Gibbs activation

The assumptions of the special model of a nonuniform surface were formulated above in terms of changes of the standard Gibbs energy, AG°, and the Gibbs activation energy, AG. It can be assumed that standard entropy, S°, of each kind of adsorbed particles and activated complexes on different sites of a nonuniform surface does not differ substantially in this case there can be given practically equivalent formulation of the model... 

It was later demonstrated that if the reaction mechanism corresponds to scheme (295) and the linear relation between standard Gibbs energy of adsorption and Gibbs activation energy of adsorption is obeyed [see (91)], then the kinetic (305) corresponds in general to the exponential nonuniformity of the surface with even nonuniformity included as a particular case (44). In the general case the exponent m is not equal to transfer coefficient a, but is connected with it according to (143).5... 

Table 5-5. Absolute and relative rate constants, Gibbs activation energies, activation enthalpies, and activation entropies of the Menschutkin reaction between triethylamine and iodoethane in twelve solvents at 50 °C [59],...

Rate constant for the reaction of pyridinyl radical in acetonitrile divided by that for the reaction in 1,2-dimethoxyethane and the corresponding change in Gibbs activation energy. 

The Gibbs activation energy is calculated from equation (7.4.15) ignoring the activity coefficients. From equation (7.4.20) the rate constant at 25°C is 1.82 X 10 M s . Thus,... 

Fig. 7.1 7 Plot of the Gibbs activation energy A G° against the Gibbs energy barrier AG° for an electron transfer reaction with Ex equal to lOOkJmoP. ...

For a homonuclear reaction AG° is zero. Since the Coulombic work terms are neglected in this calculation, the factor m is equal to 1/2. It follows from equation (7.8.27) that the outer sphere contribution to the Gibbs activation energy is equal to... 

Although the Bronsted relation was first discussed with respect to proton transfer reactions, it has been found to apply to other types of reactions including electron and atom transfer reactions. Equation (7.11.1) implies that there is also a linear relationship between the Gibbs activation energy for the reaction and the standard Gibbs energy change for the associated equilibrium. Thus, one may also write... 

Rate Constants and Gibbs Activation Energies of Walk Rearrangements and Electrocyclic Ring Openings in Ester-Substituted and Nitrile-Substituted Dimethylbicyclopentene Derivatives (25)... 

The Gibbs activation energy of the bicyclopentene rearrangement, however, turns out to be considerably smaller than that of the other rearrangements. This may be attributed to a favorable resonance stabilization of an aromatjc transition state. An alternative or additional explanation comes from an anomalously high ground state enthalpy of the bicyclopentene system. 

In the transition state of the bicyclopentene rearrangement the destabilization of the ground state vanishes and thereby the activation energy is lowered. The observed alternation of the Gibbs activation energies in Figure 10 might, in-... 

Figure 10. Comparison of the stereochemical course and the Gibbs activation enthalpies of the walk rearrangements in bicyclo[2.1.0]pentene, bicyclo[4.1.0]heptadiene, and bicyclo-[6.1.0] nonatriene. AG values are in kcal/mol.

Gibbs Activation Enthalpies of the Competing Process in Bicyclo[3.1.0]hexenyl Cations... 

Figure 14. Stereochemistry of the photochemically induced walk rearrangement in homo-tropylium cations. Gibbs activation energy of the thermal endo - exo isomerization is in kcal/mol (124B, 127).

In aqueous solution, the PCM method computes an activation enthalpy of 15.3 kcal/mol, which is 46% [3.8 kcal/mol (computed)/8.2 kcal/mol (expected)] of the estimated reduction to a 10.9 kcal/mol activation barrier. In a second comparison, the second-order rate constants between cyclopentadiene and alkyl vinyl ketones have been reported to be 740 times larger in water than in ra-octane [82], Overall, the PCM model lowers the Gibbs activation energies of the NC reaction from benzene to water by 2.0 kcal/mol, which correspond to an aqueous rate increase of ca. 30 times. Therefore despite mirroring the experimental trend in activation barrier reduction with increasing solvent polarity, the PCM method does not fully account for the observed rate of aqueous acceleration. 

In the special model of nonuniformity, several assumptions were made. The Gibbs activation energy AG is considered to be a linear function of the standard Gibbs energy of adsorbed species AG°a... 

A computational study of the concerted C(sp )-0 reductive elimination of olefin oxides from complexes 19a and 19b showed that the Gibbs activation energy of epoxide elimination increases in the following order of 19a 19b 20 [33]. In other words, migration of a secondary aUcyl from the Pt center to the oxetane oxygen atom is a more facile process than that involving a primary alkyl group. 

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