Marcus cross relationship constants

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

The acid dependence observed in the reduction of trans-[Co(Me4[14]tetraeneN4)(N3)2] by Fe (aq) is attributed to the greater reactivity of the oxidant upon protonation of an azide ligand. The application of the Marcus cross-relationship to the data for the reduction of [Co(tmen)3] (tmen = tetramethylethylenediamine) by [Ru(H20)6] " yields a self-exchange rate constant of 10 s for the [Co(tmen)3] couple. Studies of the spectroscopic... 

The electron exchange rate constants [Rh(dmpe)3]" / " couples have been determined to be 2 x 10 and 4 x 10 M" s", respectively, from the appliction of the Marcus cross-relationship to the reactions with several ruthenium(II) pentaammine complexes. The relative values are consistent with the differences in the M—P bond distance changes (Ado = 0.068 A for Tc and 0.054 A for Re) determined by EXAFS measurements. 

This is the cross relationship in terms of rate constants. There is often reason to believe (or need to assume) that = 1, and then Eq. (6.20) reduces to what is often called the simplified Marcus cross relationship. This is particularly useful because a knowledge of any three of the values, AB AA BB o " AB Hows One to predict the fourth. 

Table 63. Comparison of Some Obsaved Rate Constants (M s", 25 C) with Those Calculated from the Marcus Cross Relationship...

Table 6. Self-Exchange Rate Constants (25°C) for Various Reactions of Calculated from the Marcus Cross Relationship"...

The equilibrium constant for this last reaction, obtained from emf measurements, is Ki2- For reactants and products of the same size and charge type the simplest form of the Marcus cross-relationship is... 

A literature value for E° for the SCH2COO / SCH2COO redox couple (0.74 V) was then used in conjunction with the cross relationship of Marcus theory to derive a self-exchange rate constant of 1.5 x 105 M-1 s-1 for the SCH2COO / SCH2COO redox couple. 

Even in the domain of inorganic redox chemistry relatively little use has been made of the full potential of the Marcus theory, i.e. calculation of A, and A0 according to (48) and (52) and subsequent use of (54) and (13) to obtain the rate constant (for examples, see Table 5). Instead the majority of published studies are confined to tests of the Marcus cross-relations, as given in (62)-(65) (see e.g. Pennington, 1978), or what amounts to the same type of test, analysis of log k vs. AG° relationships. The hesitation to try calculations of A is no doubt due to the inadequacy of the simple collision model of Fig. 4, which is difficult to apply even to species of approximately spherical shape. 

Indeed, the oxidation of Fe(CN)g by O2 (as well as by H2O2 and BrOj) proceeds via the rds of dissociation of the hexa- to the penta-cyano complex. The value of k in (8.90) is 5.6 X lO M s at pH > 3.8. Traces of Fe from decomposition of the cyano complex promote catalytic oxidation (Prob. 19). A large number of complexes of the type Fe(CN)5X" for both Fe(II) and Fe(III) have been studied and cross-reaction redox kinetics abound. Care has to be exercised in the use of FeiCN) . Daylight can induce changes in the complex even within an hour and catalytic effects (traces of Cu Sec. 3.1.4) have to be considered. In addition, the sensitivity of the values of and rate constants to medium effects lessen the value of the iron-cyano complexes as reactant partners for the demonstration of Marcus relationships. Nevertheless, they, with other inorganic complexes, have been extensively employed to probe the peripheral characteristics of metallopro-teins. 

By using cyclic voltammetry, Schiffrin and coworkers [26, 186, 187, 189] studied electron transfer across the water-1,2-dichloroethane interface between the redox couple FefCNls /Fe(CN)6 in water, and lutetium(III) [186] and tin(IV) [26, 187] diphthalocyanines and bis(pyridine)-me50-tetraphenylporphyrinato-iron(II) or ru-thenium(III) [189] in the organic solvent. An essential advantage of these systems is that none of the reactants or products can cross the interface and interfere with the electron transfer reaction, which could be clearly demonstrated. Owing to a much higher concentration of the aqueous redox couple, the pseudo-first order electron transfer reactions could be analyzed with the help of the Nicholson-Shain theory. However, though they have all appeared to be quasireversible, kinetic analysis was restricted to an evaluation of the apparent standard rate constant o. which was found to be of the order of 10 cm s [186, 189]. Marcus [199] has derived a relationship between the pseudo-first-order rate constant for the reaction (8) and the rate... 

The electron self-exchange rate constant for the [Cr(CNdipp)6] couple (CNdipp = 2,6-diisopropylphenyl isocyanide) in CD2CI2 has been measured between -89 and +22 °C using H NMR line-broadening techniques, with an extrapolated value of 1.8 x 10 M s determined for 25 The kinetics of the outer-sphere oxidations of tris(polypyridine)chromium(II) complexes by a series of tris(chelate)cobalt(III) species have been studied in aqueous solution. " The cross-reaction rate constants obey the Marcus relationship, with the exception of [Co(bpy)3] " and [Co(phen)3] ", for which mild nonadiabaticity (/[Pg.18]

The rate constants and activation parameters (including AV ) for electron self-exchange in the [Mn(CNC(CH)3)6]-"/ -" and [Mn(CNC6Hu)6] couples have been determined by Mn NMR line broadening in several pure and binary organic solvent systems. The values of A V cover a range of about 12 cm moP (-9 to -21 cm mol ) with no simple correlation with solvent parameters observed. A self-exchange rate constant of 0.7 0.4 M" s" has been calculated for the [Mn(edta)(H20)] and [Mn(cdta)(H20)] couples from the application of the Marcus relationship to outer-sphere cross-reactions with a variety of metal complexes in aqueous solution. Deviations from the correlation were observed for the nonadiabatic reactions with osmium tris(polypyridine) complexes. 

The kinetics of several electron transfer reactions of the molybdenum cuboidal system [Mo4S4(edta)2]" ( = 2, 3, 4) with cross-reactants such as [Co(edta)]-, [Fe(edta)]-, [Co(dipic)2] , [Fe(H20)e], and [Pta ] -, have been investigated. The electron self-exchange rate constants determined for the [Mo4S4(edta)2] and [Mo4S4(edta)2] couples, by an application of the Marcus relationship, are 1.5 x 10 and 7.7 x 10 M s , respectively. The rate constants for the outer-sphere oxidation of two dimeric complexes, [MoW 0)2(p-edta-AT,lV )]2- and [W2(0)2(p-0)(p-S)(p-edta-Ar,iV )] -, by [IrCl ] in addic aqueous solution have been measured. While the oxidation of the former complex shows a simple second-order rate law, the kinetics of the oxidation of the latter complex exhibited a rate retardation in the presence of the [IrCl6] complex. 

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