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Potentiometric Cells with Liquid Junctions: A Combined Analytical and Computational Study

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Abstract

It is known that the electromotive force (emf) of cells with transference is dependent on an integral involving electrical transport numbers, t i , and chemical potentials. However, the origin of this integral, the conditions under which it is valid, its properties and utility are not well understood. This article aims to clarify such aspects. A general emf equation is derived in a manner in which the integral arises from the entropy production due to diffusion. Five important properties of the equation are recognized: (1) invariance with respect to the reference frame for t i measurements, (2) redundancy of single-ion activities, (3) lack of a potential function for the integral when the number of independent t i is greater than 1, (4) irrelevance of any metric on the junction 3-D space, and (5) invariance with respect to the free-diffusion time. As an application, the emf equation is tested for calibration of cells with dissimilar electrodes and junctions between the saturated potassium chloride solution and hydrogen chloride solutions in a range of concentration. It is found that (1) the standard emf can be estimated with a precision of about 0.1 mV for accurate enough data sets, and (2) the free-diffusion model is more appropriate for the flowing junctions than the continuous mixture model, although the difference between the two models is slight. In similar systems with less concentrated potassium chloride solutions, the free-diffusion mass density profiles are found to bear a sign of convective instability, because of which previously reported steady emfs for such cells may pertain to a changed solution composition in one of the two half-cells.

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Notes

  1. Any such is a curve the tangent vector to which at each point is the vector of the field at the point.

  2. For discussion of curvilinear coordinates see [26] or e.g. [27].

  3. For the topic of differential forms see, e.g. [40–44].

  4. In this connection, note the IUPAC recommendation to use the term cell potential difference instead of emf [45].

  5. In fact, the D i,m were calculated both by Miller's method and that of Leaist et al., as described, e.g., in [60]. However, we report here only on systems and concentration ranges where the latter has no advantage over the former as judged by experiment or makes only negligible difference in the calculated emf.

  6. That equation was derived specifically for a cell with a single electrolyte in a single component solvent and gave the emf in terms of the Hittorf transport number, the vapor pressure and concentration of the solution.

References

  1. Brandariz, I., Barriada, J.L., Vilariño, T., Sastre de Vicente, M.E.: Comparison of several calibration procedures for glass electrodes in proton concentration. Monatsh. Chem. 135, 1475–1488 (2004)

    Article  CAS  Google Scholar 

  2. Buck, R.P., Rondinini, S., Covington, A.K., Baucke, F.G.K., Brett, C.M.A., Camões, M.F., Milton, M.J.T., Mussini, T., Naumann, R., Pratt, K.W., Spitzer, P., Wilson, G.S.: Measurement of pH. Definition, standards, and procedures. Pure Appl. Chem. 74, 2169–2200 (2002)

    Article  CAS  Google Scholar 

  3. Helmholtz, H.: Ueber galvanische Strőme, verursacht durch Concentrationsunterschiede; Folgerungen aus der mechanischen Wärmetheorie. Ann. Physik 239, 201–216 (1878)

    Article  Google Scholar 

  4. Nernst, W.: Die elektromotorische Wirksamkeit der Ionen. Z. Phys. Chem. 4, 129–181 (1889)

    Google Scholar 

  5. Pethica, B.A.: Are electrostatic potentials between regions of different chemical composition measurable? The Gibbs-Guggenheim principle reconsidered, extended and its consequences revisited. Phys. Chem. Chem. Phys. 9, 6253–6262 (2007)

    Article  CAS  Google Scholar 

  6. de Groot, S.R., Tolhoek, H.A.: Electric and chemical potentials. Different methods of treatments and their relation. Proc. Koninkl. Nederlandse Akad. Wet. B 54, 42–53 (1951)

    Google Scholar 

  7. Haase, R.: Thermodynamik der Mischphasen. Springer, Berlin (1956)

    Book  Google Scholar 

  8. O’Keeffe, M., Spence, J.C.H.: On the average Coulomb potential (Φ0) and constraints on the electron density in crystals. Acta Cryst. A 50, 33–45 (1994)

