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Modelling of Mean Ionic Activity and Osmotic Coefficients in Aqueous Solutions of Symmetrical Tetra alkyl Ammonium Halides

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Abstract

In this work, aqueous solutions of 12 symmetrical tetra alkyl ammonium halides are modelled using the electrolyte cubic-plus-association (e-CPA) equation of state. The only adjustable parameter (the ion–water interaction parameter at reference temperature) is obtained by fitting the experimental mean ionic activity and osmotic coefficients at 298.15 K. The modelling results show that e-CPA can perform relatively well for the mean ionic activity and osmotic coefficients. To know a complete understanding of the capabilities and limitations of this modelling work, extensive analysis and discussion of experimental data, parameter estimation, and ion species is performed. Moreover, some possible improvements for the model are proposed based on the microscopic mechanism of the aqueous solutions.

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References

  1. Vilas-Boas, S.M., Abranches, D.O., Crespo, E.A., Ferreira, O., Coutinho, J.A., Pinho, S.P.: Experimental solubility and density studies on aqueous solutions of quaternary ammonium halides, and thermodynamic ssmodelling for melting enthalpy estimations. J. Mol. Liq. 300, 112281 (2020)

    Article  CAS  Google Scholar 

  2. Sakamoto, J., Hashimoto, S., Tsuda, T., Sugahara, T., Inoue, Y., Ohgaki, K.: Thermodynamic and Raman spectroscopic studies on hydrogen+ tetra-n-butyl ammonium fluoride semi-clathrate hydrates. Chem. Eng. Sci. 63, 5789–5794 (2008)

    Article  CAS  Google Scholar 

  3. Amado, E., Blanco, L.H.: Isopiestic determination of the osmotic and activity coefficients of aqueous solutions of symmetrical and unsymmetrical quaternary ammonium bromides at T=(283.15 and 288.15) K. J. Chem. Eng. Data 54, 2696–2700 (2009)

    Article  CAS  Google Scholar 

  4. Eliseo, A.G., Blanco, L.H.: Osmotic and activity coefficients of dilute aqueous solutions of symmetrical and unsymmetrical quaternary ammonium bromides at 293.15 K. Fluid Phase Equilib. 243, 166–170 (2006)

    Article  CAS  Google Scholar 

  5. Golabiazar, R., Sadeghi, R.: Vapor pressure osmometry determination of the osmotic and activity coefficients of dilute aqueous solutions of symmetrical tetraalkyl ammonium halides at 308.15 K. J. Chem. Eng. Data 59, 76–81 (2014)

    Article  CAS  Google Scholar 

  6. Belvèze, L.S., Brennecke, J.F., Stadtherr, M.A.: Modeling of activity coefficients of aqueous solutions of quaternary ammonium salts with the electrolyte-NRTL equation. Ind. Eng. Chem. Res. 43, 815–825 (2004)

    Article  Google Scholar 

  7. Simonin, J.P., Krebs, S., Kunz, W.: Inclusion of ionic hydration and association in the MSA-NRTL model for a description of the thermodynamic properties of aqueous ionic solutions: Application to solutions of associating acids. Ind. Eng. Chem. Res. 45, 4345–4354 (2006)

    Article  CAS  Google Scholar 

  8. Verrett, J., Renault Crispo, J.S., Servio, P.: Phase equilibria, solubility and modeling study of CO2/CH4 + tetra-n-butylammonium bromide aqueous semi-clathrate systems. Fluid Phase Equilib. 388, 160–168 (2015)

    Article  CAS  Google Scholar 

  9. Ll, S., Liang, D.Q.: Thermodynamic model of phase equilibria of tetrabutyl ammonium halide (fluoride, chloride, or bromide) plus methane or carbon dioxide semiclathrate hydrates. Fluid Phase Equilib. 386, 149–154 (2015)

    Article  Google Scholar 

  10. Najibi, H., Momeni, K., Sadeghi, M.T., Mohammadi, A.H.: Experimental measurement and thermodynamic modelling of phase equilibria of semi-clathrate hydrates of (CO2+ tetra-n-butyl-ammonium bromide) aqueous solution. J. Chem. Thermodyn. 87, 122–128 (2015)

    Article  CAS  Google Scholar 

  11. Perisanu, S.: Correlation of activity coefficients of alkyl-ammonium salt solutions. J. Mol. Liq. 113, 21–27 (2004)

    Article  CAS  Google Scholar 

  12. Akbari, V., Dehghani, M.R., Borhani, T.N.G., Azarpour, A.: Activity coefficient modelling of aqueous solutions of alkyl ammonium salts using the extended UNIQUAC model. J. Solution Chem. 45, 1434–1452 (2016)

    Article  CAS  Google Scholar 

  13. Papaiconomou, N., Simonin, J.-P., Bernard, O.: Solutions of alkylammonium and bulky anions: description of osmotic coefficients within the binding mean spherical approximation. Ind. Eng. Chem. Res. 51, 9661–9668 (2012)

