Self-exchange reaction rate

HL Theory of pressure effects on outei sphere self-exchange reaction rates... 

Figure C3.2.11. Log of the ET rate (A) against (l/s p-l/E ) for tire bis(biphenyl) cliromium self-exchange reaction. From 1341.

Marcus and Hush have developed a theory, which bears their names, that relates the value of kj2 to the rates (ku and 22) of the self-exchange reactions of the two... 

The reaction amounts to a vectorically directed current in the sense of occurring down a concentration gradient of reduced poly-[Fe(II)TPP] sites emanating from the reducing electrode/polymer interface. The magnitude of the current clearly conveys information about the rate of the poly-[Fe(III)TPP(X)] - poly-[Fe(II)TPP] self exchange reaction. 

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. 

This rules out, I would think completely, a dominant outer-sphere mechanism for that system, because the observed rate is just too fast to be compatible with this. The self-exchange reaction must almost certainly proceed most favourably via an inner-sphere mechanism. More data of this kind are evidently needed. 

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 success of the Marcus model is connected to the consistent description of self-exchange reactions and later to ET reactions with non-zero free energy. Using the easily measured free energy of reaction (-AGe) in the PES diagram, gives the Arrhenius rate ... 

Most of the redox centers in a polymer film cannot rapidly come into direct contact with the electrode surface. The widely accepted mechanism proposed for electron transport is one in which the electroactive sites become oxidized or reduced by a succession of electron-transfer self-exchange reactions between neighboring redox sites [22]. However, control of the overall rate is a more complex problem. To maintain electroneutrality within the film, a flow of counterions and associated solvent is necessary during electron transport. There is also motion of the polymer chains and the attached redox centers which provides an additional diffusive process for transport. The rate-determining step in the electron site-site hopping is still in question and is likely to be different in different materials. 

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). 

The rate of self-exchange reactions can generally be measured by isotopic tracer methods, but in several cases other techniques (optical rotation, nmr, epr) are more useful. Reactions like (18),... 

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