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In high school we were taught that the formula for pH is the negative of the common logarithm of hydrogen ion concentration: pH = -log[H+].

It wasn't until I took organic chemistry that the "acid dissociation constant" (pKa) was introduced. It was at that point that the textbook explained that "p" was used as a mathematical operator, meaning the negative of the common logarithm. (See https://web.mst.edu/~gbert/logs/pH.html.)

Why didn't they teach us that in high school? There would have been no rote memorization of the pH formula: the equation is right there in the name!

Is this operator restricted to chemistry? I've never seen it used in a (purely) mathematical context and have always wondered how the usage originated. Does anyone know its etymology or the first time it appeared in a publication?

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How about this...

pH
1909, from German PH, introduced by S.P.L. Sörensen, from P, for German Potenz "potency, power" + H, symbol for the hydrogen ion that determines acidity or alkalinity.

source

And, yes, it is used only in chemistry.

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The term first appeared[source] in S. P. L. Sørensen's paper “Enzyme Studies II” (1909), which did not state what it stood for. Wikipedia claims[permalink] that the meaning of p is disputed between a number of possible words beginning with p (emphasis mine):

The exact meaning of the "p" in "pH" is disputed, but according to the Carlsberg Foundation, pH stands for "power of hydrogen".[5] It has also been suggested that the "p" stands for the German Potenz (meaning "power"), others refer to French puissance (also meaning "power", based on the fact that the Carlsberg Laboratory was French-speaking). Another suggestion is that the "p" stands for the Latin terms pondus hydrogenii (quantity of hydrogen), potentia hydrogenii (capacity of hydrogen), or potential hydrogen. It is also suggested that Sørensen used the letters "p" and "q" (commonly paired letters in mathematics) simply to label the test solution (p) and the reference solution (q).[6]

The source [6] cited (doi:10.1021/ed800002c) disputes "power" since the article was published in German, French and Danish, but not English. It prefers the p and q suggestion for the test and reference cells, citing https://doi.org/10.1016/S0968-0004(99)01517-0. This final paper shows that there were equations in Sørensen's papers using the symbols $p_H^+, C_p, C_q, π_p$ and $π_q$.

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