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Isopiestic Investigation of the Osmotic and Activity Coefficients of {yMgCl2+(1−y)MgSO4}(aq) and the Osmotic Coefficients of Na2SO4⋅MgSO4(aq) at 298.15 K

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Abstract

Isopiestic vapor-pressure measurements were made for {yMgCl2+(1−y)MgSO4}(aq) solutions with MgCl2 ionic strength fractions of y=(0,0.1997,0.3989,0.5992,0.8008, and 1) at the temperature 298.15 K, using KCl(aq) as the reference standard. These measurements for the mixtures cover the ionic strength range I=0.9794 to 9.4318 mol⋅kg−1. In addition, isopiestic measurements were made with NaCl(aq) as reference standard for mixtures of {xNa2SO4+(1−x)MgSO4}(aq) with the molality fraction x=0.5000 that correspond to solutions of the evaporite mineral bloedite (astrakanite), Na2Mg(SO4)2⋅4H2O(cr). The total molalities, m T=m(Na2SO4)+m(MgSO4), range from m T=1.4479 to 4.4312 mol⋅kg−1 (I=5.0677 to 15.509 mol⋅kg−1), where the uppermost concentration is the highest oversaturation molality that could be achieved by isothermal evaporation of the solvent at 298.15 K. The parameters of an extended ion-interaction (Pitzer) model for MgCl2(aq) at 298.15 K, which were required for an analysis of the {yMgCl2+(1−y)MgSO4}(aq) mixture results, were evaluated up to I=12.075 mol⋅kg−1 from published isopiestic data together with the six new osmotic coefficients obtained in this study. Osmotic coefficients of {yMgCl2+(1−y)MgSO4}(aq) solutions from the present study, along with critically-assessed values from previous studies, were used to evaluate the mixing parameters of the extended ion-interaction model.

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References

  1. Pitzer, K.S.: Ion interaction approach: Theory and data correlation. In: Pitzer, K.S. (ed.) Activity Coefficients in Electrolyte Solutions, 2nd edn. CRC Press, Boca Raton (1991), Chap. 3

    Google Scholar 

  2. Harvie, C.E., Weare, J.H.: The prediction of mineral solubilities in natural waters: The Na–K–Mg–Ca–Cl–SO4–H2O system from zero to high concentration at 25 °C. Geochim. Cosmochim. Acta 44, 981–997 (1980)

    Article  CAS  Google Scholar 

  3. Pabalan, R.T., Pitzer, K.S.: Thermodynamics of concentrated electrolyte mixtures and the prediction of mineral solubilities to high temperatures for mixtures in the system Na–K–Mg–Cl–SO4–OH–H2O. Geochim. Cosmochim. Acta 51, 2429–2443 (1987)

    Article  CAS  Google Scholar 

  4. Møller, N.: The prediction of mineral solubilities in natural waters: A chemical equilibrium model for the Na–Ca–Cl–SO4–H2O system, to high temperature and concentration. Geochim. Cosmochim. Acta 52, 821–837 (1988)

    Article  Google Scholar 

  5. Marion, G.M., Farren, R.E.: Mineral solubilities in the Na–K–Mg–Ca–Cl–SO4–H2O system: A re-evaluation of the sulfate chemistry in the Spencer-Møller-Weare model. Geochim. Cosmochim. Acta 63, 1305–1318 (1999)

    Article  CAS  Google Scholar 

  6. Clegg, S.L., Pitzer, K.S., Brimblecombe, P.: Thermodynamics of multicomponent, miscible, ionic solutions. 2. Mixtures including unsymmetrical electrolytes. J. Phys. Chem. 96, 9470–9479 (1992)

    Article  CAS  Google Scholar 

  7. Clegg, S.L., Brimblecombe, P., Liang, Z., Chan, C.K.: Thermodynamic properties of aqueous aerosols to high supersaturation: II—A model of the system Na+–Cl−–NO −3 –SO 2−4 –H2O at 298.15 K. Aerosol Sci. Technol. 27, 345–366 (1997)

    Article  CAS  Google Scholar 

  8. Archer, D.G.: Thermodynamic properties of the NaCl + H2O system. II. Thermodynamic properties of NaCl(aq), NaCl⋅2H2O(cr), and phase equilibria. J. Phys. Chem. Ref. Data 21, 793–829 (1992)