    Article  Google Scholar 

  9. Tsirelson, V.G., Avilov, A.S., Lepeshov, G.G., Kulygin, A.K., Stahn, J., Pietsch, U., Spence, J.C.H.: Quantitative analysis of the electrostatic potential in rock-salt crystals using accurate electron diffraction data. J. Phys. Chem. B 105, 5068–5074 (2001)

    Article  CAS  Google Scholar 

  10. MacInnes, D.A., Parker, K.: Potassium chloride concentration cells. J. Am. Chem. Soc. 37, 1445–1461 (1915)

    Article  CAS  Google Scholar 

  11. Lewis, G.N., Randall, M.: Thermodynamics and the Free Energy of Chemical Substances. McGraw–Hill, New York (1923)

    Google Scholar 

  12. Taylor, P.B.: Electromotive force of the cell with transference and theory of interdiffusion of electrolytes. J. Phys. Chem. 31, 1478–1500 (1927)

    Article  CAS  Google Scholar 

  13. Guggenheim, E.A.: Modern Thermodynamics by the Methods of Willard Gibbs. Methuen, London (1933)

    Google Scholar 

  14. MacInnes, D.A.: The Principles of Electrochemistry. Reinhold, New York (1939)

    Google Scholar 

  15. Koenig, F.O.: On quasi-reversible conduction and galvanic cells with liquid–liquid junctions. J. Phys. Chem. 44, 101–135 (1940)

    Article  CAS  Google Scholar 

  16. Bearman, R.J.: The Onsager thermodynamics of galvanic cells with liquid–liquid junctions. J. Chem. Phys. 22, 585–587 (1954)

    Article  CAS  Google Scholar 

  17. Spiro, M.: The calculation of potentials across liquid junctions of uniform ionic strength. Electrochim. Acta 11, 569–580 (1966)

    Article  CAS  Google Scholar 

  18. Chen, C.-H., Frank, H.S.: Liquid junction potentials by computer simulation. II. The Lewis and Sargent cell. A Harned’s rule for single ions. J. Phys. Chem. 77, 1540–1546 (1973)

    Article  CAS  Google Scholar 

  19. Lindeberg, E.G.B., Østvold, T.: An experimental and theoretical investigation of the salt bridge in concentration cells. Acta Chem. Scand. A 28, 563–568 (1974)

    Article  CAS  Google Scholar 

  20. Breer, J., Ratkje, S.K., Olsen, G.-F.: Control of liquid junctions. The system HCl–KCl. Z. Phys. Chem. 174, 179–198 (1991)

    Article  CAS  Google Scholar 

  21. Perera, J.M., McTigue, P.T.: Emfs of galvanic cells with liquid junctions. J. Electroanal. Chem. 308, 127–149 (1991)

    Article  CAS  Google Scholar 

  22. Zarubin, D.P.: The nature of single-ion activity coefficients calculated from potentiometric measurements on cells with liquid junctions. J. Chem. Thermodyn. 43, 1135–1152 (2011)

    Article  CAS  Google Scholar 

  23. Zarubin, D.P.: Concentration dependence of single-ion activity coefficients. An analysis. Fluid Phase Equilib. 360, 188–211 (2013)

    Article  CAS  Google Scholar 

  24. Haase, R.: Thermodynamics of Irreversible Processes. Addison-Wesley, New York (1969)

    Google Scholar 

  25. Staverman, A.J.: Non-equilibrium thermodynamics of membrane processes. Trans. Faraday Soc. 48, 176–185 (1952)

    Article  CAS  Google Scholar 

  26. Morse, P.M., Feshbach, H.: Methods of Theoretical Physics, vol. 1. McGraw Hill, New York (1953)

    Google Scholar 

  27. Matthews, P.C.: Vector Calculus (Springer Undergraduate Mathematics Series). Springer, London (1998)

    Google Scholar 

  28. Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields. Fizmatlit, Moscow (2001)

