The Hammett acidity function is a measure of acidity that is used for very concentrated solutions of strong acids, including superacids. In such solutions, simple approximations such as the HendersonHasselbalch equation are no longer valid due to the variations of the activity coefficients in highly concentrated solutions. The Hammett acidity function is used in fields such as physical organic chemistry for the study of acidcatalyzed reactions, because some of these reactions use acids in very high concentrations, or even neat (pure).^{[1]}
The Hammett acidity function, H_{0}, is used as a pH surrogate. It is defined as
where a is the activity, and γ are the activity coefficients of a base B and its conjugate acid BH^{+}. H_{0} can be calculated using an equation analogous to the HendersonHasselbalch equation:
where pK_{BH+} is −log(K) for the dissociation of BH^{+}. By using bases with very negative pK_{BH+} values, the H_{0} scale may be extended to negative values. Hammett originally used a series of anilines with electronwithdrawing groups for the bases.^{[1]}
On this scale, pure H_{2}SO_{4} (18.4 M) has a H_{0} value of −12, and pyrosulfuric acid has H_{0} ~ −15.^{[2]} Take note that the Hammett acidity function clearly avoids water in its equation. It is a generalization of the pH scale—in a dilute aqueous solution (where B is H_{2}O), pH is very nearly equal to H_{0}. By using a solventindependent quantitative measure of acidity, the implications of the leveling effect are eliminated, and it becomes possible to directly compare the acidities of different substances (e.g. using pK_{a}, HF is weaker than HCl in water but stronger than HCl in glacial acetic acid; however, pure HF is "stronger" than HCl because the H_{0} of pure HF is higher than that of pure HCl.)
H_{0} for some concentrated acids:
For mixtures (e.g., partly diluted acids in water), the acidity function depends on the composition of the mixture and has to be determined empirically. Graphs of H_{0} vs mole fraction can be found in the literature for many acids.^{[1]}
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.^{[1]}