    Article  CAS  Google Scholar 

  14. Jaime-Leal, J.E., Bonilla-Petriciolet, A.: Correlation of activity coefficients in aqueous solutions of ammonium salts using local composition models and stochastic optimization methods Prod. Process Model Chem (2008). https://doi.org/10.2202/1934-2659.1237

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  16. Bradley, D.J., Pitzer, K.S.: Thermodynamics of electrolytes. 12. Dielectric properties of water and Debye-Hueckel parameters to 350°C and 1 kbar. J. Phys. Chem. 83, 1599–1603 (1979)

    Article  CAS  Google Scholar 

  17. Chen, C.C., Britt, H.I., Boston, J., Evans, L.: Local composition model for excess Gibbs energy of electrolyte systems. Part I: Single solvent, single completely dissociated electrolyte systems. AIChE J. 28, 588–596 (1982)

    Article  CAS  Google Scholar 

  18. Paricaud, P.: Modeling the dissociation conditions of salt hydrates and gas semiclathrate hydrates: application to lithium bromide, hydrogen iodide, and tetra-n-butylammonium bromide + carbon dioxide systems. J. Phys. Chem. B 115, 288–299 (2011)

    Article  CAS  Google Scholar 

  19. Ma, Q.L., Qi, J.L., Chen, G.J., Sun, C.Y.: Modeling study on phase equilibria of semiclathrate hydrates of pure gases and gas mixtures in aqueous solutions of TBAB and TBAF. Fluid Phase Equilib. 430, 178–187 (2016)

    Article  CAS  Google Scholar 

  20. Zuo, Y.X., Guo, T.M.: Extension of the Patel-Teja equation of state to the prediction of the solubility of natural gas in formation water. Chem. Eng. Sci. 46, 3251–3258 (1991)

    Article  CAS  Google Scholar 

  21. Sun, L., Liang, X., Von Solms, N., Kontogeorgis, G.M.: Modeling tetra-n-butyl ammonium halides aqueous solutions with the electrolyte cubic plus association equation of state. Fluid Phase Equilib. 486, 37–47 (2019)

    Article  CAS  Google Scholar 

  22. Maribo-Mogensen, B., Thomsen, K., Kontogeorgis, G.M.: An electrolyte CPA equation of state for mixed solvent electrolytes. AIChE J. 61, 2933–2950 (2015)

    Article  CAS  Google Scholar 

  23. Kontogeorgis, G.M., Voutsas, E.C., Yakoumis, I.V., Tassios, D.P.: An equation of state for associating fluids. Ind. Eng. Chem. Res. 35, 4310–4318 (1996)

    Article  CAS  Google Scholar 

  24. Debye, P., Hückel, E.: Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen. Z. Physik. 24, 185–206 (1923)

    CAS  Google Scholar 

  25. Born, M.: Volumen und hydratationswärme der ionen. Z. Phys. 1, 45–48 (1920)

    Article  CAS  Google Scholar 

  26. Soave, G.: Equilibrium constants from a modified Redlich–Kwong equation of state. Chem. Eng. Sci. 27, 1197–1203 (1972)

    Article  CAS  Google Scholar 

  27. Breil, M.P., Kontogeorgis, G.M., Behrens, P.K., Michelsen, M.L.: Modeling of the thermodynamics of the acetic acid−water mixture using the cubic-plus-association equation of state. Ind. Eng. Chem. Res. 50, 5795–5805 (2011)

    Article  CAS  Google Scholar 

  28. Huron, M.-J., Vidal, J.: New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures. Fluid Phase Equilib. 3, 255–271 (1979)

    Article  CAS  Google Scholar 

  29. Wertheim, M.S.: Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations. J. Stati Phys. 35, 35–47 (1984)

    Article  Google Scholar 

  30. Wertheim, M.S.: Fluids with highly directional attractive forces. I. Statistical thermodynamics, J Stat. Phys. 35, 19–34 (1984)

    Google Scholar 

  31. Michelsen, M.L., Hendriks, E.M.: Physical properties from association models. Fluid Phase Equilib. 180, 165–174 (2001)

    Article  CAS  Google Scholar 

  32. Gilkerson, W., Stewart, J.: Polarizabilities and molar volumes of a number of salts in several solvents at 25°. J. Phys. Chem. 65, 1465–1466 (1961)

    Article  CAS  Google Scholar 

  33. Hubbard, J., Onsager, L., Van Beek, W., Mandel, M.: Kinetic polarization deficiency in electrolyte solutions. Proc. Nat. Acad. Sci. 74, 401–404 (1977)

    Article  CAS  Google Scholar 

  34. Hubbard, J., Kayser, R.: Dielectric friction and dielectric dispersion in electrolyte solutions with spin. J. Chem. Phys. 74, 3535–3545 (1981)

