Number stoichiometric

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. 

The stoichiometric number, v, of a given reaction step is defined as the number of times that step must occur for one turnover of the whole reaction. The overall stoichiometric number of a reaction is specifically the number of times the rds has to occur. This is an important quantity with respect to mechanism elucidation and was originally defined by Horiuti for the hydrogen reaction.45,46 According to the stoichiometric number concept of Horiuti, V for each reaction step will multiply the Gibbs energy change (or as it is also called, its electrochemical affinity) for that step, Agi, and the affinity, AG, for the overall reaction is 

In this derivation, since it is assumed that a single step, the rds, limits the rate of the overall reaction, all other steps must be in quasi-equilib- 

Equation (50) forms the basis upon which v can be evaluated (e.g. (1) by the radioactive tracer method to evaluate simultaneously and ), (2) by comparing i values at appropriate potentials for different reactant activities (3) coupling information from high and low overpotential regions of steady-state polarization curves (extrapolated io and charge-transfer resistance, Rcr, respectively) (4) or by back-reaction correction analysis. 2 qqie first two methods involve determination of v at any single potential while the latter two procedures must assume that the same mechanism (and hence v) applies at different potentials (at which individual measurements are required) and that the reverse reaction occurs by the same path and has the same transition state and thus rate-determining step [for both forward (cathodic) and reverse reactions]. 

The third method listed above is based upon the relation 

The equations for multistep electron transfer according to the quasiequilibrium treatment can be derived on the basis of Parsons general and rigorous treatment [47]. For simplicity, mass transport limitations, double layer effects, ohmic overpotential, and specific adsorption or chemisorption are neglected in the present formalism. 

According to the absolute rate theory, the rate of the overall reaction corresponding to eqn. (126) is equal to the rate of decomposition of the activated complex corresponding to the highest activation barrier. 

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. 

The concept of stoichiometric number was first introduced in electrochemistry by Horiuti and Ikusima [48, 49] for the hydrogen evolution reaction and discussed by Bockris and Potter [50, 52] and Parsons [47]. 

According to the International Union of Pure and Applied Chemistry (IUPAC), the stoichiometric number is a positive integer that indicates the number of identical activated complexes formed and destroyed in the completion of the overall reaction as formulated with the charge number, n [8, 9], The stoichiometric number is introduced to allow for the possibility that the rate-determining step occurs more or less than once in the overall stoichiometric reaction for instance in the Tafel mechanism for the reduction of proton according to eqns. (25) and (26), reaction (25) occurs twice each time a hydrogen molecule is formed. 

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The total enthalpy correction due to chemical reactions is the sum of all the enthalpies of dimerization for each i-j pair multiplied by the mole fraction of dimer i-j. Since this gives the enthalpy correction for one mole of true species, we multiply this quantity by the ratio of the true number of moles to the stoichiometric number of moles. This gives... 

The lepiesent formulas for the chemical species and is the stoichiometric number for species i in reaction j. Each has a magnitude and a sign ... 

The stoichiometric numbers provide relations among the changes in mole numbers of chemical species which occur as the result of chemical reaction. Thus, for reactionj ... 

Methanol. Methanol is produced by stoichiometric reaction of CO and H2. The syngas produced by coal gasification contains insufficient hydrogen for complete conversion to methanol, and partial CO shifting is required to obtain the desired concentrations of H2, CO, and CO2. These concentrations are expressed in terms of a stoichiometric number, ((H2 — CO)/(H2 + CO2), which has a desired value of 2. In some cases CO2 removal is required to achieve the stoichiometric number target. CO and H2 are then reacted to form methanol in a catalytic methanol synthesis reactor. 

Matrix methods, in particiilar finding the rank of the matrix, can be used to find the number of independent reactions in a reaction set. If the stoichiometric numbers for the reactions and molecules are put in the form of a matrix, the rank of the matrix gives the number or independent reactions (see Ref. 13). 

Transfer Coefficient, Symmetry Factor and Stoichiometric Number... 

In a multistep reaction the number of times the r.d.s. must occur for each act of the overall reaction is referred to as the stoichiometric number v, and this concept can be illustrated by referring to the steps of the h.e.r. 

The slope of the Tafel curve drj/d log / is only one of the criteria that are required to determine the mechanism of the h.e.r., since different mechanisms, involving different r.d.s. often have the same Tafel slope. Parameters that are diagnostic of mechanism are the transfer coefficient, the reaction order, the stoichiometric number, the hydrogen coverage, the exchange current density, the heat adsorption, etc. 

Stoichiometric Number number of times the rate-determining step must occur for one act of the overall reaction. 

Describe clearly the use of polarographic analysis for obtaining the values of the formation constant and stoichiometric number of metal complexes. 

The final number of moles can then easily be calculated knowing the stoichiometric number as shown in Tab. 2.3. 

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... 

In this equation, it has been assumed that the adatom exerts the same blockage on hydrogen and anion adsorption (i.e., the stoichiometric number m is the same for... 

One model proposed for the rate of propylene disappearance, rp, as a function of the oxygen concentration, C0, the propylene concentration, Cp, and the stoichiometric number, n, is... 

If it is known which of the reactions determine the rate of the overall complex electrode process, then the concept of the stoichiometric number of the electrode process v is often introduced. This number is equal to the number of identical partial reactions required to realize the overall electrode process, as written in an equation of type (5.2.2).t If the rate constant of this partial rate-determining reaction is ka, then ka = /ca/v. Thus, for example, if the first of reactions (5.1.7) is the rate-determining step in the overall electrode process (5.1.4) then the stoichiometric number has the value v = 2. 

Here, Ais the free energy change of Reaction 17.3 (kJ mol 1), R is the gas constant (8.3143 J K-1 mol-1), and 7k is absolute temperature (K). Factor co is the reciprocal of the average stoichiometric number, which can be taken as the number of times the rate determining step in Reaction 17.3 occurs per turnover of the reaction (Jin and Bethke, 2005). 

It is worth noting that the values of both k+ and co in Equation 17.9 depend on how the kinetic reaction (Reaction 17.3) is written. If we were to arbitrarily double each of the reaction s coefficients, the value of the rate constant k+ would be cut in half, because twice as many of the reactant species would be consumed, and twice as many product species produced, per reaction turnover. The rate determining step, furthermore, would occur twice as often per reaction turnover, doubling the average stoichiometric number and requiring co to be halved as well. 

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... 

Experimental studies of Methanosarcina and current understanding of the organism s metabolic pathway allow us to estimate the parameters in the thermodynamic term (Qusheng Jin, personal communication). The methanogens conserve about 24 kJ (mol acetate)-1, so we set AGp to 48 kJ mol-1 and m to one half. A double proton translocation occurs within the central metabolic pathway, furthermore, so, if we take these as the rate limiting steps, the average stoichiometric number / is two. 

If we simply add the three steps, we do not recapture (A). To get around this, we introduce the stoichiometric number, s, for each step, as the number by which that step must be multiplied so that addition of the steps results in (A) ... 

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