Rate-determining step transfer coefficient

Rate of Formation of Primary Precursors. A steady state radical balance was used to calculate the concentration of the copolymer oligomer radicals in the aqueous phase. This balance equated the radical generation rate with the sum of the rates of radical termination and of radical entry into the particles and precursors. The calculation of the entry rate coefficients was based on the hypothesis that radical entry is governed by mass transfer through a surface film in parallel with bulk diffusion/electrostatic attraction/repulsion of an oligomer with a latex particle but in series with a limiting rate determining step (Richards, J. R. et al. J. AppI. Polv. Sci.. in press). Initiator efficiency was... 

In the case of Tl(III) the overall rate coefficient has been resolved into a product kK for the two steps The large positive AS is due almost entirely to the initial association, which was also studied spectroscopically. An alternative rate determining step in the Pd(II) oxidation is hydride ion transfer to Pd(II) . 

Here A(g) and B(g) denote reactant and product in the bulk gas at concentrations CA and Cg, respectively kAg and kBg are mass-transfer coefficients, s is an adsorption site, and A s is a surface-reaction intermediate. In this scheme, it is assumed that B is not adsorbed. In focusing on step (3) as the rate-determining step, we assume kAg and kBg are relatively large, and step (2) represents adsorption-desorption equilibrium. 

Examination of the peak potential locations and transfer coefficient values in a series of 16 cyclic and acyclic dibromides according to the procedures detailed in Chapter 3 points to a first dissociative electron transfer rate-determining step (Scheme 4.1). It is followed by another dissociative electron transfer step, leading directly to the olefin. Intrinsic barriers for the first, rate-determining step range from 0.6 to 0.8 eV, consisting mostly of the bond dissociation contribution (one-fourth of the bond dissociation energy). 

In this equation, aua represents the product of the coefficient of electron transfer (a) by the number of electrons (na) involved in the rate-determining step, n the total number of electrons involved in the electrochemical reaction, k the heterogeneous electrochemical rate constant at the zero potential, D the coefficient of diffusion of the electroactive species, and c the concentration of the same in the bulk of the solution. The initial potential is E/ and G represents a numerical constant. This equation predicts a linear variation of the logarithm of the current. In/, on the applied potential, E, which can easily be compared with experimental current-potential curves in linear potential scan and cyclic voltammetries. This type of dependence between current and potential does not apply to electron transfer processes with coupled chemical reactions [186]. In several cases, however, linear In/ vs. E plots can be approached in the rising portion of voltammetric curves for the solid-state electron transfer processes involving species immobilized on the electrode surface [131, 187-191], reductive/oxidative dissolution of metallic deposits [79], and reductive/oxidative dissolution of insulating compounds [147,148]. Thus, linear potential scan voltammograms for surface-confined electroactive species verify [79]... 

In the second mechanism, the first and second steps are concerted. In the case of hydrolysis of 2-(p-nitrophenoxy)tetrahydropyran, general acid catalysis was shown470 demonstrating that the substrate is protonated in the rate-determining step (p. 259). Reactions in which a substrate is protonated in the rate-determining step are called A-Se2 reactions.471 However, if protonation of the substrate were all that happens in the slow step, then the proton in the transition state would be expected to lie closer to the weaker base (p. 259). Because the substrate is a much weaker base than water, the proton should be largely transferred. Since the Brpnsted coefficient was found to be 0.5,the proton was actually transferred only... 

E vs. log(id-i)/f which should be linear with a slope of 59.1/n mV at 25 °C if the wave is reversible. This method relies however upon a prior knowledge of n, and if this is not known then the method is not completely reliable as theory predicts that when the electron transfer process itself is slow, so that equilibrium at the electrode between the oxidized and reduced forms of the couple is established slowly and the Nemst equation cannot be applied, then an irreversible wave is obtained and a similar plot will also yield a straight line but of slope 54.2/ana mV at 25 °C (a = transfer coefficient, i.e. the fraction of the applied potential that influences the rate of the electrochemical reaction, usually cu. 0.5 na = the number of electrons transferred in the rate-determining step). Thus a slope of 59.1 mV at 25 °C could be interpreted either as a reversible one-electron process or an irreversible two-electron process with a = 0.45. If the wave is irreversible in DC polarography then it is not possible to obtain the redox potential of the couple. 

This is the steady-state current which is theoretically predicted if stage 1 is the rate-determining step in the sub-stages sequence represented in Equations 4.8 1.12. An important parameter to compare both in theory and experimentally is the Tafel slope or the transfer coefficient which results from it. Therefore, Equation 4.30 has to be written in a form that contains only one exponential term. Since the considered I-E curve is an oxidation wave, the effect of the reduction (second term in the right-hand part of Equation 4.30) will be negligible with potentials that are situated sufficiently far away from the equilibrium potential, and for the anodic current the following applies ... 

The first mechanism (a) occurs if fe t < k2 and the observed rate coefficient is given by feobs = k1. The second mechanism (b) applies if fe i > fe2 and then kohs = k2 x K where K = fe1 /fe j. The two mechanisms which correspond, respectively, to a rate-determining proton transfer and a pre-equilibrium followed by a subsequent step have been discussed in detail for isotope exchange reactions in Sect. 2.2.1. The second possibility (b) is apparently favoured by Cram [120] for racemization of 2-methyl-3-phenylpropionitrile whereas Melander [119] has interpreted his results in terms of the first (a). From the variation of the rate coefficient for racemization in different solvent mixtures of methanol/ dimethylsulphoxide a Bronsted exponent j8 = 1.1 was calculated [119] using an acidity function method which will be described fully in Sect. 4.6. 

In this section rate-equilibrium correlations for proton transfer to olefins and aromatic systems will be discussed. Although the kinetic behaviour varies from one unsaturated system to another some general features will become apparent. Most results for proton transfer involving unsaturated carbon have been obtained by studies of an overall reaction in which proton transfer to carbon is involved as a rate-determining step. The mechanisms of reactions of this type were discussed in Sects. 2.2.3 and 2.2.4. In these cases the rate coefficient for proton addition to form a carbonium ion is obtained. However, a few examples will be described where the equilibrium between an unsaturated system and a carbonium ion has been measured giving rate coefficients in both directions. 

It is interesting to note that the symmetry factor P did not appear in any of these equations. This is because the rate-determining step assumed here does not involve charge transfer. The current depends indirectly on potential, through the potential dependence of the fractional coverage 0. The transfer coefficient is = 2, as can be seen in Eq. 43F, corresponding to a Tafel slope of b = - 30 mV at room temperature. 

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