Dissociation linear free-energy relationships

Equation (9.72) is known as a linear free energy relationship, and it shows that there should be a linear relationship between the logarithm of the rate constant for a reaction and the free energy for the dissociation of the acid. 

Non-Marcusian linear free energy relationships (if I may again be permitted that barbarism) provide direct evidence for this type of potential surface in octahedral ligand substitution reactions. Both dissociative (e.g., the chloropentaamine of cobalt(III)) and associative systems (e.g., chloropentaaquo chromium(III)) may have values of slopes for the linear free energy relationships indicating non-Marcusian behavior. 

If a proton-transfer reaction is visualized as a three-body process (Bell, 1959b), a linear free energy relationship is predicted between the acid dissociation constant, Aha, and the catalytic coefficient for the proton-transfer reaction, HA. Figure I shows the relationships between ground-state energies and transition-state energies. This is a particular case of the Bronsted Catalysis Law (Bronsted and Pedersen, 1924) shown in equation (9). The quantities p and q are, respectively, the number of... 

Hi) Rhenium(V) complex with NCS (191), thiourea, and other incoming ligands (205). The observed linear free-energy relationship also suggests dissociative activation for the substitution reactions of the rhenium complex (205). 

The rate constants and dissociation constants for these compounds form a linear free energy relationship (LFER), in which a plot of In qh versus In AToh is linear. 

These o° constants were evaluated by the dissociation of meto-substituted phenyla-cetic acids and esters and were defined for a selected group of /W-XC6H4- substituents which exhibit a precise linear free energy relationship. Their values are independent of whether the process is rate or equilibrium, the solvent and reaction conditions. 

Fig. 9. Linear Free Energy Relationship between acid dissociation constants of HY, expressed as concentration quotients, (logiCj/K ) (Clare et at, 1966) at 20-25°C and relative rates of reaction of Y with methyl iodide (logA /fc°) at 0°C (Cook et at, 1966 Parker, 1966) in DMF and in methanol.

Linear free energy relationships also enable the calculation of equilibrium constants (as opposed to dissociation constants). There have been no extensive compilations of these free energy correlations because ranges of equilibrium constants are difficult to measure. For the limited data available the reader is referred to the article by Jaffe and the books of Hine and Leffler and Grunwald - techniques similar to those elaborated above enable equilibrium constants to be calculated with reasonable accuracy. Selected equations are listed in Appendix 4, Table 4. 

Another standardized database for the diffuse layer model was developed for montmorillonite by Bradbury and Baeyens (2005). Surface complexation constants for strong and weak sites and cation exchange were fit to adsorption data for various metals using constant site densities and protonation-dissociation constants in a nonelectrostatic modeling approach. Linear free energy relationships were developed to predict surface complexation constants for additional metals from their aqueous hydrolysis constants. 

The Hammett-type correlation for the rate constants of 5-allyl-5-R-barbiturates has been reported by Carstensen et al. and suggested for use in stability predictions.569 Similar correlations were also found for the hydrolysis of 5-arylidenebarbituric acids.363,567 Linear free energy relationships have also been reported for dissociation constants,45,51 polarographic half-wave potentials,570 fluorescence70 and luminescence phenomena,71 and 13C-NMR chemical shifts129 for different classes of barbituric acid derivatives. Application of the dual substituent parameters method in LFER analysis of barbiturates, using Taft s polar and steric constants for various chemical and physicochemical properties, was also evaluated.571... 

Both the redox and acidity properties, and hence cdso e X-H bond dissociation energies, have been found to depend on the substituent pattern. In the majority of cases, the substituent effects have been shown to follow linear free energy relationships, even for... 

The term linear free energy relationship (LFER) appHes to a variety of relationships between kinetic and thermodynamic quantities that are important in both organic and inorganic reactions. About 80 years ago, J. N. Bronsted found a relationship between the dissociation constant of an acid, Ka, and its abihty to function as a catalyst in reactions that have rates that are accelerated by an acid. The Bronsted relationship can be written in the form... 

This equation shows that a linear relationship should exist between In k for the acid catalyzed reaction and AGa for dissociation of the acid. This is an example of a linear free energy relationship. 

Kinetic effects are related to thermodynamic effects by linear free-energy relationships (LFER). A LEER can be observed when the bond strength of a metal-ligand bond (correlated to a thermodynamic parameter) plays a major role in determining the dissociation rate of a ligand (correlated to a kinetic parameter). When this is true, a plot of the logarithm of the rate constants for [MLsX] -I- Y substitution reactions, where X is varied but Y is not, ver-... 

The Hammett linear free energy relationship is a widely used extrathermody-namic relationship for organic reactions. Although developed specifically for dissociation constants, in principle the method is applicable to any organic reaction. 

The radical clock experiments as well as the stereochemical outcome of the reaction along with the reactivity profiles observed pointed to an ET process as the operating mechanism. Linear-free energy relationships were also consistent with this mechanistic pathway (see succeeding text). ET may proceed in two ways, usually referred to as inner-sphere and outer-sphere ET, which can be contemplated as the two extremes of a continuous mechanism [204]. Both processes are dissociative in nature for alkyl halides and presumably do not involve a discrete radical anion, RX" [205]. The situation may, however, be different for aryl halides. Radical anions do exist, and aryl halides probably undergo a stepwise reaction with an electron donor to give rise to RX [206]. 

The Hammett equation is regarded as the origin of linear free energy relationships (LFER). It correlates the rates of hydrolysis of differently substituted benzoic acid esters with the acidities of the equivalently substituted benzoic adds. A linear relationship between the free energy for the add dissociation and the free activation energy for the ester hydrolysis is assumed. Both energies are sensitive to the inductive (electron-shifting) effects of a particular substituent, which are embodied in the substituent constant a, an example of a molecular descriptor. The fundamentals of the Hammett theory are summarized in Fig. 2. 

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