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Calculations of Freezing Point Depression, Boiling Point Elevation, Vapor Pressure and Enthalpies of Vaporization of Electrolyte Solutions by a Modified Three-Characteristic Parameter Correlation Model

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An Erratum to this article was published on 17 April 2013

Abstract

A method was proposed for calculating the thermodynamic properties, freezing point depression, boiling point elevation, vapor pressure and enthalpy of vaporization for single solute electrolyte solutions, including aqueous and nonaqueous solutions, based on a modified three-characteristic-parameter correlation model. When compared with the corresponding literature values, the calculated results show that this method gives a very good approximation, especially for 1-1 electrolytes. Although the method is not very suitable for some solutions with very high ionic strength, it is still a very useful technique when experimental data is scarce.

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References

  1. Adams, L.H.: The measurement of the freezing-point depression of dilute solutions. J. Am. Chem. Soc. 37, 481–496 (1914). doi:10.1021/ja02168a005

    Article  Google Scholar 

  2. Ambrose, D., Sprake, C.H.S.: Thermodynamic properties of organic oxygen compounds. XXV. Vapor pressures and normal boiling temperatures of aliphatic alcohols. J. Chem. Thermodyn. 2, 631–645 (1970). doi:10.1016/0021-9614(70)90038-8

    Article  CAS  Google Scholar 

  3. Apelblat, A.: Cryoscopy of uranyl nitrate solutions and activity coefficients. J. Inorg. Nucl. Chem. 39, 1852–1854 (1977). doi:10.1016/0022-1902(77)80220-0

    Article  Google Scholar 

  4. Apelblat, A.: The vapour pressures of water over saturated aqueous solutions of barium chloride, magnesium nitrate, calcium nitrate, potassium carbonate, and zinc sulfate, at temperatures from 283 K to 313 K. J. Chem. Thermodyn. 24, 619–626 (1992). doi:10.1016/S0021-9614(05)80033-3

    Article  CAS  Google Scholar 

  5. Apelblat, A.: The vapour pressures of saturated aqueous solutions of potassium bromide, ammonium sulfate, copper(II) sulfate, iron(II) sulfate, and manganese(II) dichloride, at temperatures from 283 K to 308 K. J. Chem. Thermodyn. 25, 1513–1520 (1993). doi:10.1006/jcht.1993.1151

    Article  CAS  Google Scholar 

  6. Apelblat, A.: The vapour pressures of saturated aqueous lithium chloride, sodium bromide, sodium nitrate, ammonium nitrate, and ammonium chloride at temperatures from 283 K to 313 K. J. Chem. Thermodyn. 25, 63–71 (1993). doi:10.1006/jcht.1993.1008

    Article  CAS  Google Scholar 

  7. Apelblat, A.: Vapour pressures of H2 16O and H2 18O, and saturated aqueous solutions of KCl from T=298 K to T=318 K by the isoteniscopic method. J. Chem. Thermodyn. 30, 1191–1198 (1998). doi:10.1006/jcht.1998.0381

    Article  Google Scholar 

  8. Apelblat, A., Korin, E.: The vapour pressures of saturated aqueous solutions of sodium chloride, sodium bromide, sodium nitrate, sodium nitrite, potassium iodate, and rubidium chloride at temperatures from 277 K to 323 K. J. Chem. Thermodyn. 30, 59–71 (1998). doi:10.1006/jcht.1997.0275

    Article  CAS  Google Scholar 

  9. Apelblat, A., Korin, E.: Vapour pressures of saturated aqueous solutions of ammonium iodide, potassium iodide, potassium nitrate, strontium chloride, lithium sulphate, sodium thiosulphate, magnesium nitrate, and uranyl nitrate from T=(278 to 323) K. J. Chem. Thermodyn. 30, 459–471 (1998). doi:10.1006/jcht.1997.0311