    Article  CAS  Google Scholar 

  9. Clegg, S.L., Rard, J.A., Pitzer, K.S.: Thermodynamic properties of 0–6 mol kg−1 aqueous sulfuric acid from 273.15 to 328.15 K. J. Chem. Soc., Faraday Trans. 90, 1875–1894 (1994)

    Article  CAS  Google Scholar 

  10. Pitzer, K.S., Wang, P., Rard, J.A., Clegg, S.L.: Thermodynamics of electrolytes. 13. Ionic strength dependence of higher-order terms; equations for CaCl2 and MgCl2. J. Solution Chem. 28, 265–282 (1999)

    Article  CAS  Google Scholar 

  11. Wang, P., Pitzer, K.S., Simonson, J.M.: Thermodynamic properties of aqueous magnesium chloride solutions from 250 to 600 K and to 100 MPa. J. Phys. Chem. Ref. Data 27, 971–991 (1998)

    CAS  Google Scholar 

  12. Rard, J.A., Platford, R.F.: Experimental methods: Isopiestic. In: Pitzer, K.S. (ed.) Activity Coefficients in Electrolyte Solutions, 2nd edn. CRC Press, Boca Raton (1991), Chap. 5

    Google Scholar 

  13. Platford, R.F.: Isopiestic measurements on the system water–sodium chloride–magnesium chloride at 25 °. J. Phys. Chem. 72, 4053–4057 (1968)

    Article  CAS  Google Scholar 

  14. Rard, J.A., Miller, D.G.: Isopiestic determination of the osmotic and activity coefficients of aqueous mixtures of NaCl and MgCl2 at 25 °C. J. Chem. Eng. Data 32, 85–92 (1987)

    Article  CAS  Google Scholar 

  15. Rard, J.A., Clegg, S.L., Platford, R.F.: Thermodynamics of {zNaCl+(1−z)Na2SO4}(aq) from T=278.15 K to T=318.15 K, and representation with an extended ion-interaction (Pitzer) model. J. Chem. Thermodyn. 35, 967–1008 (2003)

    Article  CAS  Google Scholar 

  16. Padova, J., Saad, D.: Thermodynamics of mixed electrolyte solutions. VIII. An isopiestic study of the ternary system KCl–MgCl2–H2O at 25 °C. J. Solution Chem. 6, 57–71 (1977)

    Article  CAS  Google Scholar 

  17. Kuschel, F., Seidel, J.: Osmotic and activity coefficients of aqueous K2SO4–MgSO4 and KCl–MgCl2 at 25 °C. J. Chem. Eng. Data 30, 440–445 (1985)

    Article  CAS  Google Scholar 

  18. Miladinović, J., Ninković, R., Todorović, M.: Osmotic and activity coefficients of {yKCl+(1−y)MgCl2}(aq) at T=298.15 K. J. Solution Chem. 36, 1401–1419 (2007)

    Article  CAS  Google Scholar 

  19. Robinson, R.A., Bower, V.E.: Properties of aqueous mixtures of pure salts. Thermodynamics of the ternary system: water-calcium chloride-magnesium chloride at 25 °C. J. Res. Natl. Bur. Stand., A. Phys. Chem. 70A, 305–311 (1966)

    Google Scholar 

  20. Kirgintsev, A.N., Luk’yanov, A.V.: Isopiestic investigation of ternary solutions. VII. Ternary solutions lithium chloride–caesium chloride–water, potassium chloride–caesium chloride–water, rubidium chloride–caesium chloride–water, potassium chloride–calcium chloride–water, and potassium chloride–magnesium chloride–water. Russ. J. Phys. Chem. 40, 686–688 (1966). (English translation)

    Google Scholar 

  21. Wu, Y.C., Rush, R.M., Scatchard, G.: Osmotic and activity coefficients for binary mixtures of sodium chloride, sodium sulfate, magnesium sulfate, and magnesium chloride in water at 25 °. I. Isopiestic measurements on the four systems with common ions. J. Phys. Chem. 72, 4048–4053 (1968)

    Article  CAS  Google Scholar 

  22. Platford, R.F.: Thermodynamics of the system H2O–NaCl–Na2SO4–MgSO4 to the saturation limit of NaCl at 25 °C. J. Solution Chem. 3, 771–780 (1974)

