Marcus cross-exchange relationship

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. 

Table 6.4. Self-Exchange Rate Constants (M s , 25°C) Obtained by Fitting to the Marcus Cross Relationship...

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

A thermodynamic derivation of the Marcus cross relationship [equation (1)], where and 22 are the self-exchange... 

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. 

Thus the Marcus theory gives rise to a free energy relationship of a type similar to those commonly used in physical organic chemistry. It can be transformed into other relationships (see below) which can easily be subjected to experimental tests. Foremost among these are the remarkably simple relationships that were developed (Marcus, 1963) for what have been denoted cross reactions. All non-bonded electron-transfer processes between two different species can actually be formulated as cross reactions of two self-exchange reactions. Thus the cross reaction of (59) and (60) is (61), and, neglecting a small electrostatic effect, the relationship between kn, k22 and kl2... 

A, direct measurement of the exchange reaction B, estimate of the self-exchange rate by application of the Marcus relationship to cross reactions. 

Another widely used result of Marcus theory deals with the extraction of useful kinetic relationships for cross reactions from parameters for self-exchange reactions. Consider the cross reaction, Equation (6.22), for which 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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