Self-exchange reactions rate constants

Ky and ky are the equilibrium constant and cross reaction rate constant for Eq. 2, kii and kjj are the self-exchange ET rate constants, and Z is a preexponential factor usually set at 10 (results are quite insensitive to its value). Because Ky can be calculated from the difference in formal oxidation potentials for the components, Eq. 2 states that ky only depends upon the formal oxidation potential and intrinsic (AG° = 0, or self-ET) rate constant for each couple involved. 

Esr spectroscopy has also been used to study pure solvent dynamics in electron self-exchange reactions (Grampp et al., 1990a Grampp and Jaenicke, 1984a,b). When the systems are not linked by a spacer (i.e. TCNQ- /TCNQ (TCNQ = tetracyanoquinodimethane), the homogeneous bimolecular rate constants /chom are given by (10), with fcA the association constant and kET... 

The reorganization energy of a self-exchange reaction is denoted A(0) (from the fact that AG° = 0) and is an important quantity in the Marcus theory, where it can be shown that the activation free energy of a self-exchange reaction, AG(0), is equal to X.(0)/4. It is also possible to measure rate constants of self-exchange processes experimentally and thus get access to (0) via this relationship. 

Relationships having the same form as eq 14 can also be written for the enthalpic and entropic contributions to the intrinsic free energy barriers (10). Provided that the reactions are adiabatic and the conventional collision model applies, eq 14 can be written in the familiar form relating the rate constants of electrochemical exchange and homogeneous self-exchange reactions (13) ... 

Also, the observed rates probably refer to outer-sphere pathways, and the rate constants for the corresponding homogeneous self-exchange reactions are available or can be estimated from rate data for closely related cross reactions (15). These h ex... 

Rate Constants and Thermodynamic Parameters for Selected Electrochemical Exchange and Homogeneous Self-Exchange Reactions at 25°C. 

From the experimental point of view, significant variations in kobs can be induced by changes in solvent and/or molecular size. For example, there are relatively small contributions to A for the self-exchange reactions for the Ru(NH3)63+/2+and Ru(bipy)33+/2+couples in Table 1 and the effects of the differences in molecular radii on KA and Ao are sufficient to account for the difference in self-exchange rate constants of 106. 

The second and far more common approach to testing the predicted dependence of kob on AG has been based on the so-called Marcus cross-reaction equation. The cross-reaction equation interrelates the rate constant for a net reaction, D+A- D++A ( el2), with the equilibrium constant (Kl2) and self-exchange rate constants for the two-component self-exchange reactions D+ 0 (Zen) and A0/- (k22). Its derivation is based on the assumption that the contributions to vibrational and solvent trapping for the net reaction from the individual reactants are simply additive (equation 63). The factors of one-half appear because only one of the two components of the self-exchange reactions is involved in the net reaction. The expression for A0 in equation (63) is an approximation. Note from equation (23) that k is a collective property of both reactants and the approximation in equation (63) is valid only if the reactants have similar radii. 

The derivation of the cross-reaction equation follows by (1) solving equation (63) for k for each individual self-exchange reaction, e.g. u=4RT(ln(vetKA)u/ku) (2) inserting the expressions for Au and k22 into equation (63) for A12 (3) incorporating this expression for kl2 into the rate constant expression in equation (59), assuming that = [(vet/fA)j j(vetAlA)22]1/1 - The final... 

The Marcus therory provides an appropriate formalism for calculating the rate constant of an outer-sphere redox reaction from a set of nonkinetic parameters1139"1425. The simplest possible process is a self-exchange reaction, where AG = 0. In an outer-sphere electron self-exchange reaction the electron is transferred within the precursor complex (Eq. 10.4). 

There were many predictions arising from the theory and its extension to electrochemical and other systems [11, 23, 24]. One such prediction, the cross-relation , was based on the relation between the A for reactions between two different redox systems, A 2, to the A s of the self-exchange reactions, An and A12, for each of the two systems (A,2 = l/2(An + A22)). The result for k12, the rate constant for the cross-reaction, is... 

Experimentally determined rate constants and X values for organic self-exchange reactions, together with estimates of X and r according to a spherical model and an ellipsoidal model... 

Calculation of rate constants for cross reactions from known data on self-exchange reactions. 

What first strikes the eye in Table 12 is the variation in A, which is to be expected from an inspection of the individual values of A for self-exchange reactions that are listed in Table 6. No doubt the considerable scatter of data points in the Marcus plots reflects to a large extent this variation in X. It is therefore important to study series of closely similar compounds to test the theory, as was indeed pointed out very early by Marcus (1964). Preferably, one should work with compounds of known X, determined by independent measurements of self-exchange rate constants. 

Marcus has shown (44, 45) that a relatively simple relation exists between the rate constants for reactions accompanied by a net chemical change (A G° 0) and those for the component self-exchange reactions. 

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