scale lines of water content, one can intuitively formulate how a solution composition changes as it is evaporated at 273.15 K. For instance, when a solution with an initial composition at point a in Figure 6 is evaporated at 273.15 K,

Figure 5. Dry-salt phase diagram of the quaternary system Li2SO4− K2SO4−MgSO4−H2O at 273.15 K: □, experimental values with two solid phases, ■, experimental values with three solid phases, −, predicted eutectic lines.

the solution composition will proceed along the direction a→ b→c→d→e illustrated in Figure 6 and the final liquid phase will disappear at point e.

5. CONCLUSIONS Solubility isotherms for the ternary system Li2SO4−MgSO4− H2O and the quaternary system Li2SO4−K2SO4−MgSO4−H2O at 273.15 K were determined using the isothermal method. The Pitzer−Simonson−Clegg model was applied to simulate the thermodynamic properties of the binary and ternary systems of the quaternary title system and predict the solubility isotherms of the quaternary title system at 273.15 K. The predicted and measured solubility isotherms of the quaternary title system 1695

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(7) Fang, C.; Li, B.; Li, J.; Wang, Q.; Song, P. Studies on the Phase Diagram and Solution Properties for the Quaternary System Li+, K+, Mg2+/SO42−−H2O at 25 °C. Huaxue Xuebao 1994, 52, 954−959. (8) Shevchuk, V. G.; Kost, L. L. The Lithium Sulfate−Potassium Sulfate−Magnesium Sulfate System at 35°C. Zh. Neorg. Khim. 1964, 9, 1242−1245. (9) Kost, L. L.; Shevchuk, V. G. Lithium Sulfate−Potassium Sulfate− Magnesium Sulfate−Water System at 50 °C. Zh. Neorg. Khim. 1968, 13, 271−276. (10) Kost, L. L.; Shevchuk, V. G. Lithium Sulfate−Potassium Sulfate−Magnesium Sulfate−Water System at 75 °C. Zh. Neorg. Khim. 1969, 14, 574−576. (11) Wang, S.; Gao, J.; Yu, X.; Zhang, B.; Sun, B.; Deng, T. Study on the Interference of Coexisting Lithium Ion on the Measurement of Magnesium Ion. J. Salt Lake Res. 2007, 15, 44−48. (12) Kolthoff, M.; Sandell, E. B.; Meehan, E. J. Quantitative Chemical Analysis; Macmillan: New York, 1969. (13) Clegg, S. L.; Pitzer, K. S. Thermodynamics of Multicomponent, Miscible, Ionic Solutions: Generalized Equations for Symmetrical Electrolytes. J. Phys. Chem. A 1992, 96, 3513−3520. (14) Clegg, S. L.; Pitzer, K. S.; Brimblecombe, P. Thermodynamics of Multicomponent, Miscible, Ionic Solutions. Mixtures Including Unsymmetrical Electrolytes. J. Phys. Chem. 1992, 96, 9470−9479. (15) Guo, L.; Sun, B.; Zeng, D.; Yao, Y.; Han, H. Isopiestic Measurement and Solubility Evaluation of the Ternary System LiCl− SrCl2−H2O at 298.15 K. J. Chem. Eng. Data 2012, 57, 817−827. (16) Ouyang, H.; Zeng, D.; Zhou, H.; Han, H.; Yao, Y. Solubility of the Ternary System LiCl+NH4Cl+H2O. J. Chem. Eng. Data 2011, 56, 1096−1104. (17) Li, F.; Yao, Y. Isopiestic Studies of Thermodynamic Properties in LiCl−Li2SO4−H2O System at 273.15 K. Chem. Res. Appl. (in Chinese) 2004, 16, 33−36. (18) Rard, J. A.; Clegg, S. L.; Palmer, D. A. Isopiestic Determination of the Osmotic and Activity Coefficients of Li2SO4(aq) at T = 298.15 and 323.15 K, and Representation with an Extended Ion-Interaction (Pitzer) Model. J. Solution Chem. 2007, 36, 1347−1371. (19) Holmes, H. F.; Mesmer, R. E. Thermodynamics of Aqueous Solutions of the Alkali Metal Sulfates. J. Solution Chem. 1986, 15, 495− 517. (20) Platford, R. F. Osmotic Coefficients of Aqueous Solutions of Seven Compounds at 0 °C. J. Chem. Eng. Data 1973, 18, 215−217. (21) Linke, W. F.; Seidell, A. Solubilities: Inorganic and Metal−Organic Compounds, 4th ed.; American Chemical Society: Washington DC, 1965. (22) Druzhinin, I. G.; Yanko, A. P. Polytherm of the System Lithium Sulfate−Potassium Sulfate−Water at 0−50 °C. Isvest. Kirgiz. Filiala Akad. Nauk S.S.S.R. 1954, 63−75. (23) Pelsha, A. D. Handbook of Experimental Data for Salt Solubilities, Ternary Systems; Khimia: Leningrad, 1973; Vol. 1. (24) Benrath, A.; Wazelle, H. The Reciprocal Salt Pair MgSO4+K2(NO3)2Mg(NO3)2+K2SO4. Z. Anorg. Allg. Chem. 1930, 189, 72−81.

Figure 6. Equal-scale lines of water content in the quaternary system Li2SO4−K2SO4−MgSO4−H2O at 273.15 K: −, predicted eutectic lines; ---, predicted equal-scale lines of water content. The digitals indicate the water content in grams per unit gram of salts.

agree with one another very well. A series of equal-scale lines of water content of the quaternary title system has been calculated. On the basis of the calculated equal-scale lines of water content, the behavior of isothermal evaporation of the quaternary title system at 273.15 K can be readily understood.

■

ASSOCIATED CONTENT

* Supporting Information S

The activity of water and activities of the ions as functions of salt concentration in the framework of the Pitzer−Simonson− Clegg model. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel: +86 13618496806. Fax: +86 731 88879616. E-mail: [email protected]. Funding

This work was financially supported by the 100 Top Talents Project of the Chinese Academy of Sciences. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Li, B.; Wang, Q.; Li, J.; Fang, C.; Song, P. Study of the Ternary Systems Li+, K+/SO42−−H2O and Li+, Mg2+/SO42−−H2O at 25 °C. Wuli Huaxue Xuebao 1994, 10, 536−42. (2) Lepeshkov, I. N.; Romashova, N. N. Solubility in the System Li2SO4−Na2SO4−MgSO4−H2O at 25 °C. Zh. Neorg. Khim. 1959, 4, 2812−15. (3) Aravamùdan, G. The System Lithium Sulphate−Magnesium Sulphate−Water at 30 °C. Can. J. Chem. 1962, 40, 1035−1037. (4) Shevchuk, V. G. The Equilibrium in the Systems Li2SO4− MgSO4−H2O and Rb2SO4−MgSO4−H2O at 35 °C. Zh. Neorg. Khim. 1961, 6, 1955−1958. (5) Vaisfel’d, M. I.; Shevchuk, V. G. Lithium Chloride−Magnesium Sulfate−Lithium Sulfate−Magnesium Chloride−Water System at 50 °C. Zh. Neorg. Khim. 1967, 12, 1688−1692. (6) Lepeshkov, I. N.; Romashova, N. N. The Solubility in the System Li2SO4−Na2SO4−MgSO4−H2O at 75 °C. Zh. Neorg. Khim. 1960, 5, 2512−2517. 1696

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