Self-exchange rate constant for

This is the origin of the various values for self-exchange rate constants. We may now attempt to rationalize some of these in terms of the /-electron configurations of the various oxidation states. Consider the self-exchange rate constants for some iron complexes. 

If self-exchange rate constants for the Cu(II/I) couple are calculated by applying the Marcus cross relationship to the observed second-order... 

As for the difference observed for the sepulchrate complex, that may have to do with strain in the ligand. A student of mine has done some calculations considering the fact that the ligand itself may change the preferred distance and change the frequencies. This could account for a large part of the difference between the self-exchange rate constants for the sepulchrate and trisethylenediamine complexes. 

The self-exchange rate constant for reaction 14, when M is Ru and when an excited Ru(II) product is formed, has been esti-... 

A plot of the left-hand side of (5.38b) versus InA should be linear with a slope of unity and an intercept = In (k, k 2)-Such a plot for the reactions of Co(phen)3 with Cr(bpy)f, Cr(phen)3 and their substituted derivatives yields a slope of 0.98 and an intercept of approximately —0.55. If k, the self-exchange rate constant for Co(phen)3+ is 30 M s this corresponds to k,2 = 0.13, indicating mild nonadiabaticity for reactions involving Co(phen)3+. Ref. 41. See also Fig. 8.2. 

Table 5.6 Calculated Values for the Self-Exchange Rate Constant for Ru(H20)6+ + using (5.35) and Data for a Number of Cross-Reactions (from Ref. 43)...

A values have been obtained for oxidation of benzenediols by [Fe(bipy)(CN)4], including the effect of pH, i.e., of protonation of the iron(III) complex, and the kinetics of [Fe(phen)(CN)4] oxidation of catechol and of 4-butylcatechol reported. Redox potentials of [Fe(bipy)2(CFQ7] and of [Fe(bipy)(CN)4] are available. The self-exchange rate constant for [Fe(phen)2(CN)2] has been estimated from kinetic data for electron transfer reactions involving, inter alios, catechol and hydroquinone as 2.8 2.5 x 10 dm moF s (in dimethyl sulfoxide). 

A point of note in the data in Table 1 is the extraordinary range in electron-transfer reactivity that can exist even for outer-sphere reactions among what appear to be closely related reactions. For example, the self-exchange rate constants for Co(NH3)63+/2+ and Ru(bipy)33+/2+ differ in magnitude by 1014. 

An important feature to emerge from the comparisons in Table 2 is that variations in the electronic coupling term play a relatively small role in dictating the magnitudes of self-exchange rate constants for outer-sphere reactions, at least for transition metal complexes. Even for reactions... 

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. 

Nonetheless, in Table 4 are summarized the results of a series of rate constant comparisons between calculated values using optical absorption data and experimental values.83 The experimental data are derived from self-exchange rate constants for couples which are structurally related to the mixed-valence dimers shown in the table. The experimental values cited are calculated values for electron transfer within the association complex between reactants as estimated from k kQ >JKA. values were calculated using equation (33) and it was assumed in the calculations that vet = 5 x 1012 s-1. Calculations of this kind have been extended to unsymmetrical dimers like (NHJ)5RuIII(pz)RuIICl(bipy)24+ 83 and even to outer-sphere ion-pairs like (4).88... 

Table IV. Electron Transfer Cross-Reaction and Self-Exchange Rate Constants for Blue Copper Proteins (25°, /aO.IM, pH 7)a...

Reactions of hydroquinone, catechol, and L-ascorbic acid with dicyanobis(l,10-phenan-thn>line)iion(III) were studied in dimethyl sulfoxide (DMSO). Application of the Marcus theory to the reactions of catechol and hydroquinone provided the electron exchange rate constant for the Fe(III/II) couple in DMSO. The self-exchange rate constant for the ascorbic acidAadical couple was estimated for the first time in DMSO. The one electron-oxidation process of L-ascorbic acid in an aprotic solvents such as DMSO may be completely different from that in aqueous solutions. 

An attempt was made to obtain the electron self-exchange rate constant for the [Fe(CN)2-(phen)2]" couple by an electrochemical method. Real space Laplace analysis was used for the chronoamperometric response of 7.05 x 10 4 M (M = mol dm 3) solutions of the iron(III) complex with 0.1 M tetra(/t-butyl)ammonium perchlorate as supporting electrolyte. A glassy carbon working electrode with 3 mm diameter was used for the measurements. The Butler-Volmer plot gave an excellent straight line, and the electrochemical self-exchange rate constant was obained to be 1.2 X lO cm s l from the In k value at the zero over-potential. From the... 

Electron self- exchange rate constants for macrobicychc cobalt complexes. 

Self-Exchange Rate Constants for Cu(I) and Cu(II) States of Different Blue Copper Proteins"... 

Given the measured self-exchange rate constant for stellacyanin (kn ... 

X 10 s ), the Marcus cross relation (Equation 6.26a) can be used to calculate the reaction rates for the reduction of Cu -stellacyanin by Fe(EDTA) and the oxidation of Cu -stellacyanin by Co(phen)3 +. E°(Cu ) for stellacyanin is 0.18 V vs. NHE, and the reduction potentials and self-exchange rate constants for the inorganic reagents are given in Table 6.3. For relatively small AE° values,/12 is 1 here a convenient form of the Marcus cross relation is log k,2 = 0.5[log kn + log 22 + 16.9AE°2]. Calculations with kn, 22, and AE°2 from experiments give k,2 values that accord quite closely with the measured rate constants. 

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