    Google Scholar 

  29. Guggenheim, E.A.: Liquid junction potentials. Proc. Phys. Soc. 85, 393–394 (1965)

    Article  CAS  Google Scholar 

  30. Spiro, M.: Conductance and transference determinations. In: Rossiter, B.W., Hamilton, J.F. (eds.) Physical Methods in Chemistry, Vol. 2, Electrochemical Methods, 2nd edn, pp. 663–796. Wiley, New York (1986)

    Google Scholar 

  31. Guggenheim, E.A.: Thermodynamics. An Advanced Treatment for Chemists and Physicists, 5th edn. North-Holland Pub. Co, Amsterdam (1967)

    Google Scholar 

  32. Wagner, C.: The electromotive force of galvanic cells involving phases of locally variable composition. In: Delahay, P. (ed.) Advances in Electrochemistry and Electrochemical Engineering, Vol. 4, Electrochemistry, pp. 1–46. Interscience, New York (1966)

    Google Scholar 

  33. McGlashan, M.L.: Chemical Thermodynamics. Academic Press, London (1979)

    Google Scholar 

  34. Wiebenga, E.H.: On quasi-thermodynamic treatment of diffusion potentials. Rec. Trav. Chim. 65, 273–288 (1946)

    Article  CAS  Google Scholar 

  35. de Groot, S.R.: Thermodynamics of Irreversible Processes. North Holland Publishing Co., Amsterdam (1952)

    Google Scholar 

  36. Kirkwood, J.G., Oppenheim, I.: Chemical Thermodynamics. McGraw–Hill, New York (1961)

    Google Scholar 

  37. Fitts, D.D.: Nonequilibrium Thermodynamics. McGraw–Hill, New York (1962)

    Google Scholar 

  38. de Groot, S.R., Mazur, P.: Non-Equilibrium Thermodynamics. Dover, Mineola (1984)

    Google Scholar 

  39. Guggenheim, E.A.: Studies of cells with liquid–liquid junctions. Part II. Thermodynamic significance and relationship to activity coefficients. J. Phys. Chem. 34, 1758–1766 (1929)

    Article  Google Scholar 

  40. Bamberg, P., Sternberg, S.: A Course in Mathematics for Students of Physics, vol. 1 and 2. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  41. do Carmo, M.P.: Differential Forms and Applications (Universitext). Springer, Berlin (1994)

    Book  Google Scholar 

  42. O’Neill, B.: Elementary Differential Geometry, 2nd edn. Academic Press, San Diego (2006)

    Google Scholar 

  43. Frankel, T.: The Geometry of Physics. An Introduction, 3rd edn. Cambridge University Press, Cambridge (2012)

    Google Scholar 

  44. Lee, J.M.: Introduction to Smooth Manifolds (Graduate Texts in Mathematics). Springer-Verlag, New York (2012)

    Book  Google Scholar 

  45. Cohen, E.R., Cvitaš, T., Frey, J.G., Holmström, B., Kuchitsu, K., Marquardt, R., Mills, I., Pavese, F., Quack, M., Stohner, J., Strauss, H.L., Takami, M., Thor, A.J.: Quantities, Units and Symbols in Physical Chemistry. IUPAC, 3rd edn. Royal Society of Chemistry, Cambridge (2007)

    Google Scholar 

  46. Crank, J.: The Mathematics of Diffusion, 2nd edn. Oxford University Press, Oxford (1975)

    Google Scholar 

  47. MacLagan, N.F.: The use of decinormal hydrochloric acid for standardizing electrometric pH measurements. Biochem. J. 23, 309–318 (1929)

    Article  CAS  Google Scholar 

  48. Ferguson, A.L., Van Lente, K., Hitchens, R.: Liquid junction potentials. I. Reproducible static liquid junctions constant in potential over long periods of time. J. Am. Chem. Soc. 54, 1279–1285 (1932)

    Article  CAS  Google Scholar 

  49. Finkelstein, N.P., Verdier, E.T.: Liquid junction potentials at mixed electrolyte salt bridges. Trans. Faraday Soc. 53, 1618–1625 (1957)

