# Is there any notion of pH out of solution?

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?

• pH is usually for more or less diluted water solutions. But here is some insight chemistry.stackexchange.com/a/7000/9961 Jun 11 '16 at 22:40
• 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. Jun 11 '16 at 22:43
• Edited, but it simply doesn't work the same in other situations. Jun 11 '16 at 22:46
• @Brian It does auto-ionize, but in pure CH3COOH will [CH3COOH2+] be more important then concentration of acid itself? In what context? Jun 11 '16 at 22:53
• H0 function is used is such cases. Jun 11 '16 at 22:58

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.