Unterricht: Using Activities to Correct the Henderson-Hasselbalch Equation

Using Activities to Correct the Henderson-Hasselbalch Equation

Author(s): Michael Hippler und George D. Metcalfe

Publication: Bunsen-Magazin, Issue 5 2020, Unterricht, Seiten: 102-105

Publisher: Deutsche Bunsen-Gesellschaft für physikalische Chemie e.V., Frankfurt

Language: English

DOI: 10.26125/y7p7-an56

Abstract

The Henderson-Hasselbalch equation is central in chemistry teaching and has many practical applications. The equation, however, has many inherent approximations which limit its application. Here, we focus on one particular approximation, the use of concentrations instead of activities. We show that this can be easily corrected for in a modification which extends the useful range of the equation to moderately strong electrolytes (I < 0.5). Without this correction, the calculated pH of a typical phosphate buffer is too high by up to 0.4. The correction can be easily automated in a spreadsheet and is straightforward to implement into the chemistry and biochemistry teaching and laboratory curriculum. It introduces students to the concept of activities in thermodynamic equilibrium, and to the Debye-Hückel equation. It further emphasizes the importance of using activities instead of concentrations when the ionic strength exceeds 0.005 M, in contrast to the approach found in textbooks where activities are introduced, but then ignored ‘for the sake of simplicity’, even in example calculations where the use of concentrations is clearly not appropriate. In this contribution we intend also to stimulate discussions about how to teach chemical equilibria, Brønsted-Lowry acid-base reactions and titrations, buffer solutions, the concept of activity and the concept and definition of pH.

Cite this: Hippler, Michael, Metcalfe, George D.(2020): Using Activities to Correct the Henderson-Hasselbalch Equation. Bunsenmagazin 2020, 5: 104-107. Frankfurt am Main: Deutsche Bunsen-Gesellschaft für physikalische Chemie e.V. DOI: 10.26125/y7p7-an56

References

[1] Hasselbalch, K. A. Die Berechnung der Wasserstoffzahl des Blutes auf der freien und gebundenen Kohlensäure desselben, und die Sauerstoffbindung des Blutes als Funktion der Wasserstoffzahl. Biochem. Z. 1916, 78, 112–144.

[2] Po, H. N.; Senozan, N. M. The Henderson–Hasselbalch Equation: Its History and Limitations, J. Chem. Educ. 2001, 78, 1499-1503.

[3] de Levie, R. The Henderson Approximation and the Mass Action Law of Guldberg and Waage. Chem. Educator 2002, 7, 132–135.

[4] de Levie, R. The Henderson–Hasselbalch Equation: Its History and Limitations. J. Chem. Educ. 2003, 80, 146.

[5] Christian, G. D. Analytical Chemistry (6th ed.); Wiley: Hoboken NJ, 2003.

[6] Smith, T. W.; Hippler, M. Cavity-Enhanced Raman Spectroscopy in the Biosciences: In Situ, Multicomponent and Isotope Selective Gas Maesurements To Study Hydrogen Production and Consumption by Escherichia coli. Anal. Chem. 2017, 89, 2147–2154.

[7] Metcalfe, G. D.; Alahmari, S.; Smith, T. W.; Hippler, M. Cavity-Enhanced Raman and Helmholtz Resonator Photoacoustic Spectroscopy to Monitor the Mixed Sugar Metabolism of E. coli. Anal. Chem. 2019, 91, 13096–13104.

[8] Metcalfe, G. D.; Smith, T. W.; Hippler, M. In preparation.

[9] Pardue, H. L.; Odeh, I. N.; Tesfai, T. M. Unified Approximations: A New Approach for Monoprotic Weak Acid–Base

[10] Sørensen, S. P. L. Über die Messung und Bedeutung der Wasserstoffionenkonzentration bei enzymatischen Prozessen. Biochem. Z. 1909, 21, 131–304.

[11] Working Party on pH, Buck, R. P. (Chairman) et al.. Measurement of pH. Definition, standards, and procedures (IUPAC Recommendations 2002). Pure Appl. Chem. 2002, 74, 2169–2200.

[12] McCarty, C. G.; Vitz, E. pH Paradoxes: Demonstrating That It Is Not True That pH ≡ –log[H+]. J. Chem. Educ. 2006, 83, 752–757.

[13] de Levie, R. A pH Centenary. Electrochimica Acta 2014, 135, 604–639.

[14] de Levie, R. On Teaching Ionic Activity Effects: What, When, and Where? J. Chem. Educ. 2005, 82, 878–884.

[15] Jungas, R. L. Best literature values for the pK of carbonic and phosphoric acid under physiological conditions. Anal. Biochem. 2006, 349, 1–15.

[16] Meister, E. C.; Willeke, M.; Angst, W.; Togni, A.; Walde, P. Confusing Quantitative Descriptions of Brønsted–Lowry Acid–Base Equilibria in Chemistry Textbooks – A Critical Review and Clarifications for Chemical Educators. Helv. Chim. Acta 2014, 97, 1–31.

[17] Powell, K. J.; Brown, P. L.; Byrne, R. H.; Gajda, T.; Hefter, G.; Sjöberg, S.; Wanner, H. Chemical speciation of environmentally significant heavy metals with inorganic ligands. Part 1: The Hg2+–Cl–, OH–, CO32–, SO42–, and PO43– aqueous systems (IUPAC Technical Report). Pure Appl. Chem. 2005, 77, 739–800.

[18] Debye, P.; Hückel, E. Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen. Physikalische Zeitschrift 1923, 24, 185–206.

[19] Bockris, J. O’M. ; Reddy, A. K. N. Modern Electrochemistry, Vol.1, 2nd ed.; Kluwer Academic/Plenum Publishers: New York, 2002.

[20] Davies, C. W. Ion Association; Butterworths: Washington DC, 1962; p 41.

Get PDF

Download the full article

Unterricht: Using Activities to Correct the Henderson-Hasselbalch Equation