Effect of Driving Force

Mention has been made previously of the possibility that the maximum electron-transfer rate observed in a series of reactions, as the driving force is increased, may be due to the onset of diffusion control, unrelated to the redox properties of the reactants. This has usually been discussed by amending the value of Z in the Marcus equation (1). Thus for uncharged reactants in water at room temperature Za 10 M s, but for like-charged reactants it may be very much less. Brunschwig and Sutin have now proposed a different formulation in which Z is a parameter independent of the encounter rate. Writing the general bimolecular electron-transfer mechanism as 

This series, Vol 5, p. 5, and references cited therein cf. also Vol. 6, p. 11. 

The limiting cases are ko =ki, when kz k-i, in the diffusion-controlled limit, and 

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Some of the new theoretical relations, the cross-relation between the rates of a cross-reaction of two difierent redox species with those of the two relevant selfexchange reactions, were later adapted to non-electron transfer reactions involving simultaneous bond rupture and formation of a new bond (atom, ion, or group transfer reactions). The theory had to be modified, but relations such as the crossrelation or the effect of driving force (—AG°) on the reaction rate constant were again obtained in the theory, in a somewhat modified form. For example, apart from some proton or hydride transfers under special circumstances, there is no predicted inverted effect. Experimental confirmation of the cross-relation followed, and an inverted effect has only been reported for an H+ transfer in some nonpolar solvents. The various results provide an interesting example of how ideas obtained for a simple, but analyzable, process can prompt related, yet different, ideas for a formalism for more complicated processes. 

Effect of driving force on porphyrin-quinone electron transfer rates... 

FFF methods make use of the formation of an exponential concentration distribution of each sample component across the channel with the maximum concentration at the accumulation wall, which is a consequence of constant and position-independent velocity of transversal migration of the affected species due to the field forces. This concentration distribution is combined with the velocity profile formed in the flowing liquid. Focusing FFF methods make use of transversal migration of each sample component under the effect of driving forces that vary across the channel. As a result, the sample components are focused at the positions where the... 

In the following sections, we shall explore the applicability of such relationships to experimental data for some simple outer-sphere reactions involving transition-metal complexes. In keeping with the distinction between intrinsic and thermodynamic barriers [eq 7], exchange reactions will be considered first, followed by a comparison of driving force effects for related electrochemical and homogeneous reactions. 

Mass transfer. It is not yet possible to predict the mass transfer coefficient with a high degree of accuracy because the mechanisms of solute transfer are but imperfectly understood as discussed Light and Conway(14), Coulson and Skinner(15) and Garner and Hale 16 1. In addition, the flow in spray towers is not strictly countercurrent due to recirculation of the continuous phase, and consequently the effective overall driving force for mass transfer is not the same as that for true countercurrent flow. 

Similar to those for rotaxanes, different approaches have been employed for poly-rotaxane syntheses these will be summarized in the next section. The most important parameter in polyrotaxanes, the min value, is often employed as a measure of the effectiveness of the preparation method. Because this value mainly depends on the strength of the attractive force between the cyclic and the backbone, this section is again divided into subsections according to the types of driving forces rather than the types of polyrotaxanes. 

If we decrease the air rate (i.e., increase L G), then in effect the driving force is decreased and a greater degree of difficulty is reflected in the form of a larger value for Ntu(. This is illustrated by the enthalpy-temperature diagram of Figure 6.1. The plot reflects a counterflow cooling tower at constant conditions but variable L G ratios. 

The effect of condensation upon transfer rates with application to flue-gas washing plants and cooling towers are discussed. Theoretical models were developed for determining the rate of heat and mass transfer under conditions where fog formation prevails. Derived relationships are functions of the vapor and liquid equilibria and local heat and mass transfer of driving forces. They were used for a numerical study of the amount of fog formation as a function of the operational variables of a flue-gas washing plant in which the inlet gas temperature is typically... 

Equilibrium thermodynamics is the most important, most tangible result of classical thermodynamics. It is a monumental collection of relations between state properties such as temperature, pressure, composition, volume, internal energy, and so forth. It has impressed, maybe more so overwhelmed, many to the extent that most were left confused and hesitant, if not to say paralyzed, to apply its main results. The most characteristic thing that can be said about equilibrium thermodynamics is that it deals with transitions between well-defined states, equilibrium states, while there is a strict absence of macroscopic flows of energy and mass and of driving forces, potential differences, such as difference in pressure, temperature, or chemical potential. It allows, however, for nonequilibrium situations that are inherently unstable, out of equilibrium, but kinetically inhibited to change. The driving force is there, but the flow is effectively zero. 

In some recent experiments (14) on rates of oxidation by Fe3+ of a number of related Ru(II) species, the rates of the self-exchange reactions for Ru(III)-Ru(II) couples and the equilibrium data were measured as much as possible under uniform conditions. In determining self-exchange rates, a series of reactions of the type Ru(NH3)5L2+ + Ru(NH3)5L 3+ were studied in which L and L are pyridines which differ in one substituent in the 3 or 4 position. No rate differences ascribable to differences in L and L were observed, apart from the effect on driving force. The result of these studies are summarized in Table I. 

Unlike the case of batteries, the loss of driving force is, of course, a welcome effect in corrosion. It is well known, for example, that the corrosion rate in poorly conducting solutions is lower than that in highly conducting media. 

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