    Article  CAS  Google Scholar 

  50. Chen, C.-H.: Emf measurements on Lewis and Sargent cells with free diffusion boundaries. J. Chem. Eng. Data 17, 473–475 (1972)

    Article  CAS  Google Scholar 

  51. Harbinson, T.R., Davison, W.: Performance of flowing and quiescent free-diffusion junctions in potentiometric measurements at low ionic strength. Anal. Chem. 59, 2450–2456 (1987)

    Article  CAS  Google Scholar 

  52. Wu, Y.C., Feng, D., Koch, W.F.: Evaluation of liquid junction potentials and determination of pH values of strong acids at moderate ionic strengths. J. Solution Chem. 18, 641–649 (1989)

    Article  CAS  Google Scholar 

  53. Guggenheim, E.A.: A study of cells with liquid–liquid junctions. J. Am. Chem. Soc. 52, 1315–1337 (1930)

    Article  CAS  Google Scholar 

  54. Onsager, L.: Theories and problems of liquid diffusion. Ann. N.Y. Acad. Sci. 46, 241–265 (1945)

    Article  CAS  Google Scholar 

  55. Tyrrell, H.J.V., Harris, K.R.: Diffusion in Liquids. A Theoretical and Experimental Study. Butterworths, London (1984)

    Google Scholar 

  56. Dunlop, P.J., Harris, K.R., Young, D.J.: Experimental methods for studying diffusion in gases, liquids, and solids. In: Rossiter, B.W., Baetzold, R.C. (eds.) Physical Methods of Chemistry, Vol. 6, Determination of Thermodynamic Properties, 2nd edn, pp. 175–282. Wiley, New York (1992)

    Google Scholar 

  57. Leaist, D.G.: Fick equations for the diffusion of electrolytes in ternary liquid junctions. J. Chem. Soc. Faraday Trans. 88, 2897–2902 (1992)

    Article  CAS  Google Scholar 

  58. Covington, A.K., Rebelo, M.J.F.: Reference electrodes and liquid junction effects in ion selective electrode potentiometry. Ion Sel. Electrode Rev. 5, 93–128 (1983)

    Article  CAS  Google Scholar 

  59. Ferguson, A.L., Van Lente, K., Hitchens, R.: Liquid junction potentials. II. A direct comparison of static and flowing junctions. J. Am. Chem. Soc. 54, 1285–1290 (1932)

    Article  CAS  Google Scholar 

  60. Leaist, D.G., Kanakos, M.A.: Measured and predicted ternary diffusion coefficients for concentrated aqueous LiCl + KCl solutions over a wide range of compositions. Phys. Chem. Chem. Phys. 2, 1015–1021 (2000)

    Article  CAS  Google Scholar 

  61. Miller, D.G.: Application of irreversible thermodynamics to electrolyte solutions. II. Ionic coefficients l ij for isothermal vector transport processes in ternary systems. J. Phys. Chem. 71, 616–632 (1967)

    Article  CAS  Google Scholar 

  62. Miller, D.G.: Activity coefficient derivatives of ternary systems based on Scatchard’s neutral electrolyte description. J. Solution Chem. 37, 365–375 (2008)

    Article  CAS  Google Scholar 

  63. Van Rysselberghe, P.: Transport numbers in mixed aqueous solutions of alkali chlorides. I. Theoretical remarks. J. Am. Chem. Soc. 55, 990–996 (1933)

    Article  Google Scholar 

  64. Leaist, D.G., Lyons, P.A.: Multicomponent diffusion in dilute solutions of mixed electrolytes. Aust. J. Chem. 33, 1869–1887 (1980)

    Article  CAS  Google Scholar 

  65. Leaist, D.G., Lyons, P.A.: Electrolyte diffusion in multicomponent solutions. J. Phys. Chem. 86, 564–571 (1982)

    Article  CAS  Google Scholar 

  66. Kim, H., Reinfelds, G., Gosting, L.J.: Isothermal diffusion of water–potassium chloride–hydrogen chloride and water–sodium chloride–hydrogen chloride systems at 25 °C. J. Phys. Chem. 77, 934–940 (1973)

