In the Classroom
Defining and Teaching pH Richard F. Burton Institute of Biomedical and Life Sciences, University of Glasgow, Glasgow G12 8QQ, United Kingdom;
[email protected] Two very different definitions of pH coexist: one prevailing in the classroom and the other, usually unacknowledged, in the laboratory. Best known is the 1909 definition of Sørensen (1, 2) in which pH is defined in terms of molar concentrations as ᎑log10[H+]. Of 24 consulted textbooks of general chemistry and biochemistry published in 1981–2002, all give only this definition (with one passing mention of activities and with some books substituting [H3O+] for [H+]). Difficulties with this definition became apparent in 1924 (3), and the pH scale now generally used in practice, even when not taught, relates to molal activities (employing the Bates–Guggenheim convention for chloride activity). It is defined operationally in terms of standard buffer solutions (4, 5). For example, according to IUPAC recommendations (5), the pH of 0.05000 mol kg᎑1 potassium hydrogen phthalate is 4.000 at both 0 ⬚C and 20 ⬚C. The pH of 0.1000 mol L᎑1 hydrochloric acid at 25 ⬚C is not 1.0, but 1.088 (4). While this manuscript was under review, an article was published that illustrates even more striking disparities between pH and ᎑log10[H+] (6). The most obvious way to amend a “1909” account of pH is simply to add in the concept of activity (6) and the IUPAC scale, noting the numerical disparity between scales and perhaps even retaining “[H+]” as an acknowledged approximation to 10᎑pH. However, many students find the concept of pH hard enough already and may benefit from an easier, yet sound, approach. It is perhaps the advanced theoretical basis of the modern pH scale that has kept it out of mainstream teaching, but, according to its operational definition, pH is simply “the reading on a conventionally cali-
www.JCE.DivCHED.org
•
brated pH meter”. Some students, given little more than the notions of acidity and alkalinity, will never require a deeper understanding than this, needing only to treat pH as a number on a practical scale of acidity–alkalinity (4). This is because a pH value, like a temperature, is generally meaningful only in comparison with other numbers on the same scale— such as pK values and optimum pH values for soil or patients’ blood. For students requiring the algebra of equilibria, [H+] is replaced by the “conventional activity”, equal to 10᎑pH but rarely calculated (for which no completely satisfactory one-word name exists). Even with this simple approach, the link and distinction between activity and concentration should be noted at the outset, but in a manner matched to the students’ abilities and future needs. Literature Cited 1. Sörensen, S. P. L. Biochem. Z. 1909, 21, 131–304. 2. Sørensen, S. P. L. Compt. Rend. Trav. Lab. Carlsberg 1909, 8, 1–168. 3. Sørensen, S. P. L.; Linderstrøm-Lang, K. Compt. Rend. Trav. Lab. Carlsberg 1924, 15, 1–40. 4. Bates, Roger G. Determination of pH. Theory and Practice, 2nd ed.; John Wiley & Sons: New York, 1973. 5. 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. Pure Appl. Chem. 2002, 74, 2169–2200. http://www.iupac.org/ publications/pac/2002/7411/ (accessed Mar 2006). 6. McCarty, C. G.; Vitz, E. J. Chem. Educ. 2006, 83, 752–757.
Vol. 84 No. 7 July 2007
•
Journal of Chemical Education
1129
