Hr acidity function

Compensation is not expected to be 100% effective as the two equilibria are based on two different acidity functions (HR and H0i respectively). 

The UV absorption spectra of sodium nitrite in aqueous solutions of sulfuric and perchloric acids were recorded by Seel and Winkler (1960) and by Bayliss et al. (1963). The absorption band at 250 nm is due either to the nitrosoacidium ion or to the nitrosyl ion. From the absorbancy of this band the equilibrium concentrations of HNO2 and NO or H20 —NO were calculated over the acid concentration ranges 0-100% H2S04 (by weight) and 0-72% HC104 (by weight). For both solvent systems the concentrations determined for the two (or three) equilibrium species correlate with the acidity function HR. This acidity function is defined for protonation-dehydration processes, and it is usually measured using triarylcarbinol indicators in the equilibrium shown in Scheme 3-15 (see Deno et al., 1955 Cox and Yates, 1983). 

The formation of the nitrosonium ion follows the acidity function HR and the conversion of nitrous acid to nitrosonium bisulphate is essentially complete in ca. 65% sulphuric acid. At these high acidities, there is no reason to doubt that the nitrosonium ion is the effective electrophile. The problem arises with studies at lower acidities for most of the kinetic evidence for equation (19) relates to feebly acidic media. 

According to Eq. (8), the pATr value equals the acidity function (Hr) of that solution, in which equal concentrations of carbocation and nonionized alcohol coexist. The acidity function Hr has been derived by Deno, studying equilibria as described by Eq. (7) it approaches pH in dilute aqueous solution. For the reasons discussed above, the application of this method is limited and has been used mostly to characterize aryl-substituted carbocations (Scheme 4) which do not react with their precursor alcohols. 

The data in Table 3 allow consideration of the importance of solvation of the free base. The acidity functions HR and Hc are defined for ionization of triarylcarbinols and of diarylethylenes, respectively. The conjugate acid is, in both cases, the arylcarbonium ion. The ratio 7xh+/Tx is different since the solvation requirements of the free bases are different, with the carbinol being obviously more... 

These relationships however, are not observed and protonation of olefins defines a new acidity function. Hr, viz-... 

Clearly, the previously observed acidity dependencies cannot be satisfactorily diagnostic of the nitrousacidium ion being the electrophile, and, significantly perhaps, the rate of N-nitrosation of benzamide follows the hR acidity function, which indicates that the nitrosonium ion is the electrophile122. 

De la Mare and Hilton198 measured the rates at 25 °C of bromination of benzene, benzoic acid, phthalic acid, 2-nitrobenzoic acid, trimethylanilinium perchlorate and nitrobenzene by hypobromous acid with sulphuric or perchloric acids as catalysts, in some cases in aqueous dioxan, in an attempt to discover if Br+ or H2OBr+ was the appropriate brominating species since the logarithm of the rates should then follow the acidity functions H0 or HR (J0) respectively. The results, however, were inconclusive and relative rates of bromination were determined (see Table 53). 

It was soon realized that there are problems with this approach.24,25 Log ionization ratios for weak bases that are not primary aromatic amines, while linear in H0, do not give the unit slope required by equation (8). This soon led to many other acidity functions, defined for other types of weak base, HA for amides,24 Hq for tertiary aromatic amines,25 C0 or HR for carbocations,26,27 and so on. In a recent review of addity functions,28 28 different ones were listed... 

In organic solvents the acidity functions H corresponding to hydrogen dissociation from neutral indicator acids were reported for solutions of alkali metal alkoxides in various alcohols (2), using nitroanilines (21), aminobenzenecarboxylic acids (22), or indols (23) as indicators. For addition reactions of methoxide and ethoxide ions to neutral indicator acids, acidity functions J (also denoted as Hr) based on use of nitrobenzenes (21) and a-cyanostilbenes (18) as indicators in methanol and dimethylsulfoxide-methanol and -ethanol mixtures were reported. Recently (24) the acidity function J- (denoted as Jm) was derived for methoxide ion solutions in methanol using substituted benzaldehydes as indicators. These scales involve arbitrary choice of water as the solvent for determination of the dissociation constant of the anchoring acid. 

