Classical activation energy

Figure 4.14 Schematic representation of the classical activation energy AG for different reaction energies AE. (a) is the normal thermodynamic region, (b) is the activationless reaction and (c) is the iinverted> region...

The penetration probability can be exactly calculated if one neglects the small rounding off of the top of the curve and makes it quite sharp-edged. For energies W which are not too near the classical activation energy Q, the penetration probability is... 

X for a colinear three-atomic reaction R reactants and P products regions Eq classical activation energy Q aV reaction heat at 0°K. 

The above consideration, based on parabolic surfaces (50.1), illustrates a simple example of a correlation between classical activation energy and reaction heat. Such a correlation is also to be expected, however, under certain conditions for more complicated potential energy surfaces. If, for instance, the electronic state of products is changed in any way, then the whole "diabatic" surface alters, so that, in the general case, both the saddle-point and the minimum energy difference ( aV s q) of reactants and products change simultaneously. The dependence E (Q) may be, in general, a compli-cated function however, a simple relationship, which is valid for many reactions in gas and dense phases, can be derived in the way described below. 

The existence of a correlation between the classical activation energy and the reaction heat (at O K) provides evidence for the inherent relationship between the chemical reactivity and the molecular structure or electronic state of reactants and products. 

We will restrict here oijir considerations to the consequences from the more familiar rate equations (51.III) and (67.111) both involving the classical activation energy. Similar conclusions can be made on the basis of the adiabatic rate expressions (106.III) and (124.III). 

The two equivalent adiabatic expressions (106.HI) and (124. HI) represent alternatives of the acciarate formulation of the statistical theory of reaction rates, which rest on two other definitions of the activated complex as a virtual state. In general, they do not involve the Arrhenius exponential factor which includes the classical activation energy. 

The "statistical formulation (67.Ill) cannot be applied to unimolecular reactions for which the classical activation energy and the reaction heat are equal (E = Q) without introducing some additio-nal assumptions which are necessary for the definition of the transition state. One usually considers the "activated complex (AB) as a rotating "diatomic molecule in which the centrifugal force is balanced by an attractive dipole-induced dipole or dispersion force /HO/. This "diatomic model implies that the angular momentum... 

If classical activation energy is greater than reaction heat (E >Q), the transition state is defined by the configiaration corres-... 

It should be noted, however, that for redox processes the relation between current density and electrode potential is a direct consequence of the general relationship (56.1) between classical activation energy and reaction heat. Therefore, the Tafel equation and the deviations from it predicted by this relation cannot be used for a test of the oscillator model assumed. Such deviations were first observed by FROTKIN et al./170/ for the case of reduction of Fe(CN) " ions on a mercury electrode. PARSONS et al./171/ have shown that the... 

The classical activation energy for electrilytic hydrogen evolution is given by expressioii (115 ilV). The condition (1l6.IV) at which the quadratic term can be neglected is often fulfilled, since the values of are high (10-20 kcal/mole). For the same reasons... 

The classical activation energies for the endothermic and exothermic directions of the similar reaction with mioglobin (Mb)... 

The classic activation energy Eq at absolute zero temperature (0 K), which is... 

F ure 10.9. Difference between classic activation energy and the free energy ofa true activation... 

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