    Article  CAS  Google Scholar 

  10. Apelblat, A., Korin, E.: The molar enthalpies of solution and vapour pressures of saturated aqueous solutions of aluminium chloride, aluminium nitrate and aluminium sulphate. J. Chem. Thermodyn. 34, 1919–1927 (2002). doi:10.1016/S0021-9614(02)00188-X

    Google Scholar 

  11. Apelblat, A., Korin, E.: The molar enthalpies of solution and vapour pressures of saturated aqueous solutions of some ammonium salts. J. Chem. Thermodyn. 35, 699–709 (2003). doi:10.1016/S0021-9614(02)00353-1

    Article  CAS  Google Scholar 

  12. Apelblat, A., Korin, E.: The molar enthalpies of solution and vapour pressures of saturated aqueous solutions of some cesium salts. J. Chem. Thermodyn. 38, 152–157 (2006). doi:10.1016/j.jct.2005.04.016

    Article  CAS  Google Scholar 

  13. Apelblat, A., Korin, E.: The vapour pressures over saturated aqueous solutions of cadmium chloride, cadmium bromide, cadmium iodide, cadmium nitrate, and cadmium sulphate. J. Chem. Thermodyn. 39, 1065–1070 (2007). doi:10.1016/j.jct.2006.12.010

    Article  CAS  Google Scholar 

  14. Apelblat, A., Manzurola, E.: The vapour pressures over saturated aqueous solutions of sodium and potassium acetates, chlorates, and perchlorates. J. Chem. Thermodyn. 39, 1176–1181 (2007). doi:10.1016/j.jct.2006.12.006

    Article  CAS  Google Scholar 

  15. Apelblat, A., Mariana, D., Jaime, W., Jacob, Z.: The vapour pressure of water over saturated aqueous solutions of malic, tartaric, and citric acids, at temperatures from 288 K to 323 K. J. Chem. Thermodyn. 27, 35–41 (1995). doi:10.1006/jcht.1995.0004

    Article  CAS  Google Scholar 

  16. Apelblat, A., Korin, E., Emanuel, M.: Solubilities and vapour pressures of saturated aqueous solutions of sodium peroxydisulfate and potassium peroxydisulfate. J. Chem. Thermodyn. 33, 61–69 (2001). doi:10.1006/jcht.2000.0780

    Article  CAS  Google Scholar 

  17. Bancroft, W.D., Davis, H.L.: The boiling-points of aqueous solutions. J. Phys. Chem. 33, 591–604 (1929). doi:10.1021/j150298a008

    Article  CAS  Google Scholar 

  18. Barthel, J., Lauermann, G.: Vapor pressure of non-aqueous electrolyte solutions. Part 3. Solutions of sodium iodide in ethanol, 2-propanol, and acetonitrile. J. Solution Chem. 15, 869–877 (1986). doi:10.1007/BF00646093

    Article  CAS  Google Scholar 

  19. Barthel, J., Neueder, R., Lauermann, G.: Vapor pressure of non-aqueous electrolyte solutions. Part 1. Alkali metal salts in methanol. J. Solution Chem. 14, 621–633 (1985). doi:10.1007/BF00646055

    Article  CAS  Google Scholar 

  20. Barthel, J., Lauermann, G., Neueder, R.: Vapor pressure measurements on non-aqueous electrolyte solutions. Part 2. Tetraalkylammonium salts in methanol, activity coefficients of various 1-1 electrolytes at high concentrations. J. Solution Chem. 15, 851–867 (1986). doi:10.1007/BF00646092

    Article  CAS  Google Scholar 

  21. Barthel, J., Neueder, R., Poepke, H., Wittmann, H.: Osmotic and activity coefficients of nonaqueous electrolyte solutions. 1. Lithium perchlorate in the protic solvents methanol, ethanol, and 2-propanol. J. Solution Chem. 27, 1055–1066 (1998). doi:10.1023/A:1022637316064

