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Extended Specific Ion Theory (ESIT): Theoretical development and application to Harned’s rule

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Abstract

The specific ion theory (SIT) is a convenient ion activity coefficient model that is often used in solubility and solution equilibrium studies. However, its accuracy is limited. The SIT model can be improved by adding higher-order terms, and by allowing cation–cation, and anion–anion interactions. However, extensions of the SIT model tend to lead to a rapidly increasing number of higher-order interaction parameters that need to be known for reliable predictions. Using the analogy of multicomponent extensions of the Redlich–Kister/Margules model, this paper determines how far a virial-type activity coefficient model can be extended before it becomes unmanageable. It was found that a second-order extension of the SIT model is manageable. A first-order model is sufficient to describe Harned’s Rule satisfactorily. It is found that the addition of like-ion interaction parameters (i.e., cation–cation interactions and anion–anion interactions) to the SIT model substantially improves Harned’s Rule calculations, with an error reduction of over 50%. The ion interaction parameters are presented. Like-ion interactions should be interpreted as competitive effects between ion-water interactions rather than direct ion-ion interactions. Using concentration or mole per kg solution (modified molality) as a measure of abundance does not improve the accuracy of a first-order ESIT model but the modified molality scale does improve the accuracy of a 2nd-order ESIT model.

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Harned Coeff SIT.xlsx (Excel file containing the calculation of like-ion interactions in Table 5, as well as Figs. 5 and 6).

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References

  1. Oliver, E.D.: Multicomponent Margules equations. Ind. Eng. Chem. Fundam 7, 335–335 (1968)

    Article  CAS  Google Scholar 

  2. Mukhopadhyay, B., Basu, S., Holdaway, M.J.: A discussion of Margules-type formulations for multicomponent solutions with a generalized approach. Geochim. Cosmochim. Acta 57, 277–283 (1993)

    Article  CAS  Google Scholar 

  3. Pitzer, K.S.: Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 77, 268–277 (1973)

    Article  CAS  Google Scholar 

  4. Pitzer, K.S., Mayorga, G.: Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent. J. Phys. Chem. 77, 2300–2308 (1973)

    Article  CAS  Google Scholar 

  5. Pitzer, K.S., Mayorga, G.: Thermodynamics of electrolytes. III. Activity and osmotic coefficients for 2–2 electrolytes. J. Solut. Chem. 3, 539–546 (1974)

    Article  CAS  Google Scholar 

  6. Pitzer, K.S., Kim, J.J.: Thermodynamics of electrolytes. IV. Activity and osmotic coefficients for mixed electrolytes. J. Am. Chem. Soc. 96, 5701–5707 (1974)

    Article  CAS  Google Scholar 

  7. Abrams, D.S., Prausnitz, J.M.: Statistical thermodynamics of liquid mixtures: A new expression for the Excess Gibbs energy of partly or completely miscible systems. Am. Inst. Chem. Eng. J. 21, 116–128 (1975)

    Article  CAS  Google Scholar 

  8. Anderson, T.F., Prausnitz, J.M.: Application of the UNIQUAC equation to calculation of multicomponent phase equilibria. 1. Vapor-liquid equilibria. Ind. Eng. Chem. Proc. Des. Dev. 17, 552–561 (1978)

  9. Weidlich, U., Gmehling, J.: A modified UNIFAC model. 1. Prediction of VLE, hE, and γ∞. Ind. Eng. Chem. Res. 26, 1372–1381 (1987)

    Article  CAS  Google Scholar 

  10. Gmehling, J., Li, J., Schiller, M.: A modified UNIFAC model. 2. Present parameter matrix and results for different thermodynamic properties. Ind. Eng. Chem. Res. 32, 178–193 (1993)

    Article  CAS  Google Scholar 

  11. Gmehling, J., Lohmann, J., Jakob, A., Li, J., Joh, R.: A modified UNIFAC (Dortmund) model. 3. Revision and extension. Ind. Eng. Chem. Res. 37, 4876–4882 (1998)

    Article  CAS  Google Scholar 

  12. Gmehling, J., Wittig, R., Lohmann, J., Joh, R.: A modified UNIFAC (Dortmund) model. 4. Revision and extension. Ind. Eng. Chem. Res. 41, 1678–1688 (2002)

    Article  CAS  Google Scholar 

  13. Jakob, A., Grensemann, H., Lohmann, J., Gmehling, J.: Further development of Modified UNIFAC (Dortmund): Revision and Extension 5. Ind. Eng. Chem. Res. 45, 7924–7933 (2006)

    Article  CAS  Google Scholar 

  14. Preis, W., Gamsjager, H.: Thermodynamic investigation of phase equilibria in metal carbonate-water-carbon dioxide systems. Monatsh Chem. 132, 1327–1346 (2001)

    Article  CAS  Google Scholar 

  15. Komninos, N.P., Rogdakis, E.D.: Geometrical investigation and classification of three-suffix Margules binary mixtures including single and double azeotropy. Fluid Phase Equil. 494, 212–227 (2019)

    Article  CAS  Google Scholar 

  16. Zagarzadeh, L., Elliott, J.A.W.: Comparison of the osmotic virial equation with the Margules activity model for solid-liquid equilibrium. J. Phys. Chem. B 123, 1099–1107 (2019)

    Article  Google Scholar 

  17. Song, Z., Zhou, T., Qi, Z., Sundmacher, K.: Extending the UNIFAC model for ionic liquid-solute systems by combining experimental and computational databases. Am. Inst. Chem. Eng. J. 66, e16821 (2019)

