Chemistry for Everyone
One-Hundred Years of pH Rollie J. Myers Department of Chemistry, University of California, Berkeley, Berkley, California 94720
[email protected] The concept of pH is now 100 years old. S. P. L. Sørensen of the Danish Carlsberg Laboratories formulated the concept in 1909 in an article whose short title in English is “Enzyme Studies II”. Both biologists and chemists now universally use the pH symbol as simple shorthand to indicate acidity, and the pH meter is one of the most commonly used laboratory instruments in instructional laboratories. Today every chemistry student learns about pH, but for various reasons, it took some time for its introduction into chemistry. Sørensen's article appeared in three languages, German (1), French (2), and Danish (3). The symbol he used in these publications was not identical in the three journals because there was no common symbolism for ionic charge. The major difference from today's notation of pH is that Sørensen used a “p” that was lower case but slightly larger than what was used in the body of the text and a smaller, almost subscripted “H” for hydrogen ions with an indication of its charge. For the first 10 years, there were many variations for his symbol. These included ph, pH, Ph, þ PH, Ph, PH, Pþ h , PH. The current symbol became standard after it was adopted by the editors of the Journal of Biological Chemistry (4). This journal contained no author instructions, but one can find two articles by the same author, J. F. McClendon, where the article published in 1916 uses PH and the article published in 1917 uses pH. The little p and the in-line H, used for typographical convenience, has taken on a life of its own and this p has become universal in chemistry to stand for the operator -log10 with the result that we use pOH, pCl, pKa, pKw, and so forth. It has always been popular to believe that p represents an abbreviation and many authors, including the historical reviews in this Journal (5, 6), have suggested that p stands for “power” even though Sørensen did not publish in English. Since the language used in the Carlsberg laboratory was French, a more logical choice would be exposant or puissance. A currently popular and illogical interpretation is that pH is Latin: pondus Hydrogenii. The Carlsberg Foundation, who now operates the laboratory, has a Web page that states that pH represents, “power of hydrogen”. All of these suggestions are interesting mnemonics, but the most likely reason for the use of the letter p is explained by Nørby (7): Sørensen used the letters p and q to designate the cell concentrations for his hydrogen electrodes. The q solution in his apparatus was the reference solution and the solution containing the unknown hydrogen-ion concentration was designated as the p solution. The concentrations in these cells were designated as Cp = 10-p and Cq = 10-q, and the voltages measured were designated πp and πq. One can question the use of p and q, but these are commonly paired symbols in mathematics. A classical 1907 book on algebra (8), for example, had several uses
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of the pair p and q, and most chemists know that rotationalvibrational spectroscopy has P, Q, and R branches. Could we have possibly ended up with qH instead of pH had Sørensen chosen different solutions for these letters? In his article where he first used his symbol, he referred to it as, “d'exposant des ions hydrogene”. At that point, he also wrote the equation Cp = 10-pH, but in the three publications, this equation looked quite complicated because of the attempts to include the charge on the H as a superscript. Since Sørensen never explained why he picked the letter p, we will never fully know. Similar to the glass electrode, the hydrogen electrode produces a voltage that is directly dependent on the logarithm of the apparent concentration of hydrogen ions so Sørensen's apparatus was directly measuring pH. In the old issues of the Journal of Biological Chemistry, advertisements for a Leeds and Northrup potentiometer are found, possibly used by Sørensen in his complicated hydrogen gas pH apparatus, and Clark's book (4) has an illustrated advertisement for, “A Complete H-Ion Outfit”, for $473.20 with a source of hydrogen not included. Buffers The real purpose of Sørensen's work was to establish the use of standardized buffers in biochemistry. He established the pH of citric acid, phosphoric acid, and boric acid buffers that could be used to obtain pH values from 5 to 9. Clark's book (4) also described the Clark and Lubs buffers and other buffers, including acetate, which extended the pH range. Biochemists quickly recognized that buffers were superior to the simple addition of acid or base, and they used pH very early. In 1916, K. A. Hasselbach revised the Henderson equation for the hydrogenion concentration of a buffer to express the pH of a buffer solution directly. The use of this equation and some of its history has been discussed in this Journal (9). Chemists, on the other hand, seemed to have largely ignored pH. If one searches the collective indexes of Chemical Abstracts, the first entry for pH in the subject index was for 1937-1946 where it said, “see hydrogen-ion concentration” and under hydrogen-ion concentration there were a number of citations, but only a few of these references included pH in their titles. This scant reference to pH continued in the 1947-1956, 1957-1961, and 1962-1966 subject indexes. In 1967-1971, there was no entry for pH in the subject index, but in the 1972-1976 collective index, they renamed the subject index as a new general subject index. This general subject index had an entry for pH, and it had a flood of entries that took up three pages with about 250 references! While chemistry teachers were late in introducing pH into their courses they were far ahead of Chemical Abstracts.
