Hammett equation ionization

The numerical values of the terms a and p are defined by specifying the ionization of benzoic acids as the standard reaction to which the reaction constant p = 1 is assigned. The substituent constant, a, can then be determined for a series of substituent groups by measurement of the acid dissociation constant of the substituted benzoic acids. The a values so defined are used in the correlation of other reaction series, and the p values of the reactions are thus determined. The relationship between Eqs. (4.12) and (4.14) is evident when the Hammett equation is expressed in terms of fiee energy. For the standard reaction, o%K/Kq = ap. Thus,... 

The classic example, and still the most useful one, of a LFER is the Hammett equation, which correlates rates and equilibria of many side-chain reactions of meta- and para-substituted aromatic compounds. The standard reaction is the aqueous ionization equilibrium at 25°C of meta- and para-substituted benzoic acids. 

Reactions that occur with the development of an electron deficiency, such as aromatic electrophilic substitutions, are best correlated by substituent constants based on a more appropriate defining reaction than the ionization of benzoic acids. Brown and Okamoto adopted the rates of solvolysis of substituted phenyldimeth-ylcarbinyl chlorides (r-cumyl chlorides) in 90% aqueous acetone at 25°C to define electrophilic substituent constants symbolized o-. Their procedure was to establish a conventional Hammett plot of log (.k/k°) against (t for 16 /wcra-substituted r-cumyl chlorides, because meta substituents cannot undergo significant direct resonance interaction with the reaction site. The resulting p value of —4.54 was then used in a modified Hammett equation. 

The first application of the Hammett equation to a heterocyclic system is contained in Hammett s original work, where his reaction series 9 is the ionization of 5-substituted 2-furoic acids. In addition, one of Hammett s original substituents is the CH202-group, i.e., the cr-value which compares the reactivity of... 

Jaffe (1953)52 showed that while many rate or equilibrium data conform well to the Hammett equation (as indicated by the correlation coefficient), many such data are outside the scope of the equation in its original form and mode of application. Deviations are commonly shown by para-substituents with considerable + Rot — R effect53. Hammett himself found that p-NOz (+ R) showed deviations in the correlation of reactions of anilines or phenols. The deviations were systematic in that a a value of ca. 1.27 seemed to apply, compared with 0.78 based on the ionization of p-nitrobenzoic acid. Other examples were soon discovered and it became conventional to treat them similarly in terms of a duality of substituent constants . 

Miller226 applied the Hammett equation to the rate constants for the reaction of 4-substituted l-chloro-2-nitrobenzenes with OMe in methanol at 50°C. a values (denoted ct in accordance with the practice briefly in vogue at that time, 1956) were used for + R substituents, and S02Me conformed well at a a value of 1.04952. Act value of 1.117 for S02Ph was derived from the Hammett plot, intermediate between the values based on phenol and anilinium ionizations by Szmant and Suld88 at about the same time. 

Certain physical properties of substituted ethylenes may be correlated with the extended Hammett equation. Included in this category are dipole moments and ionization potentials. 

A number of correlations of ionization potentials for substituted benzenes (40-42), benzyl (43), phenoxy (44), and alkyl (45) radicals and substituted pyridines (46) with the simple Hammett equation have been reported. Charton (47) has studied the application of the extended Hammett equation to substituted ethylenes and carbonyl compounds. The sets studied here are reported in Table II (sets 2-10 and 2-11). Results of the correlations are set forth in Table 111. The results obtained are much improved by the exclusion of the values for X = C2 H3, Ac, F, H and OAc from set 2-10 (set 2-lOA) and the value for X = H from set 2-11 (set 2-11 A). The composition of the electrical effect corresponds to that found for the Op constants as is shown by the pR values reported in Table IV. 

Ionization constants of czs-3-substituted acrylic acids have been correlated with the Hammett equation by Hogeveen (58) and by Charton (60). Charton has correlated ionization constants for a number of other c/s-vinylene sets with the Hammett equation (60). Charton and Charton have correlated some cw-vinylene sets with the extended Hammett equation [eq. (2)] (73). Sufficient data are available for twelve sets of cis-vinylene equilibria, of which four sets represent ionization constants of hydroxy compounds (sets 12-1 to 12-4) and eight sets represent ionization constants of carboxylic acids (sets 12-5 to 12-12). All sets have been correlated with eq. (24) and eq. (2). Sets studied are reported in Table XII. Results of the correlations are reported in Table XIII. Sets designated A were correlated with eq. (24), sets designated B were correlated with eq. (2). In the case of the second ionization constant of 2,3,5,6-tetrahydroxy-l,4-benzoquinone (set 12-3), it is uncertain which hydroxyl group ionizes therefore, the value for X = OH was excluded from the correlation. All of the sets 12-1 to 12-4 gave significant correlations with both eq. (24) and eq. (2),... 

