Electron number coefficients

The preceding/following electron-number coefficients (y) used here are slightly different and less general than those employed by B R (namely, Yp and y ) in their transfer coefficient analysis D3q. (1)]. They are, however, related and for a preceding dissociation, the expressions that link them are 

Substitution of these y, and expressions into the B R transfer coefficients [Eq. (1)] immediately demonstrates the equivalence of the derivations. Although, practically speaking, it is difficult to imagine examples where the stoichiometry-determining step would be far separated from the rds, we believe that the expanded transfer coefficients derived here are expressed in a fashion that is more directly relevant to their use in determining mechanism. 

The present notation, while requiring a distinction between combination and dissociation cases, shows clearly and specifically how the type of mechanism involved determines the transfer coefficients. In addition, substituting v= 1 into either of the above coefficients [Eq. (62) or (63)] reduces them to those for a simple consecutive electrochemical reaction, Eqs. (33a) and (33b). 

the conclusion is that for a preceding dissociation or a following combination, either of the non-rds terms, Jp/v or yffy, can be fractional, but the other must be a whole number. This is an important point that is not otherwise apparent In fact we have found that just such an error has been made in an analysis of the mechanism of the reaction of aluminum electroplating from a hydride hath. This error was found to he due entirely to the mistaken assumption that both anodic and cathodic non-rds terms (i.e., Yp/V and Y//V), of B R s theoretical transfer coefficients [Eqs. (la) and (lb)] could simultaneously give fractional contributions and so account for the transfer coefficients that had been derived from experimental Tafel plots. 

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At first this would appear to be a reasonable conclusion, but upon reevaluation of how a stoichiometric number becomes incorporated into the transfer coefficients, this mechanism cannot be correct since it has been shown in this review (Section VI) that it is impossible for both non-rds electron-number coefficients to be fractional. So, although one of those could be fractional, giving, say, 1/3, the other non-rds contribution would have to be a whole number integer. With this in mind, it is evident that the experimentally derived transfer coefficients for the A1 reaction, given that they are all near to about 1/2 for both bath types, must describe the transition state of the rds. 

Radical Position of odd electron Number of structures Relative values of coefficients... 

In order to calculate the rates for electron impact collisions and the electron transport coefficients (mobility He and diffusion coefficient De), the EEDF has to be known. This EEDF, f(r, v, t), specifies the number of electrons at position r with velocity v at time t. The evolution in space and time of the EEDF in the presence of an electric field is given by the Boltzmann equation [231] ... 

In a fluid model the correct calculation of the source terms of electron impact collisions (e.g. ionization) is important. These source terms depend on the EEDF. In the 2D model described here, the source terms as well as the electron transport coefficients are related to the average electron energy and the composition of the gas by first calculating the EEDF for a number of values of the electric field (by solving the Boltzmann equation in the two-term approximation) and constructing a lookup table. 

Half-reactions can be added to produce a net reaction, which is the oxidation-reduction reaction. However, this summation cannot be performed unless the electron numbers are the same on both sides of the reaction by agreement among chemists, electrons are not written into summation reactions. The way in which adjustments are made is to preserve the ratio of coefficients in the individual balanced half-reaction by multiplying all of the participants in an equation by the same number. The goal is to have the same number of electrons on opposite sides of the half-reactions. The electrons will then algebraically cancel when the half-reactions are added. Since the summation equation should not have coefficients divisible by a common factor, it is customary to choose numbers that will yield the least number of electrons for cancellation. 

A MCP is used in the PIMMS as a secondary electron multiplier (see Sect. 3.7). The electron current measured after MCP compared to the initial ion current is amplified by a factor of 10-1,000. The secondary electron emission coefficient is an averaged number of secondary electrons emitted after each impact. This number depends on the initial energies of the electrons or ions and so on the voltage applied to the MCP. The amplification factor of a MCP configuration is expressed as ... 

This is only an approximate representation, in which a is the transfer coefficient and na is the apparent electron number involved in the pseudo-elementary reaction. This na is different from the total electron transfer number of the reaction ( ). 

Another evident mechanism for energy transfer to activated ions may be by bimolecular collisions between water molecules and solvated ion reactants, for which the collision number is n(ri+ r2)2(87tkT/p )l/2> where n is the water molecule concentration, ri and r2 are the radii of the solvated ion and water molecule of reduced mass p. With ri, r2 = 3.4 and 1.4 A, this is 1.5 x 1013 s"1. The Soviet theoreticians believed that the appropriate frequency should be for water dipole librations, which they took to be equal 10n s 1. This in fact corresponds to a frequency much lower than that of the classical continuum in water.78 Under FC conditions, the net rate of formation of activated molecules (the rate of formation minus rate of deactivation) multiplied by the electron transmission coefficient under nonadiabatic transfer conditions, will determine the preexponential factor. If a one-electron redox reaction has an exchange current of 10 3 A/cm2 at 1.0 M concentration, the extreme values of the frequency factors (106 and 4.9 x 103 cm 2 s 1) correspond to activation energies of 62.6 and 49.4 kJ/mole respectively under equilibrium conditions for adiabatic FC electron transfer. 

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