Fractional stoichiometric numbers

Thus fractional stoichiometric numbers are also allowable (although it is always possible to write overall equations so that all stoichiometric numbers are integers). 

Fractional stoichiometric numbers are allowable, for example it can be written for S02 oxidation. 

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... 

Laplace parameter, stoichiometric number, surface site solid (phase) slope instantaneous fractional yield of P with respect to A, equation 5.2-8 substrate split point (of streams) entropy, J K-1... 

The compounds discussed above are not nonstoichiometric in the strict sense of the word, since they form well defined, ordered phases which can be assigned precise stoichiometric formulas. Accordingly, they are not berthollides. They may, however, be regarded as nonstoichiometric in the wider sense of the term which has become current, since fractional valence numbers must be assigned to the metal atoms and the ordered structures which they exhibit constitute a preferred alternative to the formation of disordered phases of variable composition. 

Relate equilibrium mole fractions to the equilibrium constants. By definition, K = YUf1, where the a,- are the activities of the components with the mixture, and the v, are the stoichiometric numbers for the reaction (see Example 4.4). The present example is at relatively large reduced temperatures and relatively low reduced pressures, so the activities can be represented by the equilibrium mole fractions y,-. For Reaction 4.11, Kk = yco,Vch4 A> co)2( Vh, )2- Substituting the value for K from step 2 and the values for the y, from the last column of the table in step 3 and algebraically simplifying,... 

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. 

Since the stoichiometric numbers are integers or simple fractions, Eq. (III. 10) states that v, a at the steady state bear simple integral ratios to each other. 

The number x is known from the way in which the overall electrode reaction has been written. We then obtain the ratio Sj/yj. The stoichiometric number yj is a small integer whose value will often be obvious, in which case dj is obtained. With simple mechanisms Sj should be close to and smaller than 1. The observed Tafel behavior implies that dj remains constant as i and rj vary, and if Sj is close to 1, that the fractions 5 for the other steps of the mechanism, adding up to 1 — dj, do vary with i and rj since, in the... 

If only a single gas takes part in the reaction, the mass can be connected to the fractional extent related to this gas and its derivative to the rate relative to this gas. Indeed, one can measure only the amount of gas that is fixed or that is released. If the algebraic stoichiometric number related to gas in reaction [l.R.l] is indicated by (positive for a product, negative for a reactant), it can be easily shown that if is the molar mass of gas, mass of the initial solid A, m and the masses at time... 

Olefin distribution in the Albemarle stoichiometric process tends to foUow the Poisson equation, where is the mole fraction of alkyl groups in whichp ethylene units have been added, and n is the average number of ethylene units added for an equal amount of aluminum. 

Scatter plots of temperature atx/d = 15 in turbulent Cl-14/air jet flames with Reynolds numbers of 13,400 (Flame C) and 44,800 (Flame F). The stoichiometric mixture fraction is = 0.351. The line shows the results of a laminar counterflow-flame calculation with a strain parameter of a = 100 s and is included as a visual guide. (From Barlow, R.S. and Frank, J.H., Proc. Combust. Inst, 27,1087,1998. With permission.)... 

The variable / depends on the particular species chosen as a reference substance. In general, the initial mole numbers of the reactants do not constitute simple stoichiometric ratios, and the number of moles of product that may be formed is limited by the amount of one of the reactants present in the system. If the extent of reaction is not limited by thermodynamic equilibrium constraints, this limiting reagent is the one that determines the maximum possible value of the extent of reaction ( max). We should refer our fractional conversions to this stoichiometrically limiting reactant if / is to lie between zero and unity. Consequently, the treatment used in subsequent chapters will define fractional conversions in terms of the limiting reactant. 

From a thermodynamic point of view, the heteropolymer globule in hand represents a subsystem which is composed of a macromolecule involving lu l2 units Mi, M2 and molecules of monomers Mi, M2 whose numbers are Mi,M2. Among these variables and volume fractions a in the framework of the simplest Flory-Huggins lattice model there are obvious stoichiometric relationships... 

The partial pressures are functions of the species mole fractions, yt, which are, in turn, dependent upon the extent of conversion of the reactants. A stoichiometric table may be used to relate the number of moles of all species at equilibrium, with x representing the moles of H2 consumed. The moles of each species can thus be represented as follows ... 

When several reactions occur simultaneously a degree of advancement is associated with each stoichiometric equation. Problem P4.01.26 is a application of this point. Some processes, for instance cracking of petroleum fractions, involve many substances. Then a correct number of independent stoichiometric equations must be formulated before equilibrium can be calculated. Another technique is to apply the principle that equilibrium is at a minimum of Gibbs free energy. This problem, however, is beyond the scope of this book. 

The energy, or power, of electron beam induced in the flue gas is divided and absorbed by their gas components roughly depending on their electron fraction. Therefore almost all the energy is absorbed by the main components of the flue gas, namely, N2, O2, CO2, and H2O. Table 2 shows a typical concentration of the components in coal-fired flue gas in Japan. The ratio of the total number of electrons in each gas components is also listed in the same table. The energy absorbed directly by the toxic components (SO2 and NO) is negligibly small. For electron beam treatment of flue gas, ammonia gas is added to the flue gas before the irradiation. The amount of ammonia is usually set as stoichiometrically, i.e., 2A[S02] + A[NO], where A[S02] and A[NO] are the concentrations of SO2 and NO intended to be treated, respectively. The concentration of ammonia is usually higher than the initial concentration of SO2 and NO however, it is still far lower than that of the main components. 

As can be seen from Table 4, self-association of the hydroxyl groups is a predominant type of association at room temperature. The fraction of the self-associates of the hydroxyl groups in the epoxy-amine networks of stoichiometric composition amounts to 85-90 %. An abundant literature on the self-association of the hydroxyl compounds (alcohols, phenols, acids) 38,47,48) shows that a number of different n-mer linear and cyclic self-associates exists in equilibrium. The cyclic associates usually existing in the form of the trimers... 

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