# Hammett acidity function

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 In such solutions, simple approximations such as the Henderson-Hasselbalch equation are no longer valid due to the variations of the activity coefficients in highly concentrated solutions.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 acid-catalyzed 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

<math>H_{0} = -\log h_0 = -\log \left ( a_{H_3O^+} \frac{\gamma_B}{\gamma_{BH^+}} \right )</math>

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 Henderson-Hasselbalch equation:

<math>H_{0} = \mbox{p}K_{BH^+} + \log \frac{[B]}{[BH^+]}</math>

where p*K*_{BH+} is −log(K) for the dissociation of BH^{+}. By using bases with very negative p*K*_{BH+} values, the *H*_{0} scale may be extended to negative values. Hammett originally used a series of anilines with electron-withdrawing 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 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 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.)^{[citation needed]}

H_{0} for some concentrated acids:^{[citation needed]}

- Fluoroantimonic acid (1990): −31.3
- Magic acid (1974): −19.2
- Carborane superacid (1969): −18.0
- Fluorosulfuric acid (1944): −15.1
- Triflic acid (1940): −14.9
- Sulfuric acid −12.0

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]}

## References

- ↑
^{1.0}^{1.1}^{1.2}^{1.3}Gerrylynn K. Roberts, Colin Archibald Russell.*Chemical History: Reviews of the Recent Literature*. Royal Society of Chemistry,**2005**. ISBN 0854044647. - ↑ What do you mean pH = -1? Super Acids