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pH Definition

Date: 10/20/2001 at 22:22:14
From: Lily
Subject: pH definition 

Dr. Math,

A few of my science/math teachers were having a discussion about pH 
levels one day and the question of what the 'p' in pH is arose. Nobody 
seemed to know the answer. Could you help us out?

Date: 10/20/2001 at 23:05:54
From: Doctor Peterson
Subject: Re: pH definition 

Hi, Lily.

I just learned something. I always guessed it meant "proportion," but 
I was wrong! The bottom line is that we really don't know for sure 
where the p comes from.

My first reaction to a question like this is to look it up in a 
dictionary. The old Merriam-Webster next to me doesn't say, but I went 
downstairs to get the latest edition, and it does. It says

   [G, fr. _P_otenz power + _H_ (symbol for Hydrogen)] (1909)

(The underscores mean italicized letters.)

In other words, this is an abbreviation of the German words "Potenz 
Hydrogen", or "power of hydrogen".

Merriam-Webster can also be found on-line, at

The other most likely place to find the information, Russ Rowlett's 
_How Many? A Dictionary of Units of Measurement_ at:   

doesn't give the meaning of the "p" but agrees on the date:

   The pH scale was invented by S. P. L. Sorenson in 1909.

He doesn't sound German, though.

I should mention that the German word for hydrogen is not hydrogen, 
but "Wasserstoff." In checking that, I found that "Potenz" is not 
listed in my German dictionary; the normal words for "power" are 
"Kraft" and "Macht." I guessed that "Potenz" would be related to 
"potency," and would mean "power" only in the sense of 
"effectiveness." But then, looking for the word online, I found that 
it is used in a mathematical sense for an exponent, which of course is 
exactly what a logarithm is. So pH really means "exponent of hydrogen 
concentration" in German.

And in fact, I found a reference that gives the full story:

   The pH scale - University of Waterloo   

   According to the Oxford Dictionary, the pH scale was originally
   introduced by the Danish biochemist S.P.L. Sorensen in 1909 using
   the symbol pH. Other symbols such as p_H have been used in the 
   past. The letter p is derived from the German word potenz meaning 
   power or exponent of, in this case, 10. 

   You may argue that what have we learned by looking into historical
   origin of the term? Well, the origin of concept is interesting in
   that we sometimes need to develop concepts ourselves. A concept or
   tool becomes important if many people find it convenient and 

   The reality is that many chemists have used the pH scale and the p
   scales for many other quantities that they often take it for
   granted, without realizing the logic behind their usages. For
   example, we have used the pK_a, pK_b, pK_w, notations by analogy to
   the pH notations with out asking a question. 

   Now that you know the pH is an exponent, the following relationship
   is obvious: 

    [H+] = 10^-pH

But then I searched the Web for the words "ph potenz" to check the 
story. I found a slightly different version at

   pH - Gondar Design Science   

    The "p" stands for "potenz" (this means the potential to be) and
    the "H" stands for Hydrogen.

"Potential" sounds like a good guess, but it's not quite right.


   pH Explained - Swimming Pool Owners' Guide to Water Chemistry   

    pH is the power (German 'potenz') of a solution to yield hydrogen
    ions [H+].

But then I found this:

   pH - SHiPS Resource Center   

    Jens Norby (2000) has recently clarified the origin and meaning
    of the little 'p' in pH. The H, of course, refers to H+, the
    hydrogen ion, whose concentration contributes to acid strength.
    Hence, many have supposed that the 'p' refers to power (or the
    French puissance or German Potenz). Some have taken this to mean
    the power of 10, referring to the logarithmic calculation of pH.
    Similarly, others construe the 'p' as denoting the potential, or
    intensity, of hydrogen (or in Latin, potentia).

    But Norby traces the 'p' to a simple mathematical convention of
    naming variables. Danish chemist Soren Peter Lauritz Sorensen
    proposed the pH scale in 1909. But he did not give an explicit
    reason for choosing 'p' in his original two papers. Sorensen was
    primarily concerned with determining the H+ concentration
    electrometrically. His central equation involved values for
    measurements at two electrodes, which he arbitrarily designated
    p and q. To develop a standard, he set the non-hydrogen
    component, Cq, at 1.0 and solved for the hydrogen ion
    concentration, Cp, or 10-p. The number p he suggested calling p+H. 

    Sorensen ultimately defined pH as the negative logarithm of a
    factor for hydrogen concentration relative to a normality of 1.0,
    not (as many texts today do) as the negative logarithm of the
    hydrogen ion concentration. (As Norby notes, one cannot take a
    logarithm of a measurement with units.) 

You can learn and unlearn a lot on the Web in a short time! 

- Doctor Peterson, The Math Forum   

Date: 10/21/2001 at 09:31:46
From: Lily/Sheela s.
Subject: Re: pH definition

Thank you!
Associated Topics:
High School Definitions
High School Physics/Chemistry
Middle School Definitions
Middle School Terms/Units of Measurement

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