Hammett Acidity Function - Definition

Definition

The Hammett acidity function, H₀, can replace the pH in concentrated solutions. It is defined using an equation analogous to the Henderson-Hasselbalch equation:

where lg(x) = log₁₀(x) is the common logarithm of x, and pK_BH+ is −lg(K) for the dissociation of BH+, which is the conjugate acid of a very weak base B, with a very negative pK_BH+. In this way, it is rather as if the pH scale has been extended to very negative values. Hammett originally used a series of anilines with electron-withdrawing groups for the bases.

Hammett also pointed out the equivalent form

where a is the activity, and the γ are thermodynamic activity coefficients. In dilute aqueous solution (pH 0-14) the predominant acid species is H₃O+ and the activity coefficients are close to unity, so H₀ is approximately equal to the pH. However beyond this pH range, the effective hydrogen-ion activity changes much more rapidly than the concentration. This is often due to changes in the nature of the acid species; for example in concentrated sulfuric acid, the predominant acid species ("H+") is not H₃O+ but rather H₃SO₄+ which is a much stronger acid. The value H₀ = -12 for pure sulfuric acid must not be interpreted as pH = -12 (which would imply an impossibly high H₃O+ concentration of 10+12 mol/L in ideal solution). Instead it means that the acid species present (H₃SO₄+) has a protonating ability equivalent to H₃O+ at a fictitious (ideal) concentration of 1012 mol/L, as measured by its ability to protonate weak bases.

Although the Hammett acidity function is the best known acidity function, other acidity functions have been developed by authors such as Arnett, Cox, Katrizky, Yates, and Stevens.