Free energy processes, correlation

Neither the principles of thermodynamics nor theories of reaction rates require that there should be such linear relationships. There are, in fact, numerous reaction series that fail to show such correlations. Some insight into the origin of die correlation can be gained by considering the relationship between the correlation equation and the free-energy changes involved in the two processes. The line in Fig 4.2 defines an equation in which m is the slope of the line ... 

If the polymer system was able to exist in an equilibrium state only, then a strictly defined correlation between (a, ph) and (a, ph) would exist in particular conditions, according to minimum of free energy of system formation. Consequently, there would occur only one temperature at which process initiation is thermodynamically probable. In rare ca.ses there may occur different correlations between ( ph, a) and ( ph, a ), which display one and the same value of free energy minimum of system formation. 

Summing up, the site of metabolism can be described by a probability function Psm that is correlated to, and can be considered, the free energy of the overall process ... 

Since such correlations belong to a series of treatments which are commonly identified as Linear Free Energy Relationships (LFER), and as only the standard potential is an electrochemical quantity directly linked with free energy (AG° = -n F AE°), one can make use of these mathematical treatments only in cases of electrochemically reversible redox processes (or in the limit of quasireversibility). Only in these cases does the measured redox potential have thermodynamic significance. 

These points indicate that the continuum theory expression of the free energy of activation, which is based on the Born solvation equation, has no relevance to the process of activation of ions in solution. The activation of ions in solution should involve the interaction energy with the solvent molecules, which depends on the structure of the ions, the solvent, and their orientation, and not on the Born charging energy in solvents of high dielectric constant (e.g., water). Consequently, the continuum theory of activation, which depends on the Born equation,fails to correlate (see Fig. 1) with experimental results. Inverse correlations were also found between the experimental values of the rate constant for an ET reaction in solvents having different dielectric constants with those computed from the continuum theory expression. Continuum theory also fails to explain the well-known Tafel linearity of current density at a metal electrode. ... 

A successful correlation of catalytic data for a series of related compounds is of little value for obtaining insight into the mechanism if its slope is not interpreted with respect to the sign and value. The slope a of Eq. (3) is proportional to the free energy change caused by the difference in mechanisms of the two processes being compared, the one under study and the reference one ... 

In summary, the intrinsic binding constant to be used throughout this book always refers to a specific set of sites. They are defined in terms of the molecular properties of the system through the corresponding canonical PFs. They are also interpreted as probability ratios or as free energies of binding processes. In subsequent chapters we shall see how to extract from these quantities various correlation functions or, equivalently, cooperativities. 

Three-membered ring-forming processes involving X-CH2-CH2-F or CH2-C(Y)-CH2F (X = CH2, O, or S and Y = O or S) in the gas phase have been treated by the ab initio MO method with a 6-31+G basis set." When electron correlation effects were considered, the activation (AG ) and reaction (AG°) free energies were lowered by about lOkcal mol indicating the importance of electron correlation in these reactions. The contribution of entropy of activation -TAS ) at 298 K to AG is very small the reactions are enthalpy controlled. 

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