Semenov—Polanyi relation

The procedure underlying the approximations 10.25 to 10.28 is closely related to, but not identical with, those of Evans and Polanyi [9] and Semenov [10] for reactions of homologous reactants [11,12], The empirical Pol nyi equation for the activation energy is... 

The theoretical equations (60.1) or (63.1) are similar to the empirical relations found by POLANYI et al./38/, SEMENOV /35/ a.o. for a large number of gas phase reactions /35t 49/. It should be noted, however, that the experimental values of activation energy and reaction heat, which generally depend on temperature, are not strictly equal to E and Q, respectively. This point will be discussed in Chapter III on the basis of the theory of reaction rates. 

Then, in the temperatiare range T>T- /2 the empirical Polanyi-Semenov relations (224.Ill) become identical with the theoretical equations (63.1) based on the properties of the potential energy surfaces. However, the condition T>T /2 is necessary for the validity of equations (231.Ill) but is not sufficient for the realization of inequalities (240.Ill) which lead to equations (241.III). The latter require the stronger limitation so that the reaction proceeds entirely in the classical temperature range T>2T in which the nuclear tunneling is quite negligible. This requirement may be sufficient if the motion along the classical reaction path is very fast compared to the nonreactive modes. Then, expression (216.Ill) yields, indeed, E, since for 8 =... 

Based on a large experimental material, L. Hammett in 1937 proposed the known prate constant of the reaction of an aromatic compound to the dissociation constant of the corresponding benzoic acid. A year later, M. Evans and M. Polanyi derived the empirical correlation A = oAH for the reaction of sodium atoms with alkyl halides. In 1954 N. N. Semenov considered and showed the applicability of this correlation to many reaction of radical abstraction. Simultaneously (1952-1953) R. Taft advanced a postulate about the additive influence of structural factors. A diverse experimental material on various reactions of aromatic and aliphatic compounds and application of the Hammett, Taft, and Polanyi-Semenov equations to them was obtained in fifties-seventies. 

A relation between the activation energy E and A// of the reaction is rather evident when the reaction is endothermic (A// > 0). In this case, always E S A// and the stronger the cleaved bond in the reactant, the higher E and the lower the reactivity of compounds estimated either through k or through AG. The Polanyi-Semenov correlation is very often fulfilled for exothermic reactions E-A- aq. A diverse experimental material on activation energies of radical reactions showed that for different... 

---