Taft-Pavelich equation

The hydrolysis/alcoholysis of (309 R = Pr", Bu, allyl, propargyl) with various alcohols and water caused only a slight difference in the heat of activation for R but, for a fixed R die variation was much greater. The kinetics could be described by a Taft-Pavelich equation.283... 

The data fit the Taft-Pavelich equations where the polar effect (p CT ) is constant. 

These speculations concerning the reaction mechanism resulted in four forms of the Taft equation differing in the procedure used in the calculation of polar and steric constants. Correlation analysis has revealed (78, 79) that kinetic data may be correlated in a single manner, namely, by employing the Taft-Pavelich equation in the form... 

Fig. 1. Correlation of the rate data by means of the reduced Taft-Pavelich equation 1, 1-hexene 2, l-hcptene 3, 1-octene 4, 3,3-dimethyl-l-butene 5, 4-methyl-1-pentene 6, 4,4-dimethyl-1-pentene 7, 2,3-dimethyl-1-butene 8, tran.v-3-heptene 9, zrani -4-nonene 10, (rani-4-methyl-2-pentene 11, 2-methyl-1-hexene 12, trflni-2-hexene 13, 2-methyl-2-hexene 14, 2,4-dimethyl-2-pentene 15, 2,3-dimethyl-2-butene.

In the discussed series (77) of hydrogenated compounds the reaction rate and relative adsorptivity of substrates in most solvents were affected to a comparable degree by steric and polar influences. Negative values of the parameter p and positive values of the parameter 8, were obtained in most cases in the correlation of the reaction rates by the Taft-Pavelich equation, while correlation of the relative adsorption coefficients gave opposite results. This can be seen as an example of an interesting compensation of the kinetic and adsorption terms. 

The measured data also were used (700) in a quantitative representation of the effect of structure on the reactivity and adsorptivity of substrates by means of the Taft-Pavelich equation (22). The adsorption data suffered from a larger scatter than the rate data. No substrate or substituent could be detected that would fail to satisfy completely the correlation equations. In the correlation of the initial reaction rates and relative adsorption coefficients the parameter p was negative, while the parameter S was positive. In correlations of the reaction rates obtained by the hydrogenation of a similar series of substrates on the same catalyst in a number of solvents, the parameters p and had the same sign as in the hydrogenation in solvent-free systems, while in the correlation of the adsorption coefficients the signs of the parameters p and in systems with solvents were opposite to those in solvent-free systems. This clearly indicates that solvents considerably affect the influence of the structure of substrates on their reactivity. 

The rate of chemical reactions carried out under the same conditions is affected by the structure of substrates and by the properties of solvents. Assuming the validity of the Hammett (similarly, of the Taft and Taft-Pavelich) equation expressing the effect of the structure of substrates on their reactivity in each solvent... 

Equation (31) expresses the dependence of the relative rate (equilibrium) constant on the properties of the solvent characterized by the parameters Ap and Sp. The parameter Rp is proportional to the differences between the relative Gibbs free energies for the nth and sth solvent of the given and standard substrates. The parameter Sp characterizes the effect of a change of the substrate on the rate constant of the substrate with a standard substituent. In the Hammett equation this substituent is represented by hydrogen for which a was definitionally put equal to zero, while in the Taft and Taft-Pavelich equations methyl is used as the standard substituent [a = = 0). 

The condition that is necessary and sufficient for the validity of Eq. (31) is the validity of the Hammett (Taft, Taft-Pavelich) equation with the same values of the constants ff(a, of the respective substituents in each solvent. The equation is then independent of the reaction mechanism in each solvent, but the mechanism must be the same for the whole model series of substrates. 

Similar relations are obtained using the Taft or Taft-Pavelich equations (cf. Table V). In these equations, the solvent is characterized by two or three parameters. 

The factor 2.48 puts a on the same scale as Hammett s er, and the k0 values are rate constants for acid and base hydrolysis of acetic acid esters (i.e., R is a methyl group in the reference compound). Usually R is an ethyl or methyl group, but in many cases the rate constants do not depend on the nature of R. Equation 8 is based on the fact that acid hydrolysis rates of substituted benzoic acid esters are only slightly affected by the nature of the substituent, but acid hydrolysis rates of aliphatic esters are strongly affected by substituents. These effects were taken to be caused by steric factors thus log(/c//c0)acid defines s. It is reasonable to assume that steric factors affect base-catalyzed rates in the same way. Substituent effects on base hydrolysis of aliphatic compounds are composed of both polar and steric effects, and subtraction of the latter yields a measure of the former. The parameter a is important because it allows one to evaluate substituent effects on aliphatic reaction rates by a formula analogous to the Hammett equation, or by a bivariate relationship, the Taft-Pavelich equation (Pavelich and Taft, 1957) ... 

The alkaline hydrolysis of phthalate diesters has been fit to the Taft-Pavelich equation (Eq. 9). Dimethyl phthalate (DMP) hydrolyzes to phthalic acid (PA) in two steps DMP + H20->MMP + CH30H and MMP + H20- PA + CH30H. The first step is about 12 times faster than the second, and nearly all the diester is converted to the monoester before product PA is formed. Other diesters are assumed to behave similarly. An LFER was obtained from rate measurements on five phthalate esters (Wolfe et al., 1980b). The reaction constants, p and S, were determined by multiple regression analysis of the measured rate constants and reported values of cr and Es for the alkyl substituents. The fitted intercept compares favorably with the measured rate constant (log kOH = — 1.16 0.02) for the dimethyl ester (for which a and s = 0 by definition). Calculated half-lives under pseudo-first-order conditions (pH 8.0, 30°C) range from about 4 months for DMP to over 100 years for di-2-ethylhexyl phthalate. 

Derrieu, G., Gal, J.F., Elegant, L. and Azzaro, M. (1974) Carbonyl group basicity. IV. Application of the Taft-Pavelich equation on the enthalpies of complexation of ketones (CH3COR) with horon trifluoride. C. R. Acad. Sci., Sen HC, 279, 705-707. 

The kinetics of oxidative deoximation of aldo- and keto-oximes by 2,2/-bipyridinium chlorochromate (back to the parent carbonyl compounds) have been studied in DMSO, where the reaction is found to be first order in both oxime and oxidant.89 The aldoximes proved more reactive, and rates correlated well with the Pavelich-Taft dual substituent equation. Following extension of the study to hindered cases, and to 18 other solvents (analysed by Taft and Swain multi-parametrics), a cyclic intermediate is proposed for the rate-determining step. The same reaction order behaviour is found using the pyridinium version, and again electronic, steric, and solvent effects were examined.90... 

The paucity of reactions that depend solely on steric effects is not surprising. To include electronic contributions, Pavelich and Taft (89) proposed equation 55... 

Assuming that the resonance contribution is negligible, Equation (5) can be written as the Pavelich-Taft equation (Equation 15). ... 

Despite their associated problems, attempts have been made to incorporate results from ortho substituents in free energy correlations. It might be necessary, for example, to predict physico-chemical properties of a compound with an ortho substituent which acts as a drug or is a putative intermediate in a proposed mechanism. Quantitation of the ortho substituent effect requires that both steric and polar effects be considered. The ortho effect can be fitted to a modified version of the Pavelich-Taft equation (Chapter 2, Equation 15) where the values... 

Many reactions may be correlated by a simple Taft relationship (Eqn. 71) and the success is due to the minimal effect of steric interactions in these reactions. When steric effects compete with electronic the extended Pavelich-Taft equation (Eqn. 65) is successful [53b,55j. Steric parameters may be defined by Eqn. 72 for the hydrolysis of ethyl esters. 

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