Linear free enthalpy relationship parameters

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],... 

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. 

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. 

A simple criterion, which has the same nature as Ath of the catalyst, was used to represent the electron donor power during reaction the absolute value of the potential ionization difference. A/ = /r — /p, weighed by the ratio p/ r of carbon in product and reactant molecules respectively. The linear correlations obtained between A/ and Ath show that their slope is related to the electron donor power of the reactant, positive when C-C (alkanes, alkyl-aromatics) or C-H (alcohols) bonds are to be transformed, and negative when C=C bonds are concerned. The intercept depends on the extent of oxidation, and its absolute value increases from mild to total oxidation, respectively. A main difficulty is the actual state of cations at the steady state, but each time accurate experiments allow determining the mean valence state, the calculated Ath fits well the correlations. These lines may be used as a predictive trend, and allow, for example, to precise that more basic catalysts are needed for alkane ODH than for its mild oxidation to oxygenated compound. As a variety of solids have been catalytically experienced in literature, it would be worthwhile to consider far more examples than what is proposed here to refine the relationships observed. Finally, theoretical considerations are proposed to tentatively account for these linear relationships. Optical basicity would be closely related to the free enthalpy, and, as an intensive thermodynamic parameter, it is normal that it could be related to several characteristic properties, including now catalytic properties. 

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