    Article  CAS  Google Scholar 

  67. Woolf, L.A.: Tracer diffusion of hydrogen ion in aqueous alkali chloride solutions at 25 °C. J. Phys. Chem. 64, 481–484 (1960)

    Article  CAS  Google Scholar 

  68. Hitchcock, D.I., Taylor, A.C.: The standardization of hydrogen ion determinations. I. Hydrogen electrode measurements with a liquid junction. J. Am. Chem. Soc. 59, 1812–1818 (1937)

    Article  CAS  Google Scholar 

  69. Ives, D.J.G., Janz, G.J.: Reference Electrodes. Theory and Practice. Academic Press, New York (1961)

    Google Scholar 

  70. Partanen, J.I., Covington, A.K.: Re-evaluation of the activity coefficients of aqueous hydrochloric acid solutions up to a molality of 2.0 using two-parameter Hückel and Pitzer equations. I. Results at 25 °C. J. Solution Chem. 31, 187–196 (2002)

    Article  CAS  Google Scholar 

  71. Lamb, A.B., Larson, A.T.: Reproducible liquid junction potentials: the flowing junction. J. Am. Chem. Soc. 42, 229–237 (1920)

    Article  CAS  Google Scholar 

  72. MacInnes, D.A., Yeh, Y.L.: The potentials at the junctions of monovalent chloride solutions. J. Am. Chem. Soc. 43, 2563–2573 (1921)

    Article  CAS  Google Scholar 

  73. Scatchard, G.: The activities of strong electrolytes. III. The use of the flowing junction to study the liquid-junction potential between dilute hydrochloric acid and saturated potassium chloride solutions; and the revision of some single-electrode potentials. J. Am. Chem. Soc. 47, 696–709 (1925)

    Article  CAS  Google Scholar 

  74. Gibbs, J.W.: The Scientific Papers of J. Willard Gibbs, Vol. 1, Thermodynamics, pp. 338–349. Longmans, London (1906)

    Google Scholar 

  75. Hermans, J.J., Oosterhoff, L.J.: The thermodynamical treatment of diffusion potentials. Philos. Mag. Ser. 7. 24, 304–312 (1937)

    Article  Google Scholar 

  76. Miller, D.G.: Thermodynamic theory of irreversible processes. III. The potentials of electrochemical cells in gravitational and centrifugal fields. Am. J. Phys. 24, 595–604 (1956)

    Article  CAS  Google Scholar 

  77. Onsager, L.: Reciprocal relations in irreversible processes I. Phys. Rev. 37, 405–426 (1931)

    Article  CAS  Google Scholar 

  78. Scatchard, G.: Ion exchanger electrodes. J. Am. Chem. Soc. 75, 2883–2887 (1953)

    Article  CAS  Google Scholar 

  79. Vitagliano, P.L., DellaVolpe, C., Vitagliano, V.: Gravitational instabilities in free diffusion boundaries. J. Solution Chem. 13, 549–562 (1984)

    Article  CAS  Google Scholar 

  80. Miller, D.G., Vitagliano, V.: Experimental test of McDougall’s theory for the onset of convective instabilities in isothermal ternary systems. J. Phys. Chem. 90, 1706–1717 (1986)

    Article  CAS  Google Scholar 

  81. Vitagliano, P.L., Ambrosone, L., Vitagliano, V.: Gravitational instabilities in multicomponent free-diffusion boundaries. J. Phys. Chem. 96, 1431–1437 (1992)

    Article  CAS  Google Scholar 

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    Dmitri P. Zarubin

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Zarubin, D.P. Potentiometric Cells with Liquid Junctions: A Combined Analytical and Computational Study. J Solution Chem 45, 591–623 (2016). https://doi.org/10.1007/s10953-016-0460-3

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