Electrons stoichiometric number

Taking the rate limiting step in the electron transport chain to be trans-membrane proton translocation, which occurs about five times per sulfate consumed (Rabus et al., 2006), the average stoichiometric number x (entered into REACT as to = 1/x) for Reaction 18.7 is five. Sulfate reducers conserve about 45 kJ mol-1 of sulfate consumed (Qusheng Jin, unpublished data), so we set AGp to this value and m to one. From equations 18.12 and 18.14, then, we can write... 

In Chapter 7 general kinetics of electrode reactions is presented with kinetic parameters such as stoichiometric number, reaction order, and activation energy. In most cases the affinity of reactions is distributed in multiple steps rather than in a single particular rate step. Chapter 8 discusses the kinetics of electron transfer reactions across the electrode interfaces. Electron transfer proceeds through a quantum mechanical tunneling from an occupied electron level to a vacant electron level. Complexation and adsorption of redox particles influence the rate of electron transfer by shifting the electron level of redox particles. Chapter 9 discusses the kinetics of ion transfer reactions which are based upon activation processes of Boltzmann particles. 

It was pointed out by Hume-Rothcry 4 in 1926 that certain interns etallic compounds with close]y related structures but apparently unrelated stoichiometric composition can be considered to have the same ratio of number of valence electron to number of. atoms,. For example, the j8 phases of the systems Cu—Zti, Cu—-Alv and Ou -Sn are analogous in structure, all being based on the -4.5 arrangement their compositions correspond closely to the formulas CuZn, CusAl, and CtttSn. Considering copper to be univalent, zinc bivalent, aluminum trivalent, and tin quadrivalent, we see that the ratio of valence electrons to atoms has the value f for each of these compounds ... 

The stoichiometric number is introduced in complex multi-electron kinetics by assuming that the completion of the overall process represented by eqn. (126) requires the formation and decomposition of v identical activated complexes. 

In Equation (18b), the activity quotient is separated into the terms relating to the silver electrode and the hydrogen electrode. We assume that both electrodes (Ag+/Ag and H+/H2) operate under the standard condition (i.e. the H+/H2 electrode of our cell happens to constitute the SHE). This means that the equilibrium voltage of the cell of Figure 3.1.6 is identical with the half-cell equilibrium potential E°(Ag+l Ag) = 0.80 V. Furthermore, we note that the activity of the element silver is per definition unity. As the stoichiometric number of electrons transferred is one, the Nemst equation for the Ag+/Ag electrode can be formulated in the following convenient and standard way ... 

The charge number of the cell reaction is the stoichiometric number equal to the number of electrons transferred in the -> cell reaction as formulated. 

Redox equations are often written so that the absolute value of the stoichiometric number for the electrons transferred (which are normally omitted from the overall equation) is equal to one. 

Here Ox and Red represent the oxidized and reduced form of the substance respectively, a and b are stoichiometric numbers, while n is the number of electrons exchanged. If the numbers of moles on the two sides of the equilibrium are equal (that is a = b) we have a homogeneous redox system like those (i) to (v), in other cases as (vi) and (vii) it is called inhomogeneous. In the simplest cases a = b = 1, when the system can be written as... 

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. 

Finally, here it should be noted formally that a is, of course, identical with in cases where the initial step in a reaction sequence is a one-electron charge transfer process and is itself the rate-controlling process. Also b can be related to the total number of electrons passed in the overall reaction or in the rate-controlling step through a and the stoichiometric number v. This matter has, however, been treated in various earlier works by, e.g., Horiuti and Ikusima, Bockris, and Gileadi, and so need not be examined again here since no involvement of the temperature variable arises apart from that in b itself. 

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. 

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. 

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