The Taft Equation

The Hammett equation is not successful for reactions of aliphatic compounds if the normal cr constants are used. A new scale of substituent constants, labeled cr, was invented to allow the extension of the method to such systems. The difference in the rates of hydrolysis of esters in basic versus acidic solutions is used to define the scale. The transition states are 

Both have the same steric and conjugative effects, but the polar effect is largely absent in the acid-catalyzed reactions. Subtraction of the logarithms of the two relative rates therefore leaves just the polar effect. This is written 

The value of a for the methyl esters was chosen as 2.48, (not 1.00) so that the or values would be similar to the Hammett cr constants. Once established, the or scale can be used for many such reactions. Table 10-3 presents an abbreviated list of or constants.12 

The approach Taft has presented gives rise to an equation that is obviously more powerful than the Hammett relation. It correlates more reactions and can be extended to include steric parameters. It takes the form 

The success of Eqs. (10-13)—(10-14) comes at the price of the inclusion of more adjustables, which inevitably gives a better correlation. The success of these LFERs lies in the fact that these parameters, too, are transferable to an impressively long list of reactions. 

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The application of the Taft equation, derived from the Hammett equation (262)... 

Table III-55 shows the verification of the Taft equation. The result is analogous to that obtained for 3-alkylpyridines.

TABLE m-55. VERIFICATION OF THE TAFT EQUATION FOR THE KINETICS OF OUATERNIZATION OF 5-ALKYLTHIAZOLES (254)... 

Equation (7-51), the Taft equation, provides good correlations for many aliphatic reactions. The scope of this relationship is illustrated by Table 7-10. The reaction constant p has been interpreted along the lines described for the Hammett p values. 

The Hammett equation is not the only LFER." ° Some, like the Hammett equation, correlate structural changes in reactants, but the Grunwald-Winstein relationship (see p. 452) correlates changes in solvent and the Brpnsted relation (see p. 337) relates acidity to catalysis. The Taft equation is a structure-reactivity equation that correlates only field effects. ... 

A large number of modifications and refinements have been made on this equation, the most relevant being those which attempt to separate inductive < j and mesomeric Taft equation. In addition to substituent constants based on reactivity, acidity and the like, a variety of spectroscopically derived constants such as those from... 

In terms of equilibrium constant, the Taft equation is written as... 

In order to gain an insight into the mechanism on the basis of the slope of a Type A correlation requires a more complicated procedure. Consider the Hammett equation. The usual statement that electrophilic reactions exhibit negative slopes and nucleophilic ones positive slopes may not be true, especially when the values of the slopes are low. The correct interpretation has to take the reference process into account, for example, the dissociation equilibrium of substituted benzoic acids at 25°C in water for which the slope was taken, by definition, as unity (p = 1). The precise characterization of the process under study is therefore that it is more or less nucleophilic than the reference process. However, one also must consider the possible influence of temperature on the value of the slope when the catalytic reaction has been studied under elevated temperatures there is disagreement in the literature over the extent of this influence (cf. 20,39). The sign and value of the slope also depend on the solvent. The situation is similar or a little more complex with the Taft equation, in which the separation of the molecule into the substituent, link, and reaction center may be arbitrary and may strongly influence the values of the slopes obtained. This problem has been discussed by Criado (33) with respect to catalytic reactions. 

Fig. 1. Correlation of the rates of primary alcohol dehydration (40) (series 1 from Table II) in the coordinates of the Taft equation (8) for different separations of the reactants molecules into the parts substituent-link-reaction center.

Also other Type B and C series from Table II are consistent with the above elimination mechanisms. The dehydration rate of the alcohols ROH on an acid clay (series 16) increased with the calculated inductive effect of the group R. For the dehydrochlorination of polychloroethanes on basic catalysts (series 20), the rate could be correlated with a quantum-chemical reactivity index, namely the delocalizability of the hydrogen atoms by a nucleophilic attack similar indices for a radical or electrophilic attack on the chlorine atoms did not fit the data. The rates of alkylbenzene cracking on silica-alumina catalysts have been correlated with the enthalpies of formation of the corresponding alkylcarbonium ions (series 24). Similar correlations have been obtained for the dehydrosulfidation of alkanethiols and dialkyl sulfides on silica-alumina (series 36 and 37) in these cases, correlation by the Taft equation is also possible. The rate of cracking of 1,1-diarylethanes increased with the increasing basicity of the reactants (series 33). 

The decrease in hydrogenation rate with increasing size of the alkyl group (Table VI) (93-96) can be correlated by the Taft equation. However, the correlation of the data by Smith and Pennekamp (93) (series 70) using the polar parameter Taft equation is applied that also includes steric constants. Similarly, Kieboom (34) has discussed Yoshida s correlation of series 73 based on main conclusion has been that the data do not allow a clear distinction between steric and polar effects. It seems that both operate in the same direction. Series 72 and 73, in which the rate data have been separated into the rate constants and adsorption coefficients, show opposite trends with the latter parameter. A similar problem has been encountered by Volter, Hermann, and Heise (100) and by Najemnik and Zdrazil (103) in the series of methylbenzenes (Table VII) and is discussed in this connection. 

Positive slopes in partial correlations of small series for which the Taft equation is suitable. For a resonance parameter r = 0.8. 

Some information about structure effects on the rate of dehydrogenation of alcohols to aldehydes and ketones on metals is found in the older literature 129-132) from which it follows that secondary alcohols react more easily than the primary alcohols 129) and that the reactivity decreases with the length of the carbon chain 131). Some series can be correlated by the Taft equation using a constants (Ref. 131, series 103, Cu-Cr203 catalyst, 350°C, four points, slope 18 Ref 132, series 104, Cu catalyst, four points, slope 22). Linear relationships have been used in a systematic way by... 

