Skip to main content
SpringerLink
Log in

Numerical Simulation of pH Measurement in Dilute Solutions of the System H2O–KCl–HCl

  • Published:
Journal of Solution Chemistry Aims and scope Submit manuscript

Abstract

Potentiometric pH measurements on cells with liquid junctions are known to be biased with respect to the notional pH in dilute acid solutions, but detailed evaluation of the problem is obstructed by experimental difficulties. In this work, pH measurements are simulated numerically on a kind of the Harned cell with a free-diffusion junction between the saturated solution of KCl and dilute solutions of HCl + KCl with ionic strength and acid concentration varying from 0.0001 to 0.1 in terms of molarity. The pH is standardized against the solution 0.0001 M HCl + 0.05 M KCl, and the simulations are based on known solution properties (transport numbers, activity coefficients and diffusion coefficients). The bias is found to range from −0.012 to 0.056 in the composition range studied. The cell response is nearly linear in the notional pH in solutions with varying acid concentration, but no such relation is found in solutions with varying ionic strength at fixed acid concentration. It is shown that the Henderson equation underestimates the residual liquid-junction effect in very dilute solutions, largely due to failure to account for activity coefficients varying along the junction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. Note that the EMF of liquid junction cells is independent of the free-diffusion time [6, 13] so that solving for any non-zero value of it is sufficient.

  2. Random access memory.

References

  1. 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 (IUPAC Recommendations 2002). Pure Appl. Chem. 74, 2169–2200 (2002)

    Article  CAS  Google Scholar 

  2. Kadis, R., Leito, I.: Evaluation of the residual liquid junction potential contribution to the uncertainty in pH measurement: a case study on low ionic strength natural waters. Anal. Chim. Acta 664, 129–135 (2010)

    Article  CAS  Google Scholar 

  3. Davison, W., Harbinson, T.R.: Performance testing of pH electrodes suitable for low ionic strength solutions. Analyst 113, 709–713 (1988)

    Article  CAS  Google Scholar 

  4. Metcalf, R.C.: Accuracy of Ross pH combination electrodes in dilute sulphuric acid standards. Analyst 112, 1573–1577 (1987)

    Article  CAS  Google Scholar 

  5. Davison, W., Woof, C.: Performance tests for the measurement of pH with glass electrodes in low ionic strength solutions including natural waters. Anal. Chem. 57, 2567–2570 (1985)

    Article  CAS  Google Scholar 

  6. 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 

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

    Google Scholar 

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

    Article  CAS  Google Scholar 

  9. 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 

  10. Biedermann, G., Douhéret, G.: Studies of cells with transference. III. On the liquid junction emf at equimolar levels. Chem. Scripta 16, 144–153 (1980)

  11. 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 

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

    Article  CAS  Google Scholar 

  13. Zarubin, D.P.: Potentiometric cells with liquid junctions. A combined analytical and computational study. J. Solution Chem. 45, 591–623 (2016)

    Article  CAS  Google Scholar 

  14. Covington, A.K., Bates, R.G., Durst, R.A.: Definition of pH scales, standard reference values, measurement of pH and related terminology (recommendations 1984). Pure Appl. Chem. 57, 531–542 (1985)

    Google Scholar 

  15. 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 

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

    Google Scholar 

  17. 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 

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

    Article  CAS  Google Scholar 

  19. 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 

  20. Rard, J.A., Miller, D.G.: Mutual diffusion coefficients of BaCI2–H2O and KCI–H2O at 25 °C from Rayleigh interferometry. J. Chem. Eng. Data 25, 211–215 (1980)

    Article  CAS  Google Scholar 

  21. Rizzo, P., Albright, J.G., Miller, D.G.: Measurements of interdiffusion coefficients and densities for the system HCl + H2O at 25 °C. J. Chem. Eng. Data 42, 623–630 (1997)

    Article  CAS  Google Scholar 

  22. 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 

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

    Article  CAS  Google Scholar 

  24. Miller, D.G.: Application of irreversible thermodynamics to electrolyte solutions. I. Determination of ionic transport coefficients lij for isothermal vector transport processes in binary electrolyte systems. J. Phys. Chem. 70, 2639–2659 (1966)

    Article  CAS  Google Scholar 

  25. Postler, M.: Conductance of concentrated aqueous solutions of electrolytes. I. Strong uni-univalent electrolytes. Collect. Czech. Chem. Commun. 35, 535–544 (1970)

    Article  CAS  Google Scholar 

  26. Rard, J.A., Miller, D.G.: The mutual diffusion coefficients of NaCl–H2O and CaCl2–H2O at 25 °C from Rayleigh interferometry. J. Solution Chem. 8, 701–716 (1979)

    Article  CAS  Google Scholar 

  27. Rard, J.A., Miller, D.G.: The mutual diffusion coefficients of Na2SO4–H2O and MgSO4–H2O at 25 °C from Rayleigh interferometry. J. Solution Chem. 8, 755–766 (1979)

    Article  CAS  Google Scholar 

  28. Stokes, R.H.: The diffusion coefficients of eight uni-univalent electrolytes in aqueous solution at 25 °C. J. Am. Chem. Soc. 72, 2243–2247 (1950)

    Article  CAS  Google Scholar 

  29. Harpst, J.A., Holt, E., Lyons, P.A.: Diffusion in dilute hydrochloric acid–water solutions. J. Phys. Chem. 69, 2333–2335 (1965)

    Article  CAS  Google Scholar 

  30. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in Fortran 77, vol. 1. Cambridge University Press, Cambridge (1992)

    Google Scholar 

  31. Ruskeepää, H.: Mathematica® Navigator, 3rd edn. Elsevier, Burlington (2009)

    Google Scholar 

  32. Spivak, M.: A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd edn. Publish or Perish, Houston (1999)

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

    Google Scholar 

  34. Bates, R.G., Pinching, G.D., Smith, E.R.: pH standards of high acidity and high alkalinity and practical scale of pH. J. Res. Natl. Bur. Stand. 45, 418–429 (1950)

    Article  CAS  Google Scholar 

  35. 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 

  36. Metcalf, R.C., Peck, D.V., Arent, L.J.: Effect of potassium chloride additions on pH measurements of dilute sulphuric acid standards. Analyst 115, 899–905 (1990)

    Article  CAS  Google Scholar 

  37. Covington, A.K.: Recent developments in pH standardization and measurement for dilute aqueous solutions. Anal. Chim. Acta 127, 1–21 (1981)

    Article  CAS  Google Scholar 

  38. Metcalf, R.C.: The accuracy of pH determination in glacial melt-waters. Z. Gletscher. Glazial. 20, 41–51 (1984)

    CAS  Google Scholar 

  39. Robinson, R.A., Stokes, R.H.: Electrolyte Solutions, 2nd edn. Dover, Mineola (2002)

    Google Scholar 

  40. 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 

  41. deLevie, R.: A pH centenary. Electrochim. Acta 135, 604–639 (2014)

Download references

Author information

Authors and Affiliations

  1. Moscow State University of Technology and Management, 73 Zemlyanoi Val, Moscow, Russian Federation, 109803

    Dmitri P. Zarubin

Authors
  1. Dmitri P. Zarubin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dmitri P. Zarubin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zarubin, D.P. Numerical Simulation of pH Measurement in Dilute Solutions of the System H2O–KCl–HCl. J Solution Chem 46, 1284–1298 (2017). https://doi.org/10.1007/s10953-017-0644-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10953-017-0644-5

Keywords

Search

Navigation