    Article  CAS  Google Scholar 

  22. Beyer, R., Steiger, M.: Vapour pressure measurements and thermodynamic properties of aqueous solutions of sodium acetate. J. Chem. Thermodyn. 34, 1057–1071 (2002). doi:10.1006/jcht.2002.0974

    Article  CAS  Google Scholar 

  23. Bixon, E., Guerry, R., Tassios, D.: Salt effect on the vapor pressure of pure solvents: methanol with seven salts; at 24.9 °C. J. Chem. Eng. Data 24, 9–11 (1979). doi:10.1021/je60080a005

    Article  CAS  Google Scholar 

  24. Bradley, J.B., Pitzer, K.S.: Thermodynamics of electrolytes. 12. Dielectric properties of water and Debye-Hückel parameters to 350 °C and 1 kbar. J. Phys. Chem. 83, 1599–1603 (1979). doi:10.1021/j100475a009

    Article  CAS  Google Scholar 

  25. Bridgeman, O.C., Aldrich, E.W.: Vapor pressure tables for water. J. Heat Transf. 86, 279–286 (1964)

    CAS  Google Scholar 

  26. Bromley, L.A.: Thermodynamic properties of strong electrolytes in aqueous solutions. AIChE J. 19, 313–320 (1973). doi:10.1002/aic.690190216

    Article  CAS  Google Scholar 

  27. Campbell, A.N., Bhatnagar, O.N.: Osmotic and activity coefficients of sodium hydroxide in water from 150 to 250 °C. J. Chem. Eng. Data 29, 166–168 (1984). doi:10.1021/je00036a020

    Article  CAS  Google Scholar 

  28. Chen, C.C., Evans, L.B.: A local composition model for excess Gibbs energy of electrolyte systems. AIChE J. 32, 444–454 (1986). doi:10.1002/aic.690320311

    Article  CAS  Google Scholar 

  29. Chen, C.C., Britt, H.I., Boston, J.F., Evans, L.B.: Local composition model for excess Gibbs energy of electrolyte systems. AIChE J. 28, 588–596 (1982). doi:10.1002/aic.690280410

    Article  CAS  Google Scholar 

  30. De Coppet, L.C.: On the molecular depression of the freezing-point of water produced by some very concentrated saline solutions. J. Phys. Chem. 8, 531–538 (1904). doi:10.1021/j150062a001

    Article  Google Scholar 

  31. Ge, X.L., Wang, X.D.: A simple two-parameter correlation model for aqueous electrolyte solutions across a wide range of temperature. J. Chem. Eng. Data 54, 179–186 (2009)

    Article  CAS  Google Scholar 

  32. Ge, X.L., Wang, X.D., Zhang, M., Seetharaman, S.: Correlation and prediction of activity and osmotic coefficients of aqueous electrolytes at 298.15 K by the modified TCPC model. J. Chem. Eng. Data 52, 538–547 (2007). doi:10.1021/je060451k

    Article  CAS  Google Scholar 

  33. Ge, X.L., Wang, X.D., Zhang, M., Seetharaman, S.: A new three-particle-interaction model to predict the thermodynamic properties of different electrolytes. J. Chem. Thermodyn. 39, 602–612 (2007). doi:10.1016/j.jct.2006.09.002

    Article  CAS  Google Scholar 

  34. Ge, X.L., Zhang, M., Guo, M., Wang, X.D.: Correlation and prediction of thermodynamic properties of some complex aqueous electrolytes by the modified three-characteristic-parameter correlation model. J. Chem. Eng. Data 53, 950–958 (2008). doi:10.1021/je7006499

    Article  CAS  Google Scholar 

  35. Ge, X.L., Zhang, M., Guo, M., Wang, X.D.: Correlation and prediction of thermodynamic properties of non-aqueous electrolytes by the modified TCPC model. J. Chem. Eng. Data 53, 149–159 (2008). doi:10.1021/je700446q

