Free energy standard of activation

Equation (5-43) has the practical advantage over Eq. (5-40) that the partition functions in (5-40) are difficult or impossible to evaluate, whereas the presence of the equilibrium constant in (5-43) permits us to introduce the well-developed ideas of thermodynamics into the kinetic problem. We define the quantities AG, A//, and A5 as, respectively, the standard free energy of activation, enthalpy of activation, and entropy of activation from thermodynamics we now can write... 

Fig. 20.19 (a) Analogy showing how ihe rate at which a car can travel from /I to C is determined by the narrow controlled road BC (the r.d.s.). (b) Standard free energy of activation against distance for a two-step reaction since the activation energy required to produce the activated state B is and that to produce A is only AG°, the former is the r.d.s.,... 

Fig. 3 Electrochemical and homogeneous standard free energies of activation for self-exchange in the reduction of aromatic hydrocarbons in iV.A -dimethylformamide as a function of their equivalent hard sphere radius, a. 1, Benzonitrile 2, 4-cyanopyridine 3, o-toluonitrile 4, w-toluonitrile 5, p-toluonitrile 6, phthalonitrile 7, terephthalonitrile 8, nitrobenzene 9, w-dinitrobenzene 10, p-dinitrobenzene 11, w-nitrobenzonitrile 12, dibenzofuran 13, dibenzothiophene 14, p-naphthoquinone 15, anthracene 16, perylene 17, naphthalene 18, tra 5-stilbene. Solid lines denote theoretical predictions. (Adapted from Kojima and Bard, 1975.)...

The quantity Aand like quantities, is the standard free energy of activation, which governs the rate of passage of a representative point in the system from A to B. It is not Gj - but Ga - Ga° (see Fig. 7.72). 

Sn2 Mechanism. In this first case, the standard free energy of activation A (7°, and thus the rate of the reaction, depends strongly on both the capability of the nucleophile to initiate a substitution reaction and the willingness of the organic molecule to undergo that reaction. The former factor may be expressed by the relative nucleophi-licity of the nucleophile, an entity that can be quantified (see discussion below). The latter contribution to A <7°, however, is more difficult to quantify since it incorpo-... 

Gibbs energy of activation A G (standard free energy of activation A G ) (Id mol-1) — The standard Gibbs energy difference between the -> transition state of a reaction (either an elementary reaction or a stepwise reaction) and the ground state of the reactants. It is calculated from the experimental rate constant k via the conventional form of the absolute reaction rate equation ... 

To emphasize that this is the jump frequency for a pure diffusion process, in which case the ions are not subjected to an externally applied field, a subscript D will be appended to the net jump frequency and to the standard free energy of activation, i.e.. 

How have we arrived at these equations The argument follows the reasoning that leads to the potential dependence of the rate constant. If the standard free energy of the reaction is changed by r0, the standard free energy of activation should be changed by a fraction of that quantity, namely by p r0, since the activated complex represents an intermediate state between the initial and the final states. The symmetry factor P was defined earlier as ... 

Equation 24E gives the chemical rate constant of the forward reaction as a function of the standard free energy of activation. To use this equation for electrode kinetics, it is necessary to relate the standard free energy of activation to the potential drop At]) across the interphase. 

In step (40J) an adsorbed species is removed from the surface. The standard free energy of adsorption depends on potential as a result of the effect of competition with water (in addition to the direct dependence of 0 on potential due to charge transfer). The standard free energy of activation depends on a fraction P of the same potential. I This is the reason for the introduction of the term exp[o.l4n(pFE/RT)] in Eq. 42J. 

AG1 () is the standard free energy of activation at the electrode potential ... 

This energy of activation is the electrochemical standard free energy of activation, AG1 (), which is purely chemical when d> = 0 ... 

Let us consider the system of (3.1.1), in which two substances A and B are linked by unimolecular reactions. First we focus on the special condition in which the entire system—A, B, and all other configurations—is at thermal equilibrium. For this situation, the concentration of complexes can be calculated from the standard free energies of activation according to either of two equilibrium constants ... 

Figure 3.3.2 Effects of a potential change on the standard free energies of activation for oxidation and reduction. The lower frame is a magnified picture of the boxed area in the upper frame.

Let us consider again a plot of the standard free energy " of species O and R as a function of reaction coordinate (see Figure 3.3.2), but we now give more careful consideration to the nature of the reaction coordinate and the computation of the standard free energy. Our goal is to obtain an expression for the standard free energy of activation, AG as a function of structural parameters of the reactant, so that equation 3.1.17 (or a closely related form) can be used to calculate the rate constant. In earlier theoretical work, the pre-exponential factor for the rate constant was written in terms of a collision number (37, 38, 58, 59), but the formalism now used leads to expressions like ... 

---