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| {{Acids and bases}}
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| The '''Hammett acidity function''' (H<sub>0</sub>) is a measure of acidity that is used for very concentrated solutions of strong [[acid]]s, including [[superacid]]s. It was proposed by the physical organic chemist [[Louis Plack Hammett]]<ref>L.P. Hammett and A.J. Deyrup (1932) J. Am. Chem. Soc. 54, 2721</ref><ref>L.P. Hammett (1940). Physical Organic Chemistry. (McGraw-Hill)</ref> 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.
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| In highly concentrated solutions, simple approximations such as the [[Henderson-Hasselbalch equation]] are no longer valid due to the variations of the [[activity coefficient]]s. The Hammett acidity function is used in fields such as [[physical organic chemistry]] for the study of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).<ref name=poc>Gerrylynn K. Roberts, Colin Archibald Russell. ''Chemical History: Reviews of the Recent Literature''. Royal Society of Chemistry, '''2005'''. ISBN 0-85404-464-7.</ref>
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| ==Definition==
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| The Hammett acidity function, H<sub>0</sub>, can replace the [[pH]] in concentrated solutions. It is defined using an equation<ref name=Jolly>William L. Jolly, "Modern Inorganic Chemistry" (McGraw-Hill 1984), p.202-3</ref><ref>F.A. Cotton and G. Wilkinson, "Advanced Inorganic Chemistry" (5th edition, Wiley-Interscience 1988), p.107-9</ref><ref>G.L. Miessler and D.A. Tarr, "Inorganic Chemistry" (2nd edition, Prentice-Hall 1999), p.170-1</ref> analogous to the Henderson-Hasselbalch equation:
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| :<math>H_{0} = \mbox{p}K_{BH^+} + \log \frac{[B]}{[BH^+]}</math>
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| where log(x) is the [[common logarithm]] of x, and p''K''<sub>BH<sup>+</sup></sub> is −log(K) for the dissociation of BH<sup>+</sup>, which is the [[conjugate acid]] of a very weak base B, with a very negative p''K''<sub>BH<sup>+</sup></sub>. In this way, it is rather as if the pH scale has been extended to very negative values. Hammett originally used a series of [[aniline]]s with [[electron-withdrawing group]]s for the bases.<ref name=poc/>
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| Hammett also pointed out the equivalent form
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| :<math>H_{0} = -\log \left ( a_{H^+} \frac{\gamma_B}{\gamma_{BH^+}} \right )</math>
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| where ''a'' is the activity, and the γ are thermodynamic [[activity coefficients]]. In dilute aqueous solution (pH 0-14) the predominant acid species is H<sub>3</sub>O<sup>+</sup> and the activity coefficients are close to unity, so H<sub>0</sub> is approximately equal to the pH. However beyond this pH range, the effective hydrogen-ion activity changes much more rapidly than the concentration.<ref name=Jolly/> 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 H<sub>3</sub>O<sup>+</sup> but rather H<sub>3</sub>SO<sub>4</sub><sup>+</sup> which is a much stronger acid. The value H<sub>0</sub> = -12 for pure sulfuric acid must not be interpreted as pH = -12 (which would imply an impossibly high H<sub>3</sub>O<sup>+</sup> concentration of 10<sup>+12</sup> mol/L in ideal solution). Instead it means that the acid species present (H<sub>3</sub>SO<sub>4</sub><sup>+</sup>) has a protonating ability equivalent to H<sub>3</sub>O<sup>+</sup> at a fictitious (ideal) concentration of 10<sup>12</sup> mol/L, as measured by its ability to protonate weak bases.
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| 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.<ref name=poc/>
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| ==Typical values==
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| On this scale, pure [[sulfuric acid|H<sub>2</sub>SO<sub>4</sub>]] (18.4 [[Concentration#Molarity|M]]) has a ''H''<sub>0</sub> value of −12, and [[pyrosulfuric acid]] has ''H''<sub>0</sub> ~ −15.<ref>[http://www.scienceinafrica.co.za/2002/august/ph.htm What do you mean pH = -1? Super Acids<!-- Bot generated title -->]</ref> 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<sub>2</sub>O), pH is very nearly equal to ''H''<sub>0</sub>. 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''<sub>a</sub>, HF is weaker than HCl or H<sub>2</sub>SO<sub>4</sub> in water but stronger than HCl in glacial acetic acid; and pure HF is "stronger" than H<sub>2</sub>SO<sub>4</sub> because the ''H''<sub>0</sub> of pure HF is higher than that of pure H<sub>2</sub>SO<sub>4</sub>.<ref>"The Hammett Acidity Function H<sub>0</sub> for Hydrofluoric Acid Solutions." Herbert H. Hyman, Martin Kilpatrick, Joseph J. Katz, J. Am. Chem. Soc., 1957, 79 (14), pp 3668–3671 {{doi|10.1021/ja01571a016}} http://pubs.acs.org/doi/abs/10.1021/ja01571a016</ref><ref>Liang, Jack Joan-Nan, "The Hammett Acidity Function for Hydrofluoric Acid and some related Superacid Systems" (1976). Open Access Dissertations and Theses. Paper 3850. http://digitalcommons.mcmaster.ca/opendissertations/3850</ref>)
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| H<sub>0</sub> for some concentrated acids:{{Citation needed|date=November 2007}}
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| * [[Fluoroantimonic acid]] (1990): −31.3
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| * [[Magic acid]] (1974): −19.2
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| * [[Carborane superacid]] (1969): −18.0
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| * [[Fluorosulfuric acid]] (1944): −15.1
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| * [[Triflic acid]] (1940): −14.1
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| * [[Chlorosulfuric acid|Chlorosulfuric Acid]] (1978): -12.78 <ref>The Chemistry of Nonaqueous Solvents VB: Acid and Aprotic Solvents Ed J.J. Lagowski, pp139, Academic Press, London, 1978</ref>
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| * [[Sulfuric acid|Sulfuric acid:]] −12.0
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| 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<sub>0</sub> vs [[mole fraction]] can be found in the literature for many acids.<ref name=poc/>
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| ==References==
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| <references />
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| {{Chemical equilibria}}
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| [[Category:Acid-base chemistry]]
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| [[Category:Physical organic chemistry]]
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| [[Category:Superacids|*]]
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