The oxidative dehydrogenation of secondary alcohols to ketones on iridium at 130°C has been measured by Le Nhu Thanh and Kraus (i-Zi), and the rates have been correlated by the Taft equation [series 112, four reactants of the structure R CH(OH)CH3, slope 4.7]. 

Other examples of linear free energy relationships include the Brpnsted relation, the Grunwald-Winstein relationship, and the Taft equation. See Rho Value... 

Linear-free-energy relationships such as the Hammett and Taft equations [Lowry and Richardson, 1987] have been used to correlate copolymerization behavior with structure, but the approach is limited to considering a series of monomers that are similar in structure. Walling [1957] applied the Hammett equation to copolymerization among various meta- and para-substituted styrenes. The Taft equation in the form... 

The structure of the reactant also influences the orientation, i.e. the ratio of 1- to 2-alkenes in the dehydration of 2-alkanols and the ratio of cis to trans alkenes. Table 4 shows that these ratios can also be correlated by the Taft equation. For the cis/trans ratio, a better fit was obtained with steric Es constants of substituents than with polar constants [127]. 

The relation between the acid strength of the catalysts and the mechanism has also been demonstrated by correlations [55,123] of the reaction parameter, p, of the Taft equation for the dehydration of secondary alcohols on A1203 + NaOH, Zr02, Ti02 and Si02 (see Table 4) with the sensitivity to pyridine poisoning, the heat of adsorption of water and diethylether and the kinetic isotope deuterium effects (Table 3) on the same catalysts (Fig. 5). The parameter p reflects the mechanism being... 

The rate coefficient of deamination increases with the inductive effect of the alkyl group as has been demonstrated by the published kinetic data [152] and their correlation by the Taft equation [125]. This was later... 

A clearer picture emerges from studies of substituent effects on the rate with a single catalyst. A series of alkyl chlorides (C2 to C6) was decomposed on a barium sulphate catalyst [184] and the rate data were correlated by the Taft equation. Large negative values of p were obtained, viz. —34.3 at 220°C and —40.3 at 280°C. Similarly, for a series of three alkyl bromides (ethyl, propyl and isopropyl) on silica—alumina, alumina—... 

Less information is available about the cracking of alkanes. Three sources [212,232,233] confirm that, in the series of straight-chain alkanes, the rate increases with the molecular weight. The data could be correlated by the Taft equation when the molecule was divided into the reaction centre and such substituents as R—CH2—CH3 [125]. The reactivity of hexane isomers was studied at 550°C on an A1203—Si02— Zr02... 

Effects of structure on reactivity have been studied several times. The sulphides are more stable than the thiols [248,250], In both series of thiols and of sulphides, the reactivity increases with the inductive effect of the alkyl group [248,251,252], in accordance with other elimination reactions. A linear relation between the logarithm of the rate coefficient and the enthalpy change on carbonium ion formation from the corresponding alkanes has been observed [248]. As Fig. 9 shows, linear correlation of the same rate data by means of the Taft equation is also possible. 

A quantitative correlation of structural effects of four esters and four alcohols in the vapour phase transesterification on a macroreticular ion exchanger at 120°C was made using the Taft equation [441]. The authors found that rate coefficients [from eqn. (27)] yielded better correlation with steric (Es) than with polar (a ) parameters, while there was no significant difference between the correlations of the adsorption coefficients of alcohols, Kb, with both parameters. The correlations with Es yielded the slopes 1.4 and 0.6 for the reactivity of the esters and the alcohols, respectively, and —0.4 for the adsorptivity of the alcohols. The observed... 

Nucleophilic substitutions of cycloalkylmethyl arenesulfonates C H2n-iCH20S02C6H4Z with anilines XCgH4NH2 in methanol at 65 °C have been studied.140 The reactivity order (given Z and X) n = 4>6>7>5 largely reflects the influence on steric effects of ling size, but the behaviour for n = 5 is anomalous. Application of the Taft equation in a form involving both polar and steric terms suggests that the retardation for n = 5 may be due to an enhanced polar (p cr ) term. 

Kinetic data for the HBr elimination of secondary alkyl bromide, i.e., a-substituted ethyl bromide, in the gas phase are shown in Table 11121. Contrary to primary -substituted ethyl bromides, the rate constants for these secondary halides could not be correlated by the use of the Taft equation. This limitation arised because the corresponding olefin products underwent rapid isomerization with HBr gas acting as a catalyst. The lack of a kinetic control prevented evaluation of the factor by which the Z substituent in ZCH(Br)CH3 affected the direction of elimination. However, as the electron-releasing effect of Z increases (Table 11), a small but significant increase in the overall rate constant was obtained. In view of the catalysis by HBr in the isomerization process of the olefin products, a general mechanism for this process was suggested (equation 40). 

The Hammett equation describes reasonably well the inductive and mesomeric influences on the rate constant when there are substituent changes in meta- and para-substituted aromatic compounds. Ort/io-substituted aromatics and substituted aliphatic compounds can be represented by the Taft equation [81, 83]... 

Taft [109] postulated that the rate of aliphatic ester hydrolysis is a function of substituent type. Using methyl as a standard substituent, he compared, for example, the effects of larger alkyls, and interpreted the results by means of two constants characterizing the steric and polar behaviour of the alkyls. In copolymerization theory, the Taft equation was used many times to describe the relative reactivities (See Chap. 5, Sect. 5.2) in homologous polymer series... 

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