How did the concept of pH originate and develop?

Question

Background & My research

To begin I did some research to find a few articles on the history of pH namely "The Symbol for pH"- William B. Jensen, "One-Hundred Years of pH" - Rollie J. Myers (but couldn't access it) and "The origin and the meaning of the little p in pH" - Jens G Nørby (but couldn't access this also).

So to start I did some reading on the wiki article for pH and found that S.P.L. Sørensen first introduced the term in his [paper] - "Über die Messung und die Bedeutung der Wasserstoffionenkonzentration bei enzymatischen Prozessen" ^[1] in 1909 in order to explain the acidity and basicity of the acids/bases on the "Arrhenius concept". To explain to some extent the use of the logarithmic scale I found out that his experiments contained the use of electrodes with one being a calomel electrode and the other being a normal hydrogen electrode. Upon experimental results and an equation (which I think was the Nernst Equation) he found that the electric potential of the cell was proportional to −log[H+].

To somehow explain the use of "p in pH" I found out S.P.L. Sørensen in his original paper used $P_H$ to represent this “hydrogen ion exponent”. Although as his work became more popular several more variations like Ph and pH were introduced with the latter getting officially adopted by the "Journal of Biological Chemistry" in 1910's and eventually gaining more recognition than the other variations. The origin of "P" in the original text is speculated to be related to puissance (French), potenz (German) or potens (Danish) which were the languages in which Sørensen published.

This was all I could find from my research and still have some doubts like how the little p in "pH" evolved/generalized to be used as "an operator" like - $pK_a, pK_b, pK_w$ etc. which are further expressed below in the main question.

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Question:

I was recently introduced to the concept of pH in chemistry and its value being the following: $$\mathrm{pH} =-\log[\mathrm H^+]$$ This was followed up by the "generalization of the concept of pH" in "finding the p" of a base/acid (e.g., $pK_a, pK_b, pK_w$ etc.)

Now I want to know how is it that the definition of pH evolved from being the "hydrogen ion concentration" to the "activity of hydrogen ions" as well some background on the experiments that he performed which led him to define these concepts the way they are? Also how is it that the concept became "more generalized" and evolved from being the negative common logarithm of the concentration of hydrogen ions to a more generalized "operation" applicable to things more than just the hydrogen ions?

Any sort of articles and further reading links will be very much appreciated which could help me learn more about the "history of pH" and how it originated and evolved as a concept.

Answer 1

Your question requires a lot of historical background of late 1890s and early 1900s. I requested a couple of articles from different libraries. Basically, it will be best to dispel the common myth that "p" means anything from a certain European language. It does not. Later authors developed this association. At least Sorenson never used p for power or the German Potenz and there are many more stories as shown in the Table. An interested reader should consult Nørby, Jens G. "The origin and the meaning of the little p in pH." Trends in Biochemical Sciences 25.1 (2000): 36-37 for actual excerpts and other common stories associated with the letter p. His father worked with Sorenson. See this table for example from Nørby:

Now accepting the definition that pH represented a negative logarithm (of base 10) of hydrogen ion concentration, the invention of pH concept is merely a matter of convenience. Even in the early 1900's, chemists were interested in measuring the concentration of hydrogen ions by indicators. Then it must be naturally convenient to invent a scale of hydrogen ion concentration because one can vary the concentration of "hydrogen" over several orders of magnitude in water.

I do not exactly know when the letter p became an operator of of -log, but currently it is used as such.