A Linear Free Energy Relationship

Using the terminology defined in Chapter 8 to discuss linear free energy relationships, the pKa values are the substituent constants and the a and P values are the sensitivity or reaction constants. These parameters are analogous to the crand p values, respectively, for Hammett plots. All substituent constants are defined by some reference reaction. For example, the (rvalues of Hammett plots are defined by the ionization of various benzoic acids relative to benzoic acid itself. In the Bronsted analysis, the substituent constants are defined by the abi 1 i ty of each acid to protonate water (Eq. 5.5). 

Because HAi is the reference acid to which all evaluated general-acid catalysts are compared, log fci and log Ri act as constants, leading to the Bronsted law (Eq. 9.36). 

We can reach the same conclusion by analyzing Eq. 9.38. Here, a tells how much of the thermodynamic difference between the strengths of the acids is reflected in the d i fference in the stabilities of the transition states derived from the two acids. The difference in the transition state structures must be the extent to which the proton has been transferred, and hence the Bronsted coefficient may be viewed as the extent of proton transfer in the activated complex. 

A lot of negative charge build-up on the carbon in the transition state for deprotonation 

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The ernes of ionic surfactants are usually depressed by tire addition of inert salts. Electrostatic repulsion between headgroups is screened by tire added electrolyte. This screening effectively makes tire surfactants more hydrophobic and tliis increased hydrophobicity induces micellization at lower concentrations. A linear free energy relationship expressing such a salt effect is given by ... 

Since AG and AG are combinations of enthalpy and entropy terms, a linear free-energy relationship between two reaction series can result from one of three circumstances (1) AH is constant and the AS terms are proportional for the series, (2) AS is constant and the AH terms are proportional, or (3) AH and AS are linearly related. Dissection of the free-energy changes into enthalpy and entropy components has often shown the third case to be true. °... 

Another method for studying solvent effects is the extrathermodynamic approach that we described in Chapter 7 for the study of structure-reactivity relationships. For example, we might seek a correlation between og(,kA/l ) for a reaction A carried out in a series of solvents and log(/ R/A R) for a reference or model reaction carried out in the same series of solvents. A linear plot of og(k/iJk ) against log(/ R/ linear free energy relationship (LFER). Such plots have in fact been made. As with structure-reactivity relationships, these solvent-reactivity relationships can be useful to us, but they have limitations. 

The acid cleavage of the aryl— silicon bond (desilylation), which provides a measure of the reactivity of the aromatic carbon of the bond, has been applied to 2- and 3-thienyl trimethylsilane, It was found that the 2-isomer reacted only 43.5 times faster than the 3-isomer and 5000 times faster than the phenyl compound at 50,2°C in acetic acid containing aqueous sulfuric acid. The results so far are consistent with the relative reactivities of thiophene upon detritia-tion if a linear free-energy relationship between the substituent effect in detritiation and desilylation is assumed, as the p-methyl group activates about 240 (200-300) times in detritiation with aqueous sulfuric acid and about 18 times in desilylation. A direct experimental comparison of the difference between benzene and thiophene in detritiation has not been carried out, but it may be mentioned that even in 80.7% sulfuric acid, benzene is detritiated about 600 times slower than 2-tritiothiophene. The aforementioned consideration makes it probable that under similar conditions the ratio of the rates of detritiation of thiophene and benzene is larger than in the desilylation. A still larger difference in reactivity between the 2-position of thiophene and benzene has been found for acetoxymercuration which... 

The Hammett equation is the best-known example of a linear free-energy relationship (LFER), that is, an equation which implies a linear relationship between free energies of reaction or activation for two related processes48. It describes the influence of polar meta-or para-substituents on reactivity for side-chain reactions of benzene derivatives. 

Recently, more detailed parameters for hydrogen bonding bases have been introduced and applied to many reactions demonstrating the existence of a linear free energy relationship between the hydrogen bonding donor and acceptor abilities and many kinetic or thermodynamic parameters91. 