  18. Machado, G.D., Castier, M., Voll, A.P., Cabral, V.F., Cardozo-Filho, L., Aranda, D.A.G.: Ethanol and methanol UNIFAC subgroup parameter estimation in the prediction of the liquid-liquid equilibrium of biodiesel systems. Fluid Phase Equil. 488, 79–86 (2019)

    Article  CAS  Google Scholar 

  19. Gao, Y., Li, C., Xia, S., Ma, P.: Estimation and correlation of phase equilibrium of CO2-hydrocarbon systems with PRMHV2-UNIFAC and PRMHV2-NRTL models. J. Chem. Eng. Data 65, 655–663 (2020)

    Article  CAS  Google Scholar 

  20. De Visscher, A., Vanderdeelen, J., Königsberger, E., Churgalov, B.R., Ichikuni, M., Tsurumi, M.: IUPAC-NIST Solubility Data Series. 95. Alkaline earth carbonates in aqueous systems. Part 1. Introduction, Be and Mg. J. Phys. Chem. Ref. Data 41, 013105 (2012)

    Article  Google Scholar 

  21. De Visscher, A., Vanderdeelen, J.: IUPAC-NIST Solubility Data Series. 95. Alkaline earth carbonates in aqueous systems. Part 2. Ca. J. Phys. Chem. Ref. Data 41, 023105 (2012)

  22. Crea, F., De Stefano, C., Irto, A., Milea, D., Pettignano, A., Sammartano, S.: Modeling the acid-base properties of molybdate(VI) in different ionic media, ionic strengths and temperature, by EDH, SIT and Pitzer equations. J. Molec Liq 229, 15–26 (2017)

    Article  CAS  Google Scholar 

  23. Yalcintas, E., Cevirim-Papaioannou, N., Gaona, X., Fellhauer, D., Neck, V., Altmaier, M.: Solubility of U(VI) in chloride solutions. III. The stable oxides/hydroxides in MgCl2 systems: Pitzer activity model for the system UO22+–Na+–K+–Mg2+–H+–OH––Cl––H2O(l). J. Chem. Thermodyn. 131, 375–386 (2019)

    Article  CAS  Google Scholar 

  24. Altmaier, M., Yalcintas, E., Gaona, X., Neck, V., Müller, R., Schlieker, M., Fanghängel, T.: Solubility of U(VI) in chloride solutions. I. The stable oxides/hydroxides in NaCl systems, solubility products, hydrolysis constants and SIT coefficients. J. Chem. Thermodyn. 114, 2–13 (2017)

    Article  CAS  Google Scholar 

  25. Gallego-Urrea, J.A., Turner, D.R.: Determination of pH in estuarine and brackish waters: Pitzer parameters for Tris buffers and dissociation constants for m-cresol purple at 298.15 K. Mar. Chem 195, 84–89 (2017)

    Article  CAS  Google Scholar 

  26. Hashemzadeh, M., Liu, W.: Analysis of iron and copper speciation and activities in chloride leaching solutions of high ionic strength. Hydrometallurgy 192, 105262 (2020)

    Article  CAS  Google Scholar 

  27. Tasic, A., Djordjevic, B., Grozdanic, D., Afgan, N., Malic, D.: Vapor-liquid equilibria of the systems acetone-benzene, benzene-cyclohexane and acetone-cyclohexane at 25°C. Chem. Eng. Sci. 33, 189–197 (1978)

    Article  CAS  Google Scholar 

  28. Pitzer, K.S.: Ion interaction approach: Theory and data correlation. In: Pitzer, K.S. Activity Coefficients in Electrolyte Solutions, 2nd edn. CRC Press (1991)

  29. De Visscher, A.: Salting out and salting in of benzene in water: A consistency evaluation. Monatsh. Chem. 149, 231–236 (2018)

    Article  Google Scholar 

  30. Hamer, W.J., Wu, Y.C.: Osmotic coefficients and mean activity coefficients of uni-univalent electrolytes in water at 25 °C. J. Phys. Chem. Ref. Data 1, 1047–1099 (1972)

    Article  CAS  Google Scholar 

  31. Rowland, D., May, P.M.: An investigation of Harned’s rule for predicting the activity coefficients of strong aqueous electrolyte solution mixtures at 25 °C. J. Chem. Eng. Data 62, 310–327 (2017)

    Article  CAS  Google Scholar 

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

    CAS  Google Scholar 

  33. Guggenheim, E.A.: The specific thermodynamic properties of aqueous solutions of strong electrolytes. Phil. Mag. 19, 588–643 (1935)

    Article  CAS  Google Scholar 

  34. Scatchard, G.: Concentrated solutions of strong electrolytes. Chem. Rev. (Baltimore) 19, 309–327 (1936)

    Article  CAS  Google Scholar 

  35. Krumgalz, B.S., Pogorelsky, R., Pitzer, K.S.: Volumetric properties of single aqueous electrolytes from zero to saturation concentration at 298.15 °K represented by Pitzer’s ion-interaction equations. J. Phys. Chem. Ref. Data 25, 663–689 (1996)

    Article  CAS  Google Scholar 

  36. Krumgalz, B.S., Pogorelsky, R., Sokolov, A., Pitzer, K.S.: Volumetric ion interaction parameters for single-solute aqueous electrolyte solutions at various temperatures. J. Phys. Chem. Ref. Data 29, 1123–1140 (1996)

    Article  Google Scholar 

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  1. Department of Chemical and Materials Engineering, Gina Cody School of Engineering and Computer Science, Concordia University, Montreal, Quebec, Canada

    Alex De Visscher

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De Visscher, A. Extended Specific Ion Theory (ESIT): Theoretical development and application to Harned’s rule. J Solution Chem 51, 711–733 (2022). https://doi.org/10.1007/s10953-022-01152-4

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