    Article  CAS  Google Scholar 

  36. Haghighi, H., Chapoy, A., Tohidi, B.: Freezing point depression of electrolyte solutions: experimental measurements and modeling using the cubic-plus-association equation of state. Ind. Eng. Chem. Res. 47, 3983–3989 (2008). doi:10.1021/ie800017e

    Article  CAS  Google Scholar 

  37. Hall, R.E., Harkins, W.D.: The free energy of dilution and the freezing-point lowering in solutions of some salts of various types of ionization, and of salt mixtures. J. Am. Chem. Soc. 38, 2658–2676 (1916). doi:10.1021/ja02269a009

    Article  CAS  Google Scholar 

  38. Huang, S.H., Radosz, M.: Equation of state for small, large, poly disperse, and associating molecules. Ind. Eng. Chem. Res. 29, 2284–2294 (1990). doi:10.1021/ie00107a014

    Article  CAS  Google Scholar 

  39. Hunter, J.B., Harding, B.: Thermodynamic properties of aqueous salt solutions. Latent heats of vaporization and other properties by the gas current method. Ind. Eng. Chem. 36, 945–953 (1944). doi:10.1021/ie50418a019

    Article  CAS  Google Scholar 

  40. Johnson, G.C., Smith, R.P.: The boiling point elevation. IV. Potassium bromide in water. J. Am. Chem. Soc. 63, 1351–1353 (1941). doi:10.1021/ja01850a060

    Article  CAS  Google Scholar 

  41. Li, W.C.: Physical Chemistry of Metallurgy and Materials. Metallurgy Press, Beijing (2001)

    Google Scholar 

  42. Lide, D.R. (ed.): CRC Handbook of Chemistry and Physics, 87th edn. CRC Press, Boca Raton (2006–2007)

    Google Scholar 

  43. Lide, D.R. (ed.): CRC Handbook of Chemistry and Physics, 88th edn. CRC Press, Boca Raton (2007–2008)

    Google Scholar 

  44. Lin, C.L., Tseng, H.C., Lee, L.S.: A three-characteristic-parameter correlation model for strong electrolyte solutions. Fluid Phase Equil. 152, 169–185 (1998). doi:10.1016/S0378-3812(98)00393-8

    Article  CAS  Google Scholar 

  45. Liu, C.T., Lindsay, W.T. Jr.: Vapor pressure of D2O from 106 to 300 °C. J. Chem. Eng. Data 15, 510–513 (1970). doi:10.1021/je60047a015

    Article  CAS  Google Scholar 

  46. Lu, J.F., Yu, Y.X., Li, Y.G.: Modification and application of the mean spherical approximation method. Fluid Phase Equil. 85, 81–100 (1996). doi:10.1016/0378-3812(93)80006-9

    Article  Google Scholar 

  47. Modell, M., Reid, R.C.: Thermodynamics and Its Applications. Prentice Hall, Englewood Cliffs (1974)

    Google Scholar 

  48. Mohammed, T.Z.M., Jaber, J.S.: Isopiestic determination of osmotic coefficients and evaluation of vapor pressures for electrolyte solutions of some lithium salts in ethanol. Fluid Phase Equil. 166, 207–223 (1999). doi:10.1016/S0378-3812(99)00293-9

    Article  Google Scholar 

  49. 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). doi:10.1016/0016-7037(88)90354-7

    Article  Google Scholar 

  50. Nasehzadeh, A., Noroozian, E., Omrani, H.: Experimental and theoretical studies of thermodynamics of lithium halide solutions–ethanol mixtures. J. Chem. Thermodyn. 36, 245–252 (2004). doi:10.1016/j.jct.2003.12.002

    Article  CAS  Google Scholar 

  51. Nasirzadeh, K., Neueder, R., Kunz, W.: Vapor pressures, osmotic and activity coefficients for (LiBr + acetonitrile) between the temperatures (298.15 and 343.15) K. J. Chem. Thermodyn. 36, 511–517 (2004). doi:10.1016/j.jct.2004.03.007

