Cross reaction rate

The cross reaction rates and self-exchange rates predict ket > 6 x 10 provided that the surface-confined reagent... 

The results of kinetic studies of the reduction of stellacyanin, plastocyanin, and azurin by Fe(EDTA)2" are summarized in Table III (20, 21). The order of cross reaction rate constants (ki2 values) is stellacyanin > plastocyanin > azurin, which is surprising, as considerations based on driving force alone would predict stellacyanin to be the least reactive of... 

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. 

In fact, a comparison of the observed cross-reaction rate constants and those calculated from the Marcus-Hush s Eq. (104) indicates that in most cases the amount of nonadiabaticity cannot be neglected. The observed rate constant values are much smaller than the calculated ones even for structurally very similar complexes. Thus, the correction factor p = p 2l p pny is substantially smaller than 1. This result has been interpreted in terms of metal-ligand charge transfer in the ion pairs formed in solution [363, 367] the Log p correlates with E(CT), where E CT) is the expected energy of a [CoL]3+,..X [CoL]2+...X transfer in the ion pair. The effect of... 

Marcus theory has been so successful in predicting cross reaction rates in outer-sphere electron transfer reactions that it is often used to give evidence that an outer-sphere reaction is taking place. If the observed rate constant is within an order of magnitude of the calculated rate constant, then it is likely that an outer-sphere mechanism is occurring. In this way, you will use Marcus theory to give evidence for the reaction mechanism assigned to your rate constant, kos, determined in Experiment 5.5. 

Equation 7 0a has been used to extract the ratio of rate constants from the final fraction of Y in the reactions of Scheme 29.94 The cross-reaction rate constant was found to be considerably smaller than diffusion-controlled values, and it is similar to the rate constants for the coupling of transient radicals with nitroxides (Table 1) or the deactivation step in ATRP (Table 2). 

The reactions of Eu and V give too low a prediction of cross-reaction rate when K,j is large in fact. In (k j /k, ) is a roughly linear function of In with negative slope of ca. 0.1. Likewise, comparison of ca. 40 reactions shows that ... 

For these reactions, AG° 0. The experimental measurement of cross-reaction rates is generally more straightforward than the measurement of self-exchange rates. Either the reactants are simply mixed together, or a thermodynamically unstable system is generated rapidly (via pulse radiolysis, flash photolysis, or temperature-jump relaxation) to initiate the redox reaction. Absorption spectroscopy has almost always been used to monitor the progress of protein cross reactions. The primary goal of theory, as will become evident, is to provide a relationship between AG° and AG" " for cross reactions. 

When the self-exchange rates ki i are corrected for work terms or when the latter nearly cancel, the cross-reaction rate ki2 is given by the Marcus cross relation,... 

R in the upper right comer of the diagram, which also shows the normalized concentration profiles of A and Q (see also Figure 14.4.5). If we now consider this case as decreases, so that movement of A in the film becomes slower, we find a change in behavior, first to Case R + S and then to Case SR. In the latter case, which often occurs in practical studies, both the cross-reaction rate and diffusion of A in the film affect the behavior. The relevant expressions for the various limiting cases and subcases are given in Table 14.4.1. In this table i is the plateau current corresponding to reduction of A via reaction with Q (the catalytic reaction) and 1 2 represents the plateau current for the direct reduction of A. The latter is observed only in certain situations where A can penetrate the film and reach the metal substrate before it is all consumed by reaction with Q. For example, one can see in Table 14.4.1 that Case SR will produce a linear Koutecky-Levich plot (l/ij vs. or l/ij vs. 1//a) with an intercept of l/ip + l/(/j /s). Also, 1 2 = for this case. 

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]

TABLE 10.5 Observed Cross-Reaction Rate Constants, ky (M s ), Reaction Free Energies, (kcal/mol). Reorganization Energies,... 

Further derivations are simplified if what is known as the copolymerization parameter, or reactivity ratio, r, is defined as the ratio of homoreaction to cross-reaction rate constants ... 

The Marcus theory also allows to compare homogeneous electron-transfer reactions with the same reactions at electrode surfaces and cross-reaction rates in terms of the individual self-exchange reactions, that is, A.i 2 = l/2(A.i4 + 2.2,2)-Experimental verification over 20 orders of magnitude has been the greatest success of this theory. 

S.S. Kristjansddttir and J.R. Norton, Agreement of proton transfer cross reaction rates between transition metals with those predicted by Marcus theory, J. Am. Chem. Soc., 113 (1991) 4366. 

Equation 3 indicates that for redox-polymer mediated reactions that comply with "SR kinetics, fast mediator-substrate cross-reaction rates (large ik) and poor substrate permeation through the polymer phase (low is) will tend to decrease the thickness of the reaction zone. Situations may thus arise in which only the outermost layers of mediator sites attached to the coating participate in the reaction with substrate. Such a surface process is observed for the oxidation of catechol at a carbon electrode modified with a Nation film containing Fe(bipy)3 + as mediator. The homogeneous solution rate constant for the oxidation of catechol by Fe(bipy)3 is estimated a to be 2 x 10 and is roughly 1000 times... 

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