TheHammett acidity function (H0) is a measure of acidity that is used for very concentrated solutions of strongacids, includingsuperacids. It was proposed by the physical organic chemistLouis Plack Hammett[1][2] and is the best-knownacidity function used to extend the measure ofBrønsted–Lowry acidity beyond the diluteaqueous solutions for which thepH scale is useful.
In highly concentrated solutions, simple approximations such as theHenderson–Hasselbalch equation are no longer valid due to the variations of theactivity coefficients. The Hammett acidity function is used in fields such asphysical organic chemistry for the study ofacid-catalyzed reactions, because some of these reactions use acids in very high concentrations, or even neat (pure).[3]
The Hammett acidity function,H0, can replace thepH in concentrated solutions. It is defined using an equation[4][5][6] analogous to the Henderson–Hasselbalch equation:
where log(x) is thecommon logarithm of x, and pKBH+ is −log(K) for the dissociation of BH+, which is theconjugate acid of a very weak base B, with a very negative pKBH+. In this way, it is rather as if the pH scale has been extended to very negative values. Hammett originally used a series ofanilines withelectron-withdrawing groups for the bases.[3]
Hammett also pointed out the equivalent form
wherea is the activity, and theγ are thermodynamicactivity coefficients. In dilute aqueous solution (pH 0–14) the predominant acid species is H3O+ and the activity coefficients are close to unity, soH0 is approximately equal to the pH. However, beyond this pH range, the effective hydrogen-ion activity changes much more rapidly than the concentration.[4] This is often due to changes in the nature of the acid species; for example in concentratedsulfuric acid, the predominant acid species ("H+") is not H3O+ but rather H3SO4+[citation needed], which is a much stronger acid. The valueH0 = −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 inideal solution). Instead it means that the acid species present (H3SO4+) has aprotonating 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 knownacidity function, other acidity functions have been developed by authors such as Arnett, Cox, Katrizky, Yates, and Stevens.[3]
On this scale, pureH2SO4 (18.4M) has aH0 value of −12, andpyrosulfuric acid hasH0 ~ −15.[7] 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 H2O), pH is very nearly equal toH0. By using a solvent-independent quantitative measure of acidity, the implications of theleveling effect are eliminated, and it becomes possible to directly compare the acidities of different substances (e.g. using pKa, HF is weaker than HCl or H2SO4 in water but stronger than HCl in glacial acetic acid.[8][9])
| Name | H0 | Ref |
|---|---|---|
| Trifluoroacetic acid | −2.7 | [10] |
| Phosphoric acid | −4.66 | [11] |
| Nitric acid | −6.3 | [12] |
| Methanesulfonic acid | −7.86 | [11] |
| Sulfuric acid | −11.93 | [13] |
| Perchloric acid | −13 | [14] |
| Triflic acid | −13.7 | [10] |
| Chlorosulfuric acid | −13.79 | [13] |
| Oleum (50 mole% SO3) | −14.44 | [13] |
| Fluorosulfuric acid | −15.07 | [13] |
| Hydrogen fluoride | −15.1 | [15] |
| Magic acid (1:1 FSO3H-SbF5) | −23.0 | [16] |
| Fluoroantimonic acid (1:1 HF-SbF5) | −28 | [16] |
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 ofH0 vsmole fraction can be found in the literature for many acids.[3]
