Bimolecular rate constant, relation

Table 1. A compilation of specific bimolecular rate constants (/tc) for the reaction of hydrated electrons with Li battery related materials (61,62]...

Some related work has been undertaken with aluminum cations150 for purposes of comparison to the anion work. Bimolecular rate constants were measured for the disappearance of Al+ through Aljj. We did not observe a slow rate for the reaction of AI3 which would be expected to have a closed electronic shell and hence would be expected to be comparatively unreactive. However, in the case of the cations, oxidation often leads to the retention of an oxide unit on the cation in contrast to the anion work. 

Apparent site-specific bimolecular rate constant, obtained by relating the kB app iimol-gcat."1 s"1) to the concentration of Bronsted acid sites (pmol-gc., 1). 

Compound I will accept a further electron from azurin and decays to a species known as compound II with a bimolecular rate constant of 6 X 10 M s (84). It is anticipated that compound II is a form of CCP containing two ferric hemes, but possibly not identical to the structurally defined fully oxidized enzyme as isolated. This is because during turnover at room temperature there is no obvious reason for the histidine ligand displaced from the peroxidatic heme iron to return. Consequently, it might be assumed that compound II is structurally related to the MV conformer rather than the resting enzyme. 

This simplified approach is analogous to the more rigorous absolute rate treatment. The important conclusion is that the bimolecular rate constant is related to the magnitude of the barrier that must be surmounted to reach the transition state. Note that there is no activation barrier (/.e., that AG = 0) in cases where no chemical bond is broken prior to chemical reaction. One example is the combination of free radicals. (In other cases where electrons and hydrogen ions can undergo quantum mechanical tunneling, the width of the reaction barrier becomes more important than the height.)... 

Pick s laws describe the interactions or encounters between noninteracting particles experiencing random, Brownian motion. Collisions in solution are diffusion-controlled. As is discussed in most physical chemistry texts , by applying Pick s Pirst Law and the Einstein diffusion relation, the upper limit of the bimolecular rate constant k would be equal to... 

Moving leftward, we express ki as the real forward rate constant (in this case ki) multiplied by a factor that relates the fraction of ES reacting in the forward direction as opposed to the fraction that returns to E. [Note All of these constants are unimolecular rate constants, and all bimolecular rate constants must be multiplied by the concentration of substrate or product. This will become clearer in the later steps of this algorithm for deriving rate equations.] In this case, we get ... 

The value of ket > 6 x 108 cm8mol ls - - in the usual units for a bimolecular rate constant for homogeneous solution is > 6 x 105 M-ls l. The ferrocene self-exchange constant is 5 x 106 M-Ts-1 (29). Various cross reactions of substituted ferrocenes and ferricenium derivatives have bimolecular rate constants that exceed 10 M - -s l where the equilibrium constant exceeds unity (30). Further, in the cross reactions, the rate constants varied by almost two orders of magnitude for a change in driving force of -0.25 V (30). Thus, the data in Table II relating to the ferrocene-like molecules is reasonable. 

We begin by establishing the relation between the so-called reaction cross-section bimolecular rate constant. Let us consider an elementary gas-phase reaction,... 

This equation relates the bimolecular rate constant to the state-to-state rate constant ka(ij l) and ultimately to vap(ij, v l). Note that the rate constant is simply the average value of vcrR(ij,v l). Thus, in a short-hand notation we have ka = (vap(ij,v l)). The average is taken over all the microscopic states including the appropriate probability distributions, which are the velocity distributions /a va) and /b( )(vb) in the experiment and the given distributions over the internal quantum states of the reactants. 

Broadly speaking, dynamic electron transfer involves two steps. The first step is the diffusion controlled formation of an encounter complex between the electron/hole acceptor molecule and the particle. The second step is the electrochemical interfacial charge-transfer, which may be characterized by a rate constant kct. Albery et al. [143] and Gratzel et al. [129] have independently arrived at the same result, relating the observed effective bimolecular rate constant for hole/electron acceptor oxidation/re-duction, /cobs (m3mor s I) to reactant diffusion and A ct. 

The magnitude of km, the experimentally determined bimolecular rate constant for chemiluminescence, is related to several of the rate constant specified in Fig. 8. The data on the hydrocarbon- or amine-activated chemiluminescence indicated that kJ0 > k ACT. Thus simple analysis of the kinetics yields (33), where Kn is the equilibrium constant for complex... 

Figure 2.12 illustrates schematically the essential features of the thermodynamic formulation of ACT. If it were possible to evaluate A5 ° and A// ° from a knowledge of the properties of aqueous and surface species, the elementary bimolecular rate constant could be calculated. At present, this possibility has been realized for only a limited group of reactions, for example, certain (outer-sphere) electron transfers between ions in solution. The ACT framework finds wide use in interpreting experimental bimolecular rate constants for elementary solution reactions and for correlating, and sometimes interpolating, rate constants within families of related reactions. It is noted that a parallel development for unimolecular elementary reactions yields an expression for k analogous to equation 128, with appropriate AS °. 

However, the bimolecular rate constant changes as a function of the pK of the nucleophilic group according to the Bronsted relation (eq. 4.12) where y is a reaction constant which depends on the nature of the modification reaction and p describes the sensitivity of a series of nucleophiles on the pK. ... 

Encounter of excited sensitizer with the electron relay leads to the formation of a precursor complex. The electron transfer event occurs within this pair to yield a successor complex. The latter subsequently dissociates into free product ions or reacts back to the starting material. When the stationary state approximation is used the observed (bimolecular) rate constant for product formation can be related to the specific rates of the individual steps in Scheme I by ... 

It is the current flowing between oxidized and reduced sites (of concentrations a and 6, respectively), in the polymer when AG = 0 (i.e., when AE = = 0). The exchange current density is related to the bimolecular rate constant ke,E for self-exchange under conditions of a potential gradient. This latter quantity is given by Marcus theory according to the following expression ... 

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