acid base - 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?

Answer

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.