Stoichiometric number general formulation

In many electrochemical reactions the individual steps differ in their stoichiometric numbers, in contrast to what was found for reactions of the type of (13.2). A two-step reaction can generally be formulated as... 

It can readily be shown that eqn. (27) is equivalent to the quasi-steady-state condition in its general formulation. In unit time and in unit reaction space there forms Tint w of an intermediate, where Tint is the stoichiometric intermediate matrix. Let us recall that the dimension of Fint is (/tot x S), where 7tot is the total number of independent intermediates and S is the number of steps. After substituting uj from eqn. (27), we obtain... 

One must not underestimate, however, the importance of the general results obtained in terms of the steady-state reaction theory. Its informative concepts are used in theoretical kinetics, in particular the concept of Horiuti (stoichiometric) numbers and a new formulation for the steady-state... 

A feasible reaction scheme includes all the reactants and products, and it generally includes a variety of reaction intermediates. The validity of an elementary step in a reaction sequence is often assessed by noting the number of chemical bonds broken and formed. Elementary steps that involve the transformation of more than a few chemical bonds are usually thought to be unrealistic. However, the desire to formulate reaction schemes in terms of elementary processes taking place on the catalyst surface must be balanced with the need to express the reaction scheme in terms of kinetic parameters that are accessible to experimental measurement or theoretical prediction. This compromise between molecular detail and kinetic parameter estimation plays an important role in the formulation of reaction schemes for analyses. The description of a catalytic cycle requires that the reaction scheme contain a closed sequence of elementary steps. Accordingly, the overall stoichiometric reaction from reactants to products is described by the summation of the individual stoichiometric steps multiplied by the stoichiometric number of that step, ai. 

A general relationship between Zintl-Klemm concept and defect formation has been formulated [15, 16] recently. For a compoimd AaB, nstoichiometric numbers) the total number of valence electrons E per formula unit relates to the average number of bonds per atom N and to the number of defects d. 

The formulation of the path probability function entirely depends on the kinetics assumed in the study. The vacancy-mediated kinetics or the exchange kinetics(Kawasaki dynamics ) requires a large number of path variables which make numerical operations intractable. The spin flipping kinetics(Glauber dynamics ) generally does not conserve the species with time, however the conservation is assured at 1 1 stoichiometric composition without imposing any additional constraints. In this regard, the spin system... 

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