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Estimation of activity coefficients of ionic species of aqueous strong electrolytes within the extended Debye–Hückel concentration range

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Abstract

The concentration curve of mean activity coefficient to the required power was fitted by a product function. The product function can be factorized in factor functions which represent the concentration dependence of the single-ion species (J Solid State Electrochem, in press, 1). With a simplified procedure of this method, it is possible to split the mean activity coefficients into the individual parts for the ionic species within the extended Debye–Hückel concentration range. This method is applicable to all strong electrolytes because it is not necessary to have further data or additional assumptions.

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Notes

  1. Concerning the case k = lower bound of summation 1 and upper bound of summation 3, the relationship (4) is written in the paper by Ferse and Müller [1] dissolved in summands with a different designation of the parameters:

    $$ \gamma_{\pm }^{{{\nu_{ + }} + {\nu_{ - }}}}(J) = \bar{\gamma }_{\text{C}}^{{{\nu_{ + }}}}(J) \cdot \bar{\gamma }_{\text{A}}^{{{\nu_{ - }}}}(J) \approx {\left[ {{c_1}{e^{{{{c'}_7} \cdot {J^{{\frac{1}{2}}}}}}} + {c_3}{e^{{{c_9} \cdot J}}} + {c_5}{e^{{{c_{{11}}} \cdot {J^{{\frac{3}{2}}}}}}}} \right]^{{{\nu_{ + }}}}}{\left[ {{c_2}{e^{{{{c'}_8} \cdot {J^{{\frac{1}{2}}}}}}} + {c_4}{e^{{{c_{{10}}} \cdot J}}} + {c_6}{e^{{{c_{{12}}} \cdot {J^{{\frac{3}{2}}}}}}}} \right]^{{{\nu_{ - }}}}} $$

  2. The following values [20] are used after the year 1977: A′ = 1.17625 (A = 0.510839), B = 0.32866; all values are valid for aqueous solutions and a temperature of 298.15 K.

  3. Hamer and Wu [21], for example, used the following relationship (11) for the calculation of the mean activity coefficients but for an extended concentration range:

    $$ \log {\gamma_{\pm }} = \frac{{ - {\text{A}}\left| {{z_{\text{C}}} \cdot {z_{\text{A}}}} \right|\sqrt {J} }}{{1 + B*\sqrt {J} }} + \beta \cdot J + C \cdot {J^2} + D \cdot {J^3} + ... $$
    (11)

    B*, ß, C, D…: empirical constants, the values are different for all electrolytes.

    Note: B* in (11) is not identical with “B \( \tilde{a} \)” in the extended Debye–Hückel Eq. 10!

  4. Extremely high accuracy is certainly not really important. They afford excellent services as operands.

References

  1. Ferse A, Müller H-O (2011) J Solid State Electrochem. doi:10.1007/s10008-011-1413-9

  2. Guggenheim EA (1929) J Phys Chem 33:842–849

    Article  CAS  Google Scholar 

  3. Malatesta F (2000) J Solution Chem 29:771–779

    Article  CAS  Google Scholar 

  4. Malatesta F (2010) Fluid Phase Equil 295:244–248

    Article  CAS  Google Scholar 

  5. Ferse A, Ferse E (1966) Z Chem 6:241–255

    Article  CAS  Google Scholar 

  6. Schwabe K, Kelm H, Queck C (1974) Z Phys Chem (Leipzig) 255:1149–1156

    CAS  Google Scholar 

  7. Ferse A (2008) Z Anorg Allg Chem 634:797–815

    Article  CAS  Google Scholar 

  8. Schwabe K, Ferse A (1962) Die Zuckererzeugung 6:194–198

    CAS  Google Scholar 

  9. Ferse A, Schwabe K (1965) Z Phys Chem (Leipzig) 230:20–41

    CAS  Google Scholar 

  10. Schwabe K (1967) Electrochim Acta 12:67–93

    Article  CAS  Google Scholar 

  11. Ferse A (1977) Z Phys Chem (Leipzig) 258:257–279

    CAS  Google Scholar 

  12. Ferse A (1981) Z Phys Chem (Leipzig) 262:977–995

    CAS  Google Scholar 

  13. Ferse A, Neumann P (1977) Mathem Operationsforschg und Statistik. Ser Statistics 8:529–543

    Article  Google Scholar 

  14. Monk CB (1961) Electrolytic dissociation. Academic, London, pp. 8 and 30

    Google Scholar 

  15. Bates DM, Watts DG (1988) Nonlinear regression analysis and its applications. Wiley, New York

    Book  Google Scholar 

  16. Neter J, Kutner MH, Nachtsheim ChJ, Wasserman W (1996) Applied nonlinear statistical models, 4th edn. McGraw-Hill, Boston

    Google Scholar 

  17. Seber GAF, Wild CJ (2003) Nonlinear regression. Wiley, New York

    Google Scholar 

  18. Debye P, Hückel E (1923) Physik Z (Leipzig) 24:185–206

    CAS  Google Scholar 

  19. Debye P, Hückel E (1923) Physik Z (Leipzig) 24:305–325

    CAS  Google Scholar 

  20. Staples BR, Nuttall RL (1977) J Phys Chem Ref Data 6:385–407

    Article  CAS  Google Scholar 

  21. Hamer WJ, Wu Y-Ch (1972) J Phys Chem Ref Data 1:1047–1099

    Article  CAS  Google Scholar 

  22. Kielland J (1937) J Am Chem Soc 59:1675–1678

    Article  CAS  Google Scholar 

  23. Bates RG (1964) Determination of pH. Theory and Practice. John Wiley & Sons, New York

    Google Scholar 

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Acknowledgment

I want to express my sincere thanks to Prof. Dr. Waldfried Plieth, Technische Universität Dresden, Germany. This paper could not have been realized without his encouraging interest and his decisive support.

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  1. Armin Ferse

    Present address: , Wiesenstr. 8, 01277, Dresden, Germany

Authors and Affiliations

  1. Institute of Physical Chemistry and Polymer Physics, Leibniz-Institute of Polymer Research Dresden, Hohe Str. 6, 01069, Dresden, Germany

    Armin Ferse

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Correspondence to Armin Ferse.

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Ferse, A. Estimation of activity coefficients of ionic species of aqueous strong electrolytes within the extended Debye–Hückel concentration range. J Solid State Electrochem 15, 2177–2184 (2011). https://doi.org/10.1007/s10008-011-1530-5

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  • DOI: https://doi.org/10.1007/s10008-011-1530-5

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