The Hammett equation is a linear free energy relationship (LFER). This can be demonstrated as follows for the case of equilibrium constants (for rate constants a similar demonstration can be made with AG instead of AG). For each reaction, where X is any group,... 

The effect of solvent has been treated quantitatively (for SnI mechanisms, in which the solvent pulls off the leaving group) by a linear free energy relationship "... 

As proximity electrical effects are a function of the a and Or constants, and secondary bonding interactions when present may be a function of the Oi constants the effect of an ortho- or a ds-vinylene substituent may be represented by an equation including electrical and steric terms. The presence or absence of a steric effect may be ascertained in the following manner (72). There are four major cases of interest, (a) The steric effect obeys a linear free energy relationship. Then we may write the equation... 

Ledaal and co-workers (101-105) have proposed a linear free energy relationship for predicting the percent zwitterion formed at the rth carbon atom in substituted quinones, substituted dibenzoylethylenes, and substituted acetylenes. Fliszar and Granger (106) have proposed the equation... 

If equation 5 is valid, if a linear relationship exists between AH and the calculated AE(t) parameters, and if a linear free energy relationship exists between AH and EA , we might expect that the following linear relationship might hold for the decomposition of reactant Y to produce free radicals R(Y) ... 

Sander and Jencks introduced a linear free energy relationship for nucleophilic addition to carbonyls. The equilibrium nucleophilicity of a species HNu is given by... 

Complexes [Ni(H)(diphosphine)2]+ can be prepared by two ways, either by reaction of [Ni11 (diphosphine)2]2+ with H2 in the presence of base, or by reaction of [Ni°(diphosphine)2] with NH4+. A linear free energy relationship exists between the half-wave potentials of the Ni /Ni" couples of different [Ni(diphosphine)2] complexes and the hydride donor ability of the corresponding [Ni(H)(diphosphine)2]+.2320 Several methods have been used to determine those hydride... 

Before terminating our discussion of the Hammett equation, we should note that the existence of linear correlations of the type indicated by equation 7.4.20 implies a linear free energy relationship. The rate or equilibrium constants can be eliminated from this equation using equation 7.4.1 that is,... 

Equation (12) is a linear free-energy relationship, since activity coefficients/can be represented as AG° values. The reason for defining the slope parameter as in equation (12) (subscript e for equilibrium) is that a little rearranging of equations (11) and (12) leads to the easy-to-use Bunnett-Olsen equation for equilibria, equation (13) 30... 

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. 

A comparison of the rate constants for the [Cun(FLA)(IDPA)]+-cata-lyzed autoxidation of 4/-substituted derivatives of flavonol revealed a linear free energy relationship (Hammett) between the rate constants and the electronic effects of the para-substituents of the substrate (128). The logarithm of the rate constants linearly decreased with increasing Hammett o values, i.e. a higher electron density on the copper center yields a faster oxidation rate. 

The structure-reactivity relationship is a concept familiar to every organic chemist. As commonly used it refers to a linear free energy relationship, such as the Bronsted or Hammett equations, or some more general measure of the effect of changing substituent on the rate or equilibrium of a reaction. A substituent constant is conveniently defined as the effect of the substituent on the free-energy change for a control reaction. So the so-called structure-reactivity relationship is in fact usually a reactivity-reactivity relationship. 

Freitas, A. A., Quina, F.H., and Carroll, F.A. Eshmahon of water-organic interfacial tensions. A linear free energy relationship analysis of interfacial adhesion, J. Phys. Chem. B, 101 (38) 7488-7493, 1997. 

There is also a relationship between p a-values of ethanol, phenol and acetic acid on the one hand, and ethylamine, aniline and acetamide on the other (Liler, 1971c, p. 108), which may be presented as a linear free energy relationship (Figure 6) by regarding Et, Ph and CH3 CO as substituents (R). This excellent relationship leaves no doubt that the acidic group in the R—NH3 series remains unchanged, i.e., that acetylammonium ion is formed in the protonation of acetamide in aqueous acid (half-protonation in ca. 19% sulphuric acid). 

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