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For example, could one define a $\mathrm{pH}$ for pure acetic acid? It's a weak acid in water, but if someone handed you $1~\mathrm L$ of pure acetic acid, what would its $\mathrm{pH}$ be?

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  • $\begingroup$ pH is usually for more or less diluted water solutions. But here is some insight chemistry.stackexchange.com/a/7000/9961 $\endgroup$
    – Mithoron
    Jun 11 '16 at 22:40
  • $\begingroup$ Is it? Strictly, it's just $-\log_{10}{\left[\ce{H+}\right]}$, right? Acetic acid may be a bad example, since I would think it wouldn't auto-ionize, but in general, if any solvated proton is present, I would think a $\mathrm{pH}$ could be defined, even if it wasn't particularly useful. $\endgroup$
    – hBy2Py
    Jun 11 '16 at 22:43
  • $\begingroup$ Edited, but it simply doesn't work the same in other situations. $\endgroup$
    – Mithoron
    Jun 11 '16 at 22:46
  • $\begingroup$ @Brian It does auto-ionize, but in pure CH3COOH will [CH3COOH2+] be more important then concentration of acid itself? In what context? $\endgroup$
    – Mithoron
    Jun 11 '16 at 22:53
  • $\begingroup$ H0 function is used is such cases. $\endgroup$
    – Mithoron
    Jun 11 '16 at 22:58
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The IUPAC definition of pH is:

The quantity pH is defined in terms of the activity of hydrogen(1+) ions (hydrogen ions) in solution:

$pH = − lg [a(H^+)] = − lg [m(H^+) γ_m (H^+) / m^⦵]$

where a$(\ce{H+})$ is the activity of hydrogen ion (hydrogen 1+) in aqueous solution, $(\ce{H+})$(aq), $γ_m(\ce{H+})$ is the activity coefficient of $\ce{H+}$(aq) (molality basis) at molality m$(\ce{H+})$, and m$^⦵ = 1$ mol kg $^{−1}$ is the standard molality.

So since the definition specifically refers to "aqueous solution", pH is undefined unless an aqueous solution is being considered.

There would be a p[H+] in pure acetic acid based upon the self dissociation of acetic acid, where [H+] is the concentration of hydrogen ions in acetic acid solution, but this is not pH according to the IUPAC definition.

According to Acid-Base Equilibria in Glacial Acetic Acid. III. Acidity Scale. Potentiometric Determination of Dissociation Constants of Acids, Bases and Salts J. Am. Chem. Soc., 1956, vol. 78, pages 2974–2979:

the autoprotolysis constant of acetic acid is calculated to be $3.5 \times 10^{-15}$ (pK = 14.45)

Therefore p[H+] = 7.2 for pure acetic acid.

This value is not a measure of acidity, but simply the concentration of solvated hydrogen ions in pure acetic acid.

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