Gibbs energies of activation

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

Damjanovic A, SepaDB. 1990. An analysis of the pH dependence of enthalpies and Gibbs energies of activation for O2 reduction at Pt electrodes in acid solutions. Electrochim Acta 35 1157-1162. 

For proton transfer from an acid (HA) to a series of bases (B ) the Gibbs energy of activation for the reaction is predicted to vary with the standard Gibbs energy for the proton transfer according to (18) The value of the... 

The phenomenological treatment assumes that the Gibbs energies of activation Gox and Gred depend on the electrode potential , but that the pre-exponential factor A does not. We expand the energy of activation about the standard equilibrium potential >0o of the redox reaction keeping terms up to first order, we obtain for the anodic reaction ... 

The transfer coefficient a has a dual role (1) It determines the dependence of the current on the electrode potential. (2) It gives the variation of the Gibbs energy of activation with potential, and hence affects the temperature dependence of the current. If an experimental value for a is obtained from current-potential curves, its value should be independent of temperature. A small temperature dependence may arise from quantum effects (not treated here), but a strong dependence is not compatible with an outer-sphere mechanism. 

The Gibbs energy of activation in Eq. (5.4) can be split into an enthalpy and an entropy term AGjx = AH x - T AS]x. Define two transfer coefficients... 

Some reactions are characterized by straight-line plots of TAS versus having a slope of approximately one, where this linearity results from compensatory, or off-setting, changes of AH and TAS. For this reason, the change in the Gibbs energy of activation, AG = AH - TAS, is a better description of the variation in the reaction than either AH or alone . See also Isokinetic Relationship... 

The parameter G is the Gibbs energy of activation of the forward and backward process. The BV approximation assumes G to change linearly with changes in the thermodynamic driving force, that is, the overpotential ) = (E — E0), according to... 

Here, AGq is the standard Gibbs energy of activation and represents the intrinsic barrier of the process. AG becomes the common activation barrier of the forward and backward reactions if the driving force (overpotential 77 = (E — E0)) is zero (that is E = E0). 

The quadratic dependence of the Gibbs energy of activation on the driving force implies that the transfer coefficient a is no longer a constant. Instead, it depends linearly on the overpotential. Figure 6.7 illustrates the free energy profile curves along the reaction coordinates for the reaction... 

The development of a consistent theory for a dissociative electron transfer is a recent challenge in the field of theoretical electrocatalysis. Progress in this field of electrochemistry has involved the use of an harmonic Morse curves [25] instead of harmonic approximations. Applying the principles of the theory of the activated complex to adiabatic dissociative electron transfer reactions, the work of Saveant resulted in the following expressions [24] for the Gibbs energy of activation... 

While the examples chosen here concern only dissociation of protons, the Hammett equation has a much broader application. Equilibria for other types of reactions can be treated. Furthermore, since rates of reactions are related to Gibbs energies of activation, many rate constants can be correlated. For these purposes the Hammett equation can be written in the more general form in which k may be either an equilibrium constant or a rate constant.13 The subscript / denotes the reaction under consideration and i the substituent influencing the reaction. 

Gibbs energy of activation standard Gibbs energy of activation Gibbs energy of activation for forward reaction film thickness... 

According to - Polanyis rule the relationship between AG and the - Gibbs energy of activation (AG ) is... 

If the concentration units are mol dm-3, the true and apparent enthalpies of activation differ by (n - l)/(aRT2), where n is the order of reaction and a - the thermal expansivity. See also - Gibbs energy of activation. 

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