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Chemistry for Everyone
Indicators The use of litmus to indicate acid or base goes back to alchemy, and the phrase “litmus test” is part of our language. Naturally derived litmus is highly impure and a poor acid-base indicator. In 1904, the Zeitscrift fur Electrochemie had an issue dedicated to Wilhelm Ostwald's 50th birthday celebration, and since he had proposed the accepted theory of indicators, it was logical that this issue had several articles about indicators. Kolthoff (10) said that these were the first published summaries of modern indicators, and one article gave an indicator color table similar to what might be found in a current text, but without the use of pH. In 1908, the ionization constants of indicators such as methyl orange and phenolphthalein were determined in phosphate buffers by the use of a simple visual colorimeter. There were enough established indicators available in 1909 for Sørensen to test 20 for their color change in his buffers. Clark's book also included a colored plate showing the colors for eight indicators in his recommend buffers (4). While indicator colors were the primary method for pH determination for many years, they could not be utilized in colored or reactive solutions. Beckman's pH Meter By 1909, the properties of the glass electrode had been discovered, but its high resistance made it difficult to use. In 1934, a friend from the local citrus industry approached Arnold O. Beckman at the California Institute of Technology and told him about their difficulty in establishing pH in some products. The friend had even tried to use a thin and fragile glass electrode, but his simple bridge potentiometer was tiresome and it required a sensitive galvanometer. Beckman knew how the vacuum tubes of the day could be adapted to have a high input resistance. He utilized a small company that he had previously established and produced the first commercial glass-electrode vacuum-tube pH meter just in time for the San Francisco ACS meeting in late 1935. Despite the fact that most chemical supply companies had thought that the pH meter would not sell, this simple portable wooden-boxed instrument was a great success. It was the standard for many years, and the desire for pH values served as the foundation of our modern chemical instrumentation industry. pH in Introductory Chemistry A quick search of the Internet today finds pH values for foods, soils (even those on Mars), beverages, and rainwater, and in today's popular culture a reference to pH is often displayed in advertisements for beauty products. It has almost become a part of everyday vocabulary. While the average citizen today may not know how pH is defined, it is surprising that for the first 40 years after its invention most introductory chemistry courses did not even discuss pH. The biochemists appreciated the concept of pH and adopted it in their research. For many years, introductory chemistry courses covered descriptive chemistry and stoichiometry, but little or no chemical equilibrium. Acids were discussed only in general and buffers were not discussed, so there was little reason to introduce pH. In addition, log tables or slide rules were the only tools for their calculation. Today, electronic calculators have solved that problem and the concept of pH is taught in all introductory chemistry courses.
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As an example of pH use in introductory chemistry, we review how the concept of pH was introduced into the curriculum at UC Berkeley. Joel Hildebrand taught introductory chemistry at UC Berkeley for over 30 years. He wrote his own textbook, first published in 1918, and it went through seven editions. The first mention of pH was in the fourth edition (1940) where he had a table of the colors for various indicators for every factor of 10 in hydrogen-ion concentration (11). In this text, he does not define pH but only says that its meaning is obvious from the table and “that it is much used in biological work”. In the fifth edition (1947), while there was no entry for pH in the index, buffers and a titration curve were shown labeled with pH. In the text, he also finally defined it as -log[Hþ]. It is interesting that this introduction of pH in chemistry came just over 10 years after the development of the Beckman pH meter. Many chemistry departments purchased this instrument, and it helped to force them to use pH values. On the more modest side, multi-indicator pH paper, replacing the old litmus paper, also became popular for the general chemistry laboratory. The sixth and seventh additions (1952 and 1964) of Hildebrand's text, revised by R. E. Powell, slowly increased their coverage of pH with it finally making it to the index in the seventh edition. In other schools such as the California Institute of Technology where Linus Pauling taught the introductory chemistry course, pH was discussed in detail at least 10 years earlier than was done by Hildebrand. What Is pH? While the simplest definition of pH is -log[Hþ], only the hydrogen-ion molality in a dilute strong acid solution is known. For buffers or bases, the equilibrium constant calculations along with a knowledge of mean ionic activities are used. In Sørensen's electrochemical apparatus, a salt bridge between the hydrogen electrode and reference electrode was used. This salt bridge introduced a “liquid junction potential”. In 1924, Sørensen decided that he could correct for this potential by properly defining the potential of the reference electrode. The result was that he felt that pH would be more precisely defined as -log(activity of Hþ). This involves the activity of a single ion and it is not a thermodynamically based mean activity. Sørensen proposed a new symbol based on activities as, paH, but this symbol is not used. The modern definition of pH is based on this single-ion activity. Over the years, workers have tried to accurately estimate these liquid junction potentials, but none of these calculations are satisfactory. Most workers now agree that singleion activities can never be measured exactly, but those based on estimated liquid junction potentials are not satisfactory. The glass electrode produces a potential that can measure the activity of the hydrogen ion, but it also requires a salt bridge. As a result, calibration is required to measure pH. The 2002 recommendations about pH by the International Union of Pure and Applied Chemistry are summarized by G. K. Baucke (12). The result is an operational definition of pH based on a set of standard buffers. These buffers are calibrated by the use of an electrochemical cell that has no salt bridge but has a small amount of chloride added and uses a silver/silver chloride reference electrode. This forms a Harned cell. The result, after some extrapolation, is the determination of the mean ionic activity of HCl in the buffer. To estimate the activity of the hydrogen ion, the chloride-ion activity must be
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estimated. This is done by using the Bates-Guggenheim convention, which uses a version of the Debye-Hu.ckel limiting law extended to higher ionic strengths to calculate the activity of the chloride ion. This value is then used to obtain the activity of the hydrogen ion. Once standardized, these buffers can be used to calibrate a pH meter. This is, of course, just an operational definition that establishes a single pH value for every solution.