    Article  CAS  Google Scholar 

  52. Nasirzadeh, K., Neueder, R.: Measurement and correlation of osmotic coefficients and evaluation of vapor pressure for electrolyte solutions of LiClO4 and LiNO3 in methanol at 25 °C. J. Mol. Liq. 113, 13–20 (2004). doi:10.1016/j.molliq.2004.02.028

    Article  CAS  Google Scholar 

  53. Nasirzadeh, K., Salabat, A.: Isopiestic determination of osmotic coefficients and evaluation of vapor pressures for solutions of sodium bromide and sodium thiocyanate in methanol at 25 °C. J. Mol. Liq. 106, 1–14 (2003). doi:10.1016/S0167-7322(03)00016-3

    Article  CAS  Google Scholar 

  54. Nasirzadeh, K., Neueder, R., Kunz, W.: Vapor pressures and osmotic coefficients of aqueous LiOH solutions at temperatures ranging from 298.15 to 363.15 K. Ind. Eng. Chem. Res. 44, 3807–3814 (2005). doi:10.1021/ie0489148

    Article  CAS  Google Scholar 

  55. Patil, K.R., Tripathi, A.D., Pathak, G., Katti, S.S.: Thermodynamic properties of aqueous electrolyte solutions. 1. Vapor pressure of aqueous solutions of LiCl, LiBr, and LiI. J. Chem. Eng. Data 35, 166–168 (1990). doi:10.1021/je00060a020

    Article  CAS  Google Scholar 

  56. Patil, K.R., Tripathi, A.D., Pathak, G., Katti, S.S.: Thermodynamic properties of aqueous electrolyte solutions. 2. Vapor pressure of aqueous solutions of NaBr, NaI, KCl, KBr, KI, RbCl, CsCl, CsBr, CsI, MgCl2, CaCl2, CaBr2, CaI2, SrCl2, SrBr2, SrI2, BaCl2, and BaBr2. J. Chem. Eng. Data 36, 225–230 (1991). doi:10.1021/je00002a021

    Article  CAS  Google Scholar 

  57. Pepela, C.N., Dunlop, P.J.: A re-examination of the vapor pressure of aqueous sodium chloride solutions at 25 °C. J. Chem. Thermodyn. 4, 255–258 (1972). doi:10.1016/0021-9614(72)90064-X

    Article  CAS  Google Scholar 

  58. Pitzer, K.S., Mayogra, G.: Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 77, 268–277 (1973). doi:10.1021/j100621a026

    Article  CAS  Google Scholar 

  59. Randall, M., Scott, G.N.: The freezing point and activity coefficient of aqueous barium nitrate, sodium sulfate and sulfuric acid. J. Am. Chem. Soc. 49, 647–656 (1927). doi:10.1021/ja01402a007

    Article  CAS  Google Scholar 

  60. Safarov, J.T.: Study of thermodynamic properties of binary solutions of lithium bromide or lithium chloride with methanol. Fluid Phase Equil. 236, 87–95 (2005). doi:10.1016/j.fluid.2005.07.002

    Article  CAS  Google Scholar 

  61. Safarov, J.T.: Vapor pressures of lithium bromide or lithium chloride and ethanol solutions. Fluid Phase Equil. 243, 38–44 (2006). doi:10.1016/j.fluid.2006.02.012

    Article  CAS  Google Scholar 

  62. Safarov, J.T.: Investigation of the vapor pressure p of zinc bromide or zinc chloride solutions with methanol by static method. J. Chem. Thermodyn. 38, 304–311 (2006). doi:10.1016/j.jct.2005.05.017

    Article  CAS  Google Scholar 

  63. Safarov, J.T.: Vapor pressure measurements of binary solutions of CaCl2 with methanol and ethanol at (298.15 to 323.15) K using a static method. J. Chem. Eng. Data 51, 360–365 (2006). doi:10.1021/je0502086

