Stoichiometric numbers greater than

The effect of the occurrence, within a generalized reaction scheme, of chemical steps, multielectron transfers, or an rds that is a dissociation or combination step (i.e., one that involves a change of stoichiometric coefficients) wiU be examined as well as mechanisms where the rds (and hence the ovCTaU reaction) has a stoichiometric number greater than 1. This latter case is more complicated than these others and, since it is the only mechanistic situation in a consecutive reaction scheme that can give... 

Reaction Mechanisms Involving a Stoichiometric Number Greater than 1... 

In the closed reaction sequences considered in this work, stoichiometric numbers greater than 1 can arise only in order to satisfy a material balance for a reaction step preceding or following the rds that creates or consumes V intermediates in a single transition state. 

We now turn to two of the problems we have sidestepped until now. In this section we consider the polymerization of reactants in which a stoichiometric imbalance exists in the numbers of reactive groups A and B. In the next section we shall consider the effect of monomers with a functionality greater than 2. 

A catalytic reaction is one in which more than one turnover or event occurs per reaction center or catalytically active site (that is, the turnover number [TON] is greater than 1). Thus a reaction is not catalytic if it is stoichiometric or if its TON is less than 1. A reaction might indeed involve a true catalyst and under some circumstances be catalytic, but if one or fewer turnovers occur per active site, it is not a catalytic reaction. 

The compound will be stoichiometric, with an exact composition of MX10ooo when the number of metal vacancies is equal to the number of nonmetal vacancies. At the same time, the number of electrons and holes will be equal. In an inorganic compound, which is an insulator or poor semiconductor with a fairly large band-gap, the number of point defects is greater than the number of intrinsic electrons or holes. To illustrate the procedure, suppose that the values for the equilibrium constants describing Schottky disorder, Ks, and intrinsic electron and hole numbers, Kc, are... 

An expression of this kind is known as the rate equation for the reaction. The indices, m and n, are the orders of the reaction with respect to A and B, respectively, and you will notice that they bear no relation to the stoichiometric coefficients a and b. The reaction is said to be m order with respect to A and n order with respect to B. The orders, m and n, are usually small whole numbers (including zero) and are rarely greater than two. 

This limitation was recognized by Milner (5), who introduced the concept of direct paths, each of which is unique in the sense that it cannot be considered to result from the superposition of any other member of the set of elementary reactions. Milner applied this idea to the enumeration of mechanisms for a number of simple overall reactions involving electrochemistry. He arrived at the rule that for such a reaction the number of nonzero stoichiometric numbers specifying a direct path can be no more than one greater than the number of intermediates. By a trial-and-error procedure he was able to count all mechanisms consistent with a given choice of possible unit steps. 

Let us point out that the minimum number of invariants is equal to c = c— s, i.e. to the number of independent constituents the corresponding invariants are classically obtained by doing the mass balances for each element. But it has been seen that it is possible, in fact, to have a number, s, of stoichiometric equations less than s = c —c if this happens, the number of invariants is greater than the number, c, of independent constituents or of elements involved in the system. Consequently, the invariant theory provides an optimal exploitation of the stoichiometric results. 

The second limits are quite reproducible over long periods using the same apparatus, and the limits from independent investigations also agree well. This is shown by Table 6, wliich quotes limits for stoichiometric mixtures in potassium chloride coated vessels. According to Willboum and Hinshelwood [27] the use of a number of similar coatings (KCl, KI, CsCl, Csl) does not alter the limit much. The results of Lewis and von Elbe [23] and Warren [25] in Table 6 also show that the limit is virtually independent of vessel diameter, provided the latter is greater than 4—5 cm. Clearly the limits are not determined primarily by competition between gas phase and wall effects. 

It is at this point that we depart from the terminology used by Bockris and Reddy (Ref. 3, p. 1007) in their often-cited and generalized discussion of transfer coefficients [Eqs. (la) and (lb)] (i.e., and y ) and introduce the related terms y. and y p. The difference between these sets of electron-number parameters is that in the latter, an electron transferred in a step that occurs, say, v times (i.e., it has a stoichiometric number v greater than 1) is counted only once and not the v times it actually has to occur for one turnover of the overall reaction. This added complication of the electron accounting has the advantage of showing more clearly how stoichiometric coefficients and numbers enter into experimentally obtainable transfer coefficients and hence can demonstrate one of the links between mechanism and experiment. 

Tafel slopes that are not infinite but are substantially greater than 118 mV dec- can be explained by (1) an arbitrary and trivial assumption that P < 1/2 (2) the effect (footnote f) of barrier-layer films such as oxide on Zr02 or Ti0242 (but this is usually only in the case of anodic reactions, particularly those involving valve-metal barrier oxide films) and (3) an electrochemical reaction mechanism where the rds is a chemical step and has a stoichiometric number, v, greater than 2 [refer to Eq. (1)]. This latter possibility will be developed in the next section in terms of a general multistep reaction mechanism. 

Definitions. Early in the history of chemical kinetics a catalyst was defined as a chemical species that changes the rate of a reaction without undergoing an irreversible change /fse//(Ostwald, 1902). Subsequent definitions of a catalyst included (1) a catalyst is a chemical species that may be chemically altered but is tan involved in a whole number stoichiometric relationship among reactants and prodacts and (2) a catalyst is a chemical species that appears in the rate law with a reaction order greater than its stoichiometric coefficient. In the latter case it was realized that either a product of the reaction (autocatalysis) or a reactant may also function as a catalyst. From a practical perspective, a catalyst is a chemical species that influences the rate of a chemical reaction regardless of the fate of the catalytic species. However, a catalyst has no influence on the thermodynamics of n reaction. In other words, the concentration of a catalyst is reflected in the rate law but is not reflected in the equilibrium constant. This latter definition was modified and approved by the International Union of Pure and Applied < hemistry (IUPAC, 1981) to read as follows ... 

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