    Article  CAS  Google Scholar 

  23. Platford, R.F.: Thermodynamics of the system H2O–NaCl–MgCl2–Na2SO4–MgSO4 at 25 °C. Mar. Chem. 3, 261–270 (1975)

    Article  CAS  Google Scholar 

  24. Saad, D., Padova, J., Marcus, Y.: Thermodynamics of mixed electrolyte solutions. VI. An isopiestic study of a pseudo-ternary system: NaCl–KCl–MgCl2–H2O at 25 °C. J. Solution Chem. 4, 983–993 (1975)

    Article  CAS  Google Scholar 

  25. Filippov, V.K., Cheremnykh, L.N.: The thermodynamic study of the Mg∥Cl, SO4–H2O system at 25 °C. Sov. Prog. Chem. 50(10), 20–24 (1984). (English translation)

    Google Scholar 

  26. Seidel, J., Rossner, K., Kuschel, F.: Isopiestic determination of the osmotic and activity coefficients of aqueous mixtures of potassium chloride and magnesium sulfate up to high concentrations at 25 °. J. Chem. Eng. Data 30, 289–292 (1985)

    Article  CAS  Google Scholar 

  27. Filippov, V.K., Korobkova, E.V., Belova, L.V.: Thermodynamics of phase equilibria at 50 °C in quaternary water–salt systems containing the chlorides and sulfates of sodium, potassium, and magnesium. J. Appl. Chem. USSR 61, 874–878 (1988). (English translation)

    Google Scholar 

  28. Srna, R.F., Wood, R.H.: Heats of mixing aqueous electrolytes. XIII. The reciprocal salt pair Na+, Mg2+ ∥Cl−, SO 2−4 . J. Phys. Chem. 79, 1535–1540 (1975)

    Article  CAS  Google Scholar 

  29. Duer, W.C., Leung, W.H., Oglesby, G.B., Millero, F.J.: Seawater—A test of multicomponent electrolyte solution theories. II. Enthalpy of mixing and dilution of the major sea salts. J. Solution Chem. 5, 509–528 (1976)

    Article  CAS  Google Scholar 

  30. Wood, R.H., Mayrath, J.E.: Enthalpies of mixing of some aqueous electrolytes at 373.15 K. J. Chem. Thermodyn. 14, 1135–1141 (1982)

    Article  CAS  Google Scholar 

  31. Zdanovskii, A.B., Afonichkin, O.V.: Mixed isopiestic aqueous solutions of sodium and magnesium sulphates at 25 °C. Russ. J. Phys. Chem. 50, 481–482 (1976). (English translation)

    Google Scholar 

  32. Rard, J.A., Miller, D.G.: Isopiestic determination of the osmotic coefficients of aqueous Na2SO4, MgSO4, and Na2SO4–MgSO4 at 25 °C. J. Chem. Eng. Data 26, 33–38 (1981)

    Article  CAS  Google Scholar 

  33. Pavićević, V., Ninković, R., Todorović, M., Miladinović, J.: Osmotic and activity coefficients of {yNaH2PO4+(1−y)Na2SO4}(aq) at the temperature 298.15 K. Fluid Phase Equilib. 164, 275–284 (1999)

    Article  Google Scholar 

  34. Rard, J.A.: Solubility determinations by the isopiestic method and application to aqueous lanthanide nitrates at 25 °C. J. Solution Chem. 14, 457–471 (1985)

    Article  CAS  Google Scholar 

  35. Rard, J.A.: Isopiestic determination of the osmotic and activity coefficients of {zH2SO4+(1−z)MgSO4}(aq) at the temperature T=298.15 K. I. Results for z=(0.85811, 0.71539, and 0.57353). J. Chem. Thermodyn. 29, 533–555 (1997)

    Article  CAS  Google Scholar 

  36. Archer, D.G.: Thermodynamic properties of the KCl + H2O system. J. Phys. Chem. Ref. Data 28, 1–17 (1999)

    Article  CAS  Google Scholar 

  37. Archer, D.G., Rard, J.A.: Isopiestic investigation of the osmotic and activity coefficients of aqueous MgSO4 and the solubility of MgSO4⋅7H2O(cr) at 298.15 K: Thermodynamic properties of the MgSO4+H2O system to 440 K. J. Chem. Eng. Data 43, 791–806 (1998); errata, 45, 716 (2000)

    Article  CAS  Google Scholar 

  38. Robinson, R.A., Stokes, R.H.: A thermodynamic study of bivalent metal halides in aqueous solution. Part I. The activity coefficients of magnesium halides at 25 °. Trans. Faraday Soc. 36, 733–734 (1940)