    Article  CAS  Google Scholar 

  64. Salimi, H.R., Taghikhani, V., Ghotbi, C.: Application of the GV-MSA model to the electrolyte solutions containing mixed salts and mixed solvents. Fluid Phase Equil. 231, 67–76 (2005). doi:10.1016/j.fluid.2004.12.015

    Article  CAS  Google Scholar 

  65. Sardroodi, J.J., Seyedahmadian, S.M., Sadr, M.H., Kazemi, Y.: Isopiestic study of the solutions of MnCl2, CoCl2 and NiCl2 in methanol and ethanol at 298.15 K. Fluid Phase Equil. 240, 114–121 (2006). doi:10.1016/j.fluid.2005.12.014

    Article  CAS  Google Scholar 

  66. Saxton, B., Smith, R.P.: The activity coefficient of potassium chloride in aqueous solution from boiling point data. J. Am. Chem. Soc. 54, 2626–2636 (1932). doi:10.1021/ja01346a005

    Article  CAS  Google Scholar 

  67. Smith, R.P.: The boiling point elevation. II. Sodium chloride 0.05 to 1.0 M and 60 °C to 100 °C. J. Am. Chem. Soc. 61, 500–503 (1939). doi:10.1021/ja01871a079

    Article  CAS  Google Scholar 

  68. Spencer, R.J., Møller, N., Weare, J.H.: The prediction of mineral solubilities in natural waters: a chemical equilibrium model for the Na-K-Ca-Mg-Cl-SO4−H2O system at temperatures below 25 °C. Geochim. Cosmochim. Acta 54, 575–590 (1990). doi:10.1016/0016-7037(90)90354-N

    Article  CAS  Google Scholar 

  69. Tomasula, P., Czerwienski, G.J., Tassios, D.: Vapor pressure and osmotic coefficients: electrolyte solutions of methanol. Fluid Phase Equil. 38, 129–153 (1987). doi:10.1016/0378-3812(87)90008-2

    Article  CAS  Google Scholar 

  70. Verevkin, S., Safarov, J.T., Bich, E., Hassel, E., Heintz, A.: Study of vapour pressure of lithium nitrate solutions in ethanol. J. Chem. Thermodyn. 38, 611–616 (2006). doi:10.1016/j.jct.2005.07.015

    Article  CAS  Google Scholar 

  71. Washburn, E.W.: International Critical Tables of Numerical Data, Physics, Chemistry and Technology, 1st electronic edn., pp. 1926–1930. Knovel, New York (2003)

    Google Scholar 

  72. Worth, H.R.: The Freezing points of concentrated solutions and the free energy of solution of salts. J. Am. Chem. Soc. 40, 1204–1213 (1918). doi:10.1021/ja02241a008

    Article  Google Scholar 

  73. Zafarani-Moattar, M.T., Jahanbin-Sardroodi, J.: Measurement and correlation of osmotic coefficients and evaluation of vapor pressures for solutions of CaCl2 and Ca(NO3)2 in ethanol at 298 K. Fluid Phase Equil. 172, 221–235 (2000). doi:10.1016/S0378-3812(00)00372-1

    Article  CAS  Google Scholar 

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  1. Department of Materials Science and Engineering, Royal Institute of Technology, 10044, Stockholm, Sweden

    Xinlei Ge

  2. College of Engineering, Peking University, Beijing, 100871, China

    Xidong Wang

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  1. Xinlei Ge
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Correspondence to Xinlei Ge.

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An erratum to this article is available at http://dx.doi.org/10.1007/s10953-013-9993-x.

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Ge, X., Wang, X. Calculations of Freezing Point Depression, Boiling Point Elevation, Vapor Pressure and Enthalpies of Vaporization of Electrolyte Solutions by a Modified Three-Characteristic Parameter Correlation Model. J Solution Chem 38, 1097–1117 (2009). https://doi.org/10.1007/s10953-009-9433-0

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