Polanyi-Semenov equations

The activation energy, E2, is not known. The empirical Semenov-Polanyi equation (46) (E = 11.5 + 0.25 AH) gives 8 E 10 kcal. per mole, depending on the nature of the C—H bond broken. Heicklen (29) prefers E = 5 kcal. per mole. Values of 6 to 8 kcal. per mole (Table I) have therefore been assumed. Benson (12) estimates that A2 — 10 12 2 cc. molecule 1 sec."1 hence, k2 has been calculated (Table I). 

Reaction 8. The energetics of the addition to alkenes of R02 and of H02 will be reasonably similar. For the former reactions (10), AH = —12 kcal. per mole the Semenov-Polanyi equation suggests then that E — 8.5 kcal. per mole. As, however, the activation energy for addition of R02 to styrene (31) is 8.4 kcal. per mole whereas AH = —25 kcal. per mole, it is likely that for monoalkenes E is higher than 8.5. A value of E8 = 11.5 kcal. per mole would seem reasonable. Benson (12) estimates that As — 10"12 8 cc. molecule"1 sec.1. Thus, k8 = 10"17 3 cc. molecule"1 sec.1. Knox (33) has calculated that Ks = 10"20 8 cc. molecule"1, from which k 8 = 103r) per second. 

The activation energy may now be estimated from the Semenov— Polanyi equation and is found to be 8.25 kcal. mole". For a preexponential factor of 10 sec" this gives a value of 10 sec" forfe2i at 600 °K. Fish [107] has suggested E21 - 12 kcal. mole" and 21 =... 

Low Energy Activation in Each Step. In certain cases, the rule is, the better the thermodynamic of the step, the lower the energy activation (Polanyi-Semenov, Bronsted equations, for example). 

P3-20c For families of reactions, the Polanyi-Semenov equation can be used to estimate activation energies om the heats of reaction, AH/, according to the... 

The conformity of given reaction parameters to those obtained from empirical correlations for reactions of the same type for one reactant with other partners and/or even with participation of other species. For instance, the Polanyi-Semenov equation is a good approximation for activation energy of hydrogen atom transfer between two species (radicals or molecules) (see, for instance, Kondratyev and Nikitin, 1974). If the parameters for some reaction seriously... 

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 activation energy of this reaction is usually low. To estimate the activation energy ( ) as the function of the reaction heat Q), one may use a simple approximate equation (so called Polanyi-Semenov rule) [10] ... 

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 =... 

In this equation, ka and kb should remain nearly constant in the presence of hydrogen or deuterium, and thus these terms do not contribute to kinetic isotope effect. Small differences in kc can be estimated from the Evans-Polanyi-Semenov rule. (11)... 

From what has been said so far, and from the published papers [6,7,9,14, 16,98,145,151-153] it follows that there exist logical relationships between the characteristics of low-temperature thermal decomposition and those of initiation and detonation, respectively. The homolytic character of primary fission in both the detonation and low-temperature thermal decompositions of energetic materials (for relevant quotations, see [9]) was a motive for Zeman to use the Evans-Polanyi-Semenov equation (E-P-S) [ 168] to study the chemical micro-mechanism governing initiation of energetic materials [9]. A relationship formally similar to the E-P-S equation can also be obtained by mutual comparison of the dependences shown in Figs. 2 and 17 it has the following form ... 

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. 

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