    Article  CAS  Google Scholar 

  39. Stokes, R.H.: A thermodynamic study of bivalent metal halides in aqueous solution. Part XIV. Concentrated solutions of magnesium chloride at 25 °. Trans. Faraday Soc. 41, 642–645 (1945)

    Article  CAS  Google Scholar 

  40. Frolov, Yu.G., Nikolaev, V.P., Karapet’yants, M.Kh., Vlasenko, K.K.: Excess thermodynamic functions of mixing of aqueous isopiestic solutions without common ions. Russ. J. Phys. Chem. 45, 1054–1055 (1971). (English translation)

    Google Scholar 

  41. Rard, J.A., Miller, D.G.: Isopiestic determination of the osmotic and activity coefficients of aqueous MgCl2 solutions at 25 °C. J. Chem. Eng. Data 26, 38–43 (1981)

    Article  CAS  Google Scholar 

  42. Gibbard, Jr., H.F., Gossmann, A.F.: Freezing points of electrolyte mixtures. I. Mixtures of sodium chloride and magnesium chloride in water. J. Solution Chem. 3, 385–393 (1974)

    Article  CAS  Google Scholar 

  43. Rard, J.A., Clegg, S.L.: Critical evaluation of the thermodynamic properties of aqueous calcium chloride. 1. Osmotic and activity coefficients of 0–10.77 mol⋅kg−1 aqueous calcium chloride solutions at 298.15 K and correlation with extended Pitzer ion-interaction models. J. Chem. Eng. Data 42, 819–849 (1997)

    Article  CAS  Google Scholar 

  44. Archer, D.G., Wang, P.: The dielectric constant of water and Debye-Hückel limiting law slopes. J. Phys. Chem. Ref. Data 19, 371–411 (1990)

    Article  CAS  Google Scholar 

  45. Rodil, E., Vera, J.H.: Individual activity coefficients of chloride ions in aqueous solutions of MgCl2, CaCl2 and BaCl2 at 298.2 K. Fluid Phase Equil. 187–188, 15–27 (2001)

    Article  Google Scholar 

  46. Pitzer, K.S.: Thermodynamics of electrolytes. V. Effects of higher-order electrostatic terms. J. Solution Chem. 4, 249–265 (1975)

    Article  CAS  Google Scholar 

  47. Kim, H.-T., Frederick, W.J. Jr.: Evaluation of Pitzer ion interaction parameters of aqueous mixed electrolyte solutions at 25 °C. Ternary mixing parameters. J. Chem. Eng. Data 33, 278–283 (1988)

    Article  CAS  Google Scholar 

  48. Scatchard, G.: Osmotic coefficients and activity coefficients in mixed electrolyte solutions. J. Am. Chem. Soc. 83, 2636–2642 (1961)

    Article  CAS  Google Scholar 

  49. Rard, J.A., Clegg, S.L., Palmer, D.A.: Isopiestic determination of the osmotic coefficients of Na2SO4(aq) at 25 and 50 °C, and representation with ion-interaction (Pitzer) and mole fraction thermodynamic models. J. Solution Chem. 29, 1–49 (2000)

    Article  CAS  Google Scholar 

  50. Mounir, A., El Guendouzi, M., Dinane, A.: Hygrometric determination of the thermodynamic properties of the system MgSO4–Na2SO4–H2O at 298.15 K. Fluid Phase Equil. 201, 233–244 (2002)

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Inorganic Chemical Technology, Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, Belgrade, Serbia

    Jelena Miladinović, Rozalija Ninković & Milica Todorović

  2. Energy and Environment Directorate, Lawrence Livermore National Laboratory, University of California, Livermore, CA, 94550, USA

    Joseph A. Rard

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  1. Jelena Miladinović
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  2. Rozalija Ninković
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  3. Milica Todorović
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  4. Joseph A. Rard
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Correspondence to Jelena Miladinović or Joseph A. Rard.

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Miladinović, J., Ninković, R., Todorović, M. et al. Isopiestic Investigation of the Osmotic and Activity Coefficients of {yMgCl2+(1−y)MgSO4}(aq) and the Osmotic Coefficients of Na2SO4⋅MgSO4(aq) at 298.15 K. J Solution Chem 37, 307–329 (2008). https://doi.org/10.1007/s10953-007-9238-y

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