Linear free enthalpy relationship

Fig. 2. Linear free enthalpy relationship between the difference in enthalpy of activation for the halogen transfer from CCI4 and BrCCl3 to alkyl radicals and the steric substituent parameters of alkyl radicals83 ...

All these test procedures cannot help in the selection of another colnmn with identical properties when the used one fails and a replacement is not available or a different colnmn has to be selected with similar selectivity. In these cases, the whole and often tedions procednre of method development with a new brand of colnmn has to be started. Recently, on the basis of LFER (linear free enthalpy relationship), retentive parameters were determined by Snyder et al. to describe the properties of commercially available colnmns. The principles were presented in a series of papers [65,66],... 

Linear Free Enthalpy Relationships (LFERs) Bronsted and Hammett Effects... 

Fig. 2. Linear free enthalpy relationship between the difference in enthalpy of activation for...

The thermal bleaching reaction was recently shown, through linear free enthalpy relationships, to be useful in designing organic reactions of the electrophile-nucleophile type and predicting the rates of these reactions [94]. Study of the reactions of di- and triarylmethyl cations with various nucleophiles afforded a scale of nucleophilicity in weakly polar non-nucleophilic solvents [94] and provided support for a relationship with the Ritchie [82] N scale of nucleophilicity [87] in water. 

The kinetics of the reactions of benzhydryl cations with some heterocyclic aromatic compounds have been determined. Application of a linear free enthalpy relationship allows the determination of nucleophilicity parameters for the aromatic compounds which correlate linearly with cr+ values. " Absolute rate constants for reactions of aromatic compounds having substituents of known <7+ parameters with carbocations and diazonium ions can be calculated. Scales of nucleophilicity and electrophilicity were drawn up and can be used predictively. 

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. °... 

Therefore, reaction series with constant entropy have been accorded great significance and have been investigated thoroughly. The condition in eq. (8) was even considered necessary for any linear free energy relationship to hold (16). However, as experimental data accumulated and precision improved, it was clear that for many theoretically important reaction series, this condition is not fulfilled (1, 17). It was also proved that a LFER can hold if entropy is not constant, but linearly related to enthalpy (18, 19). The linear equation... 

It is perhaps interesting, in view of the very considerable success of Hammett plots, to say a word finally about the thermodynamic implications of linear free energy relationships in general. We have already mentioned (p. 359) the relationship between free energy change, AG, and log k or log K and each AG term is, of course, made up of an enthalpy, AH, and an entropy, AS, component ... 

The existence of an enthalpy-entropy relationship has some important mechanistic implications. As the subject has been reviewed (Leffler, 1955) it will suffice here to make only a few brief comments. One important consequence of the compensation law is that linear free-energy relationships appear to apply to reactions with variable entropy only when the entropy is a linear function of the enthalpy (Jaffe, 1953 Taft, 1956c). 

The linear dependence of the activation energy on the logarithm of the frequency factor (both quantities calculated by the Arrhenius equation) is usually classified also as a linear free-energy relationship (cf. Wells, 2 Lefiler and Grunwald, 3). In terms of the transition state theory, this is a relationship between activation entropy and activation enthalpy ... 

The phenomenon of compensation is not unique to heterogeneous catalysis it is also seen in homogeneous catalysts, in organic reactions where the solvent is varied and in numerous physical processes such as solid-state diffusion, semiconduction (where it is known as the Meyer-Neldel Rule), and thermionic emission (governed by Richardson s equation ). Indeed it appears that kinetic parameters of any activated process, physical or chemical, are quite liable to exhibit compensation it even applies to the mortality rates of bacteria, as these also obey the Arrhenius equation. It connects with parallel effects in thermodynamics, where entropy and enthalpy terms describing the temperature dependence of equilibrium constants also show compensation. This brings us the area of linear free-energy relationships (LFER), discussion of which is fully covered in the literature, but which need not detain us now. 

In discussions of substituents as electron-donating or electron-withdrawing groups, it is easy to think about intramolecular interactions primarily in terms of enthalpy effects. We must not forget that rate constants and equilibria depend on AG and AG, respectively, not just on AH and AH. Thus, we should expect the Hammett and related linear free energy relationships to hold only when one of two conditions applies. Either (i) the entropy change is constant for all of the reactants in the data set, or (ii) there is a linear relationship between the values of AH and AS (or AH° and AS°) for all of the reactants in the data set. The latter condition is expressed by equation 6.99, where a and jS are constants. ... 

Fig. 8 Relationship between the reduction peak potential, Epc, of a-K6P2Wig062 or a-K4SiWi2O40 versus the reduction peak potential, EpcFc+, of ferricinium and the free enthalpy of transfer of the chloride ion, ACtr(Cl ), taking DMF as the reference solvent. Abbreviations are the same as in Tables 6 and 7. The solid line is the best linear regression fit to all the experimental points, including water as a solvent, (a) a-K6P2Wig062 correlation coefficient for the solid line 0.996. The correlation coefficient for the best fit to nonaqueous solvents only is 0.999. (b) a-K4SiWi204o correlation coefficient for the solid line 0.999. The correlation coefficient for the best fit to nonaqueous solvents only is also 0.999 (taken from Ref 34).

Notably, pKa values pertaining to solution equilibria are not usually distorted by special solvation effects. The same acidity order for 4-substituted pyridinium ions is found in the gas phase. In fact, a linear free energy (aqueous solution)-enthalpy (gas phase) relationship exists substituent effects are 3.5 times larger in the gas phase. In other words, the aqueous solvent, relative to the gas phase, attenuates the effect of substituents by its higher dielectric constant and by hydrogen bonding.52... 

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