Values of pKa for substituted amidines were correlated with the Hammett equation by Charton (190). Data are available for one set of substituted amidinium ions and one set of C-substituted-N-phenylamidinium ions. The sets studied are shown in Table XXX. Results of the correlations are set forth in Table XXXI and values of pj in Table XXXII. Significant correlations were obtained for both sets. In the case of the ionization of N-phenyl amidinium ions, the possibility of tautomerism exists, Charton (170) has presented arguments which suggest that the predominant tautomer is 30. The localized effect is predominant in both of the sets of amidinium ions studied. 

Data are extant in the literature for two other sets of ethynylene compounds. The sets studied are reported in Table XXXIII. Results of correlation are set forth in Table XXXIV and values of Pr in Table XXXV. The ionization constants of 3-substituted propiolic acids, which were first correlated with the Hammett equation by Charton (18), gave an excellent correlation with eq. (2) (set 22-27-1). The results are very much improved by the elimination of the value for X = H (set 33-27-2). The composition of the electrical effect corresponds approximately to that of the Op constants. The magnitude of the electrical effect is significantly less than that observed for the rrans-3-substituted acrylic acids. 

The Hammett equation is the best-known and most widely studied of the various linear free energy relations for correlating reaction rate and equilibrium constant data. It was first proposed to correlate the rate constants and equilibrium constants for the side chain reactions of para and meta substituted benzene derivatives. Hammett (37-39) noted that for a large number of reactions of these compounds plots of log k (or log K) for one reaction versus log k (or log K) for a second reaction of the corresponding member of a series of such derivatives was reasonably linear. Figure 7.5 is a plot of this type involving the ionization constants for phenylacetic acid derivatives and for benzoic acid derivatives. The point labeled p-Cl has for its ordinate log Ka for p-chlorophenylacetic acid and for its abscissa log Ka for p-chloroben-zoic acid. The points approximate a straight line, which can be expressed as... 

By the use of a model reaction (ionization of benzoic acids), die ability of a substituent to modify die electron-donating or electron-withdrawing ability of die phenyl group and tiius influence tiiat reaction can be defined quantitatively by the Hammett equation,... 

These data were plotted according to the Hammett equation to give the plot in Figure 5.17. The first thing to note is that the Hammett plot is linear. The linearity of die plot implies that the substituent constants determined for the ionization of... 

This kind of procedure, i. e. empirical estimation of solvent polarity with the aid of actual chemical or physical reference processes, is very common in chemistry. The well-known Hammett equation for the calculation of substituent effects on reaction rates and chemical equilibria, was introduced in 1937 by Hammett using the ionization of meta-ox /iflra-substituted benzoic acids in water at 25 °C as a reference process in much the same way [10]. Usually, the functional relationships between substituent or solvent parameters and various substituent- or solvent-dependent processes take the form of a linear Gibbs energy relationship, frequently still referred to as a linear free-energy (LFE) relationship [11-15, 125-127]. 

In Eq. (7-14), k and ko are the specific rate constants for the SnI solvolysis of RX (in this case t-BuCl) in a given solvent and in the standard solvent, respectively, m is the sensitivity of the specific rate of solvolysis of RX to changes in the solvent ionizing power (T), T is a parameter characteristic of the given solvent, and c is the intercept (zero for an ideally behaved solvolysis). Eq. (7-14) is expected to be applicable to reactions very similar to the standard reaction, that is, SnI substitutions. The similarity between Y and m of Eq. (7-14), and a and g of the Hammett equation (7-6) is obvious. Y values are known for some pure, mainly protic solvents and for various binary mixtures of organic solvents with water or a second organic solvent [35, 36]. Typical Y values are... 

The numerous reactions and physical properties that can be correlated with electronic substituent constants suggest that they reflect a basic mechanism for the effect of the substituent on the reaction or the property. Many reactions were correlated by the Hammett equation, such as electrophilic (4, 31, 32, 33), nucleophilic (4, 34) and radical (35, 36, 37). Spectroscopic properties, such as infrared and ultraviolet absorption frequencies and intensities (38). nuclear magnetic resonance shifts of various nuclei, e.g., -H, F, (39), and mass spectroscopic ionization... 

Historically, QSRR has its foundation in the efforts of physical organic chemists who rationalize solute substituent effects on reaction rates and equilibria. The most notorious of all, the Hammett equation (9), inaugurates the linear free energy relationships (LFER), where the logarithm of the reaction equilibrium constant, K, is a linear function of the substituent constant (o), an arbitrarily derived parameter based on the ionization of benzoic acid derivatives in water, as follows ... 

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