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A New Concept for pH-Potential Calculations K. L. Cheng Department of Chemistry, University of Missouri-Kansas City, Kansas City, MO 64110;
[email protected] In quantitative analysis textbooks, many basic concepts and reactions have never been experimentally proved. I have previously reported that some of them may, in principle, be erroneous (1–5). This paper discusses an important concept regarding the potential calculation of the pH glass electrode. It is generally accepted that the pH glass electrode is a halfcell, its potential expressed as the cell potential (Ecell). The potential calculation of a glass electrode is commonly done according to the Nernst equation E cell = E ° + 0.059 log(H+) = E ° – 0.059 pH
(1)
I was taught this way many decades ago. Then about 10 years ago I proposed the capacitor concept (2). At present, textbooks still use the Nernst equation for nonfaradaic potentiometry, which deals with methods that do not involve redox reactions. Recently, experimental demonstrations of misleading Nernst slope (6 ) and misleading conventional redox mechanisms of calomel and Ag/AgCl reference electrodes (4) have been reported. The capacitor concept emphasizes that the pH glass electrode is not a half-cell and that its potential is a capacitance potential with no redox involved (7). This is important for clear understanding of the potential origin and underlying mechanism of the pH glass electrode. Though a short note has been published to correct the apparent pH-potential miscalculations (8 ), new analytical textbooks have ignored the new capacitor concept. In some textbooks, the following incorrect expression is often seen: E cell = E° – 0.059 log(H+) = E° + 0.059 pH
(2)
There is a difference between eqs 1 and 2: the former with a minus sign is correct and the latter with a plus sign is incorrect. This paper describes how the incorrect equation was derived. We first consider the glass electrode as a capacitor, not a half-cell, as is commonly done. It is well known that no redox reaction is involved at the glass electrode surface. In my view, the equilibrium redox-based Nernst equation is invalid for the pH glass electrode. This has been supported by theory and experimental results (1–6 ). As of one-half century ago, it was common to consider the following cell: Ag/AgCl|Cl{ ||H+ |glass membrane| H+, Cl{ |AgCl/Ag outside
inside
The potential mechanism has been vaguely misrepresented because it has been traditionally believed that the glass electrode behaves as a cell, the Ecell = Er, half-cell – E 1, half cell. The potential of the cell (∆E ) is given by E = E r – E l = + 0.241 (SCE) – 0.059 log(H+)
Rearrangement yields
E cell – 0.241 + = {log H = pH 0.059
(4)
Thus, the pH of the solution in the left half-cell can be computed from the measured cell potential. The highly respected authors Harned (7) and Kolthoff (9) introduced the above concepts in their books, and many other textbook authors just copied them. The problem has been that practically all analytical textbooks consider the pH glass electrode a voltaic cell (10). Some of them (10–15) explain pH glass electrode potential with the incorrect eqs 3 and 4. However, some textbooks present the correct equations to obtain the correct answer, even though they still use the term Ecell rather than Ecapacitance (16, 17 ). If we accept that the potential of the glass electrode is not that of a half-cell, then its potential is not the difference between an anode and a cathode; it is the addition of the measured potential to the reference potential, thereby forming a capacitance potential: Ecapacitance = E indicator + Ereference Both the glass electrode and the Ag/AgCl (or SCE) derive their potentials from the surface charges following the capacitance law, E = q/C, q being the charge density and C the capacitance. The charges may be discharged and recharged (18). Calculated potentials using eq 1 demonstrate a trend of more positive potentials for more acidic solutions (lower pH), and more negative potentials for more basic solutions (higher pH). This agrees with the capacitor theory that in an acidic solution, hydrogen ions are adsorbed on the electrode surface and in a basic solution, hydroxide ions are adsorbed on the electrode. The adsorbed ions make the electrode surface either positively charged or negatively charged. The surface charge density yields the potential when the capacitance is constant. Furthermore, the capacitor theory explains the interference phenomenon (2, 11). In conclusion, this paper discusses the concept of pHpotential calculations and points out that the pH glass electrode may be considered as a capacitor instead of a half-cell and emphasizes that important concepts and equations should be scrutinized in light of new concepts and experiments. We want to be sure to teach correct concepts to our future chemists.
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JChemEd.chem.wisc.edu • Vol. 76 No. 7 July 1999 • Journal of Chemical Education
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Literature Cited 1. Cheng, K. L. In Electrochemistry, Past and Present; Stock, J. T.; Orna, M. V., Eds.; ACS Symposium Series 390, 1989; Chapter 20. Cheng, K. L. The Second Nernst Hiatus; Paper presented at the Pittsburgh Conference, 1992. 2. Cheng, K. L. Microchem. J. 1990, 42, 5-24. 3. Cheng, K. L. Microchem. J. 1998, 59, 323–325. Huang, C.-.M.; Jean, Y. C.; Cheng, K. L. J. Electrochem. Soc. 1995, 142, L175–L176. 4. Cheng, K. L.; Temsamani, K. R. Challenges to Conventional Redox Mechanisms of Calomel and Ag/AgCl Reference Electrodes; Paper No. 196, presented at the ACS National Meeting, Div. Colloid and Surface, Dallas, March 31, 1998. 5. Cheng, K. L.; Ashraf, N. Talanta 1990, 37, 659. 6. Cheng, K. L. Microchem. J. 1998, 59, 457–461. 7. Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions, 3rd ed.; Reinhold: New York: Reinhold, 1958; pp 427–431, 443. 8. Cheng, K. L. Microchem. J. 1986, 33, 132–133. 9. Kolthoff, I. M.; Sandell, E. B.; Meehan, E. J.; Brukenstein, S. Quantitative Chemical Analysis, 4th ed.; Macmillan: Toronto, 1969; p 943. 10. Flaschka, H. A.; Barnard, A. J. Jr.; Sturrock, P. E. Quantitative Analytical Chemistry, 2nd ed.; Willard Grant: Boston, 1980; p 285. 11. Galster, H. pH Measurement; VCH: Weinheim, 1991. 12. Pietrzyk, D. J.; Frank, C. W. Analytical Chemistry; Academic: New York, 1974; p 416. 13. Robinson, J. W. Undergraduate Instrumental Analysis, 5th ed.; Dekker: New York, 1995. 14. Willard, H. H.; Merrit, L. L. Jr.; Dean, J. A.; Settle, A. Jr. Instrumental Methods of Analysis; Wiley: New York, 1988; p 677. 15. Skoog, D. A.; West, D. M.; Haller, F. J. Fundamentals of Analytical Chemistry, 6th ed.; Saunders: Fort Worth, 1992; p 425. 16. Christian, G. Analytical Chemistry, 4th ed.; Wiley: New York, 1986; p 296. 17. Stumm, W.; Morgan, J. J. Aquatic Chemistry, 3rd ed.: Wiley: New York, 1996; Chapter 8. 18. Ashraf, N. New Developments in Understanding the Mechanism of pH Glass Electrode; Dissertation, University of Missouri-Kansas City, 1991; Fig. 17.
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