Hammett acidity function

The Hammett acidity function (''H''₀) is a measure of acidity that is used for very concentrated solutions of strong acids, including superacids. It was proposed by the physical organic chemist Louis Plack Hammett and is the best-known acidity function used to extend the measure of Brønsted–Lowry acidity beyond the dilute aqueous solutions for which the pH scale is useful.

In highly concentrated solutions, simple approximations such as the Henderson–Hasselbalch equation are no longer valid due to the variations of the activity coefficients. The Hammett acidity function is used in fields such as physical organic chemistry for the study of acid-catalyzed reactions, because some of these reactions use acids in very high concentrations, or even neat (pure).Gerrylynn K. Roberts, Colin Archibald Russell. ''Chemical History: Reviews of the Recent Literature''. Royal Society of Chemistry, 2005. .

Definition

The Hammett acidity function, ''H''₀, can replace the pH in concentrated solutions. It is defined using an equationWilliam L. Jolly, ''Modern Inorganic Chemistry'' (McGraw-Hill 1984), p.202-3 analogous to the Henderson–Hasselbalch equation:

:$H_ = \mboxK_\ce + \log \frac\ce\ce$

where log(x) is the common logarithm of x, and p''K''_BH⁺ is −log(''K'') for the dissociation of BH⁺, which is the conjugate acid of a very weak base B, with a very negative p''K''_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

:$H_ = -\log \left ( a_\ce \frac \right )$

where 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 ''H''₀ 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 ''H''₀ = −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.

Typical values

On this scale, pure H₂SO₄ (18.4 M) has a ''H''₀ value of −12, and pyrosulfuric acid has ''H''₀ ~ −15. 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 to ''H''₀. By using a solvent-independent 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 p''K''_a, HF is weaker than HCl or H₂SO₄ in water but stronger than HCl in glacial acetic acid.Liang, Jack Joan-Nan
"The Hammett Acidity Function for Hydrofluoric Acid and some related Superacid Systems"
(1976). Open Access Dissertations and Theses. Paper 3850.)

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.

References

{{Chemical equilibria

Acid–base chemistry
Physical organic chemistry
*