    Article  CAS  Google Scholar 

  35. Maribo-Mogensen, B., Kontogeorgis, G.M., Thomsen, K.: Modeling of dielectric properties of aqueous salt solutions with an equation of state. J. Phys. Chem. B 117, 10523–10533 (2013)

    Article  CAS  Google Scholar 

  36. Kirkwood, J.G.: The dielectric polarization of polar liquids. J. Chem. Phys. 7, 911–919 (1939)

    Article  CAS  Google Scholar 

  37. Fröhlich, H.: General theory of the static dielectric constant. Trans. Faraday Soc. 44, 238–243 (1948)

    Article  Google Scholar 

  38. Scaife, B.K.: Principles of Dielectrics. Clarendon Press, Oxford (1989)

    Google Scholar 

  39. Pitzer, K.: The Nature of the chemical bond and the structure of molecules and crystals: an introduction to modern structural chemistry. J. Am. Chem. Soc. 82, 4121–4121 (1960)

    Article  Google Scholar 

  40. Pauling, L.: The nature of the Chemical Bond, p. 260. Cornell University Press Ithaca, New York (1960)

    Google Scholar 

  41. Masterton, W., Bolocofsky, D., Lee, T.P.: Ionic radii from scaled particle theory of the salt effect. J. Phys. Chem. 75, 2809–2815 (1971)

    Article  CAS  Google Scholar 

  42. Latimer, W.M., Pitzer, K.S., Slansky, C.M.: The free energy of hydration of gaseous ions, and the absolute potential of the normal calomel electrode. J. Chem. Phys. 7(2), 108–111 (1939)

    Article  CAS  Google Scholar 

  43. Kaatze, U.: Bound water: evidence from and implications for the dielectric properties of aqueous solutions. J. Mol. Liq. 162, 105–112 (2011)

    Article  CAS  Google Scholar 

  44. Buchner, R., Hölzl, C., Stauber, J., Barthel, J.: Dielectric spectroscopy of ion-pairing and hydration in aqueous tetra-n-alkylammonium halide solutions. PhysChemChemPhys 4, 2169–2179 (2002)

    CAS  Google Scholar 

  45. Kaatze, U.: Kinetic depolarization in aqueous solutions of alkylammonium bromides. Ber. Bun. Phys. Chem. 84, 1195–1197 (1980)

    Article  CAS  Google Scholar 

  46. Wen, W.-Y., Kaatze, U.: Aqueous solutions of azoniaspiroalkane halides. 3. Dielectric relaxation. J. Phys. Chem. 81, 177–181 (1977)

    Article  CAS  Google Scholar 

  47. Cole, R., Berberian, J., Mashimo, S., Chryssikos, G., Burns, A., Tombari, E.: Time domain reflection methods for dielectric measurements to 10 GHz. J. Appl. Phys. 66, 793–802 (1989)

    Article  Google Scholar 

  48. Wen, W.Y., Saito, S., Lee, C.M.: Activity and osmotic coefficients of four symmetrical tetraalkylammonium fluorides in aqueous solutions at 25°. J. Phys. Chem. 70, 1244–1248 (1966)

    Article  CAS  Google Scholar 

  49. Lindenbaum, S., Boyd, G.: Osmotic and activity coefficients for the symmetrical tetraalkyl ammonium halides in aqueous solution at 25. J. Phys. Chem. 68, 911–917 (1964)

    Article  CAS  Google Scholar 

  50. Lindenbaum, S., Leifer, L., Boyd, G., Chase, J.: Variation of osmotic coefficients of aqueous solutions of tetraalkylammonium halides with temperature. thermal and solute effects on solvent hydrogen bonding. J. Phys. Chem. 74, 761–764 (1970)

    Article  CAS  Google Scholar 

  51. Schreckenberg, J.M., Dufal, S., Haslam, A.J., Adjiman, C.S., Jackson, G., Galindo, A.: Modelling of the thermodynamic and solvation properties of electrolyte solutions with the statistical associating fluid theory for potentials of variable range. Mol. Phys. 112, 2339–2364 (2014)

    Article  CAS  Google Scholar 

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Acknowledgements

The authors acknowledge the support from the College of Mechanical and Electrical Engineering, Hohai University. This work was supported by the Applied Basic Research Program of Changzhou (Grant Agreement No. CJ20210057) and “the Fundamental Research Funds for the Central Universities” (Grant Agreement No. B210201039).

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Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Hohai University, Changzhou, 213022, Jiangsu, China

    Yufei Mao, Fei Cao, Jianbo Bai & Li Sun

  2. Department of Mechanical Engineering, Technical University of Denmark, Koppels Allé, 2800 Kgs, Lyngby, Denmark

    Jierong Liang

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Mao, Y., Cao, F., Bai, J. et al. Modelling of Mean Ionic Activity and Osmotic Coefficients in Aqueous Solutions of Symmetrical Tetra alkyl Ammonium Halides. J Solution Chem 52, 19–50 (2023). https://doi.org/10.1007/s10953-022-01211-w

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