Acknowledgment We would like to thank Jens Nørby for sending us some historical material about the Carlsberg Laboratory from his family's collection. Literature Cited
Teaching pH Some students are first confused by the fact that the higher pH values correspond to lower acidities. This is only a minor problem in teaching pH, and the real complication comes from the manner in which pH is now defined. For teaching purposes, particularly at the high school and introductory college level, we should probably repeat Sørensen's original definition, since anything beyond that is terribly complicated. The actual hydrogenion concentration is at least a real quantity that students can understand. So at this level, the common question is “What is the pH of a 0.10 M HCl solution?” The answer should still be that it is 1.0. At the upper-division college level, we could reply that it is close to 1.0, but nonidealities in the solution will affect the answer. At the graduate level, we could say that this is outside the range of the carefully calibrated buffers, and since single-ion activities can not be truly calculated in any concentrated solution, the question does not have a unique answer. As far as the pH of a buffer solution such as one formed by acetic acid and sodium acetate, it should be measured with a pH meter and the calibrated buffers. It is unfortunate that it is not possible to equate a measured pH to the hydrogen-ion concentrations calculated with acid dissociation constants and thermodynamically based mean activities. To calculate a pH, we must know the activity of the hydrogen ion in the solution. We can only estimate hydrogen-ion activities with the nonthermodynamic Debye-Hu. ckel equation and that is valid only in very dilute solutions. Such problems have probably been the subject of
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more than one presentation (13) about these modern pH values and teaching in chemistry.
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1. Sørensen, S. P. L. Biochem. Zeit. 1909, 21, 131–199. Sørensen, S. P. L. Biochem. Zeit. 1909, 22, 352–356. 2. Sørensen, S. P. L. Compt. Rend. Trav. Lab. Carlsberg 1909, 8, 1–162. 3. Sørensen, S. P. L. Meddelelsierfra. Carlsberg Laboratoriet 1909, 8, 1–168. 4. Clark, W. M. The Determination of Hydrogen Ions; Williams and Wilkens: Baltimore, MD, 1920; p 26. Clark, W. M. The Determination of Hydrogen Ions, 2nd ed.; Williams and Wilkens: Baltimore, MD, 1922; p 35. 5. Szabadvary, F. J. Chem. Educ. 1964, 41, 105–107. 6. Jensen, W. B. J. Chem. Educ. 2004, 81, 21. 7. Nørby, J. G. Trends Biochem. Sci. 2000, 25, 36-37. Similar material was presented by R. J. Myers in his presentation, Who Put the “p” in the pH Symbol and Why Was It Chosen? In Book of Abstracts, Proceedings of the 219th ACS National Meeting, San Francisco, CA, March 26-30, 2000. 8. B^ocher, M. Introduction to Higher Algebra; Macmillan Company: New York, 1907; pp 104, 206, 280. 9. Po, H. N.; Senozan, N. M. J. Chem. Educ. 2001, 78, 1499–1503. 10. Kolthoff, I. M. Acid-Base Indicators; Macmillan Company: New York, 1937; p 106. 11. Hildebrand, J. H. Principles of Chemistry, 4th ed.; Macmillan Company: New York, 1940; p 17. 12. Baucke, G. K. Anal. Bioanal. Chem. 2002, 374, 772–777. 13. Pratt, K. W. The Truth about pH: A Look at What Is Swept Under the Rug. In Book of Abstracts, Proceedings of the 215th ACS National Meeting, Dallas, TX, March 29-April 2, 1998.
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