There are other instances, however, where unusually large extents of elimination are encountered which cannot be explained in this way. An example is provided by a study of the nucleophilic and elimination reactions of the dipentamethyl benzhydryl cation 69.247 Comparisons of pA"R values (from extrapolations based on the HR acidity function) with those of the unmethylated and partially methylated benzhydryl cations shown below, indicate that methylation cumulatively stabilizes the cation relative to the alcohol (possibly in part because the latter is destabilized by steric congestion). 

The corresponding acidity function described as HR is then written in Eq. (1.18). 

Hr function.53 546 A better correlation, up to nearly 89% sulphuric acid, is obtained by comparing the results at 25 °C with the acidity function — (i/ + log aHa0). 31>42a>43a In these comparisons a straight line of approximately unit slope is obtained (fig. 2.4), although for the nitration of benzene in acidities greater than 68% sulphuric acid,57 the slope becomes 1-20 (fig. 2.5). 

The correlations of rates with acidity functions provide a convenient means of treating results, and their uses will frequently be illustrated. However, their status is empirical, for whilst the acidity dependence of nitration becomes less steep with increasing temperature, the slope of —Hr increases.53 57 . 

The Hr function is also known as the C function (22) and is closely related to the J function (23) ancT the well known Hammett s acidity°function (2JT-It is reasonable to assume... 

Although the theoretical values for the slopes are often obtained from kinetic data at room temperature, this is not the case (and the recalculation of the free-base rate coefficients also fails) for data obtained at higher temperature. This discrepancy may be attributed to the variation of acidity function with temperature. In a redetermination of the variation of HR... 

For A-Se 2 reactions, log k has been found to be linearly dependent on H0 in most cases [20, 85—87] even though the protonation equilibria of some of the substrates depend on H R if carbon protonation takes place [85]. The acidity function H r is related to the function Hr which can be determined with the aid of triarylcarbinols as indicators [88], according to the equations... 

Figure 10. Cumulative acidity in micromoles per square meter on silica-20 (A), silica-40 silica-60 (%), silica-100 (V), and silica-200 (O) as a function of the acidity strength Hr. (Reproduced with permission from reference 54.

Snyder HR, Strohmayer HF, Mooney RA (1958) The insecticidal principles of Haplophyton cimicidum. III. The nature of the acidic function of haplophytine. J Am Chem Soc 80 3708-3710... 

For a large number of organic functionalities, significant protonation is only achieved in more concentrated acid solutions e.g. alcohols, ethers, ketones, esters, sulfides, sulfoxides). More concentrated acid solutions cannot be treated as ideal, and Ka values cannot be measured in terms of concentrations as in eqn (3.4). In strong acid media, the significantly decreased water concentration results in additional solvent effects on pA"a that are not accounted for by the pH scale. To account for acid-base behaviour in strong acid media, a number of acidity functions have been established. One of the earliest examples was the Hammett Ho acidity function based on a pairwise comparison of spectrophotometric changes in a series of aniline bases in concentrated acid solution. However, this scale could only be applied for structurally similar bases with similar protonation behaviour. Several other acidity functions have been proposed for other classes of bases such as the Hr acidity function for the ionisation of alcohols. As recently reviewed by Scorrano and More O Ferrall, later treatments by Bunnett and... 

Ladenheim, H., Bender, M. L. (1960). Acylium Ion Formation in the Reactions if Carboxylic Acid Derivatives. /. Application of the HR Acidity Function to the Diazotization ofBenzamide in Sulfuric Acid. Journal of the American Chemical Society, 82, 1895-1900. 

Hr is an acidity function which provides a reference point for the pK + scale. The more positive the pK + value, the more stable is the carbonium ion (Table 9.2). The property of stabilizing a-carbonium ions is also shared by similar organomet-allic groups. Their effectiveness lies in the order... 

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