Reduced to monomolecular

If the transformation pathway cannot be reduced to monomolecular reactions, nonunit stoichiometric coefficients may appear at some junction points of the kinetic resistors. In terms of electric circuits, this means that the absence of the balance of the current inflow and outflow at this June tion point may cause norJinearity and deviations from the canonical form of the KirchhofF equation. 

These speculations are of extreme importance because they lead to the conclusion that the analysis of any stationary stepwise process involving an arbitrary series of monomolecular (or reduced to monomolecular) transfor mations can be substituted for by an analysis of only one effective... 

This specific feature of the stationary state of chemical systems that undergo their evolution via an arbitrary combination of only monomolec ular (or reduced to monomolecular) transformations, as well as transforma tions that are linear in respect to the intermediates, is of practical importance to simplify the analysis of complex stepwise chemical processes with the use of methods of nonequilibrium thermodynamics. 

It is easy to demonstrate that in the reactive system with an arbitrary set of monomolecular (or reduced to monomolecular) reactions, the station ary state with respect to the intermediate concentration corresponds to the minimum in the value of functional (3.6) even under conditions that are far from equilibrium of the system. In other words, the functional 0( Ao( ) is, by definition, the Lyapunov function of this system. In fact, for a system that consists of monomolecular reactions in its stationary state, in respect to linearly independent (i.e., not related via mass balance with other intermediates) intermediate A , the following expression is valid ... 

Thus, the approach to the stationary state of any simple (i.e., undergoing monomolecular or reduced to monomolecular transformations) reaction of the catalytic intermediates means the catalyst functioning at the minimal rate of energy dissipation in terms of the identical electric circuit. 

In this way, the problem is reduced to that of the monomolecular EC case, considering 2fegcg as a formal rate constant. The surface concentrations can therefore be formulated as in eqns. (191) with the substitutions... 

Due to the existence of two quite different distinctive distances (scale factors) - lo and l - the recombination kinetics also reveals two stages called monomolecular and bimolecular respectively. The defects survived in their geminate pairs go away, separate and start to mix and recombine with dissimilar components from other pairs. It is clear that the problem of kinetics of the monomolecular process is reduced to the time development of the probability w(f) to find any single geminate pair AB as a function of the initial spatial distribution of the pair components f(r), recombination law cr(r) and interaction Uab (r). The smaller the initial concentration of defects, n(0) —> 0, as lo —> oo, the more correct is the separation of the kinetics into two substages, whereas the treatment of the case of semi-mixed geminate pairs is a very difficult problem discussed below. 

The rates of chemical reactions are in linear dependence on thermody namic rushes of the reaction groups of several reactants. When the pertinent kinetic schemes are reducible to a set of the intermediate monomolecular reactions (see Section 1.3.2), the minimization of functional ( Aor ) can be used to find the stationary state of these systems that are far from equilibrium. Let us demonstrate this. 

With regard to the sulfur bound on the catalyst surface, differences exist between the various types of ammonia catalysts, especially between those that contain alkali and alkaline earth metals and those that are free of them. Nonpromoted iron and catalysts activated only with alumina chemisorb S2N2 and thiophene. When treated with concentrations that lie below the equilibrium for the FeS bond, a maximum of 0.5 mg of sulfur per m2 of inner surface or free iron surface is found this corresponds to monomolecular coverage [382], [383], The monolayer is also preserved on reduction with hydrogen at 620 °C, whereas FeS formed by treatment above 300 °C with high H2S concentrations is reducible as far as the monolayer. For total poisoning, 0.16-0.25 mg S/m2 is sufficient. Like oxygen, sulfur promotes recrystallization of the primary iron particle. 

The n-component monomolecular system may be treated in exactly the same manner except that an n-dimensional composition space is used. Although n-dimensional spaces with n > 3 cannot be simply put into pictures, a geometrical language still aids our ability to solve problems using the concepts, language, and techniques of two and three dimensional systems. The set of Eqs. (5) reduces to a single equation identical to Eq. (11) except that a is now the column matrix or vector in n-dimensional space given by... 

When only monomolecular adsorption is involved, the BET relation (Eq. 1) reduces to the familiar Langmuir isotherm. With p P, and Kb i>> 1, it becomes (LI)... 

When A = 1, this expression reduces to Langmuir s equation for monomolecular adsorption. If 0 < A < 1, there is a finite maximum hygroscopic moisture content. While many textile fibers approach such a moisture content asymptotically at high relative humidities, some man-made fibers such as nylon and viscose appear to have well-defined maximum hygroscopic moisture contents [9]. In many cases, the coefficient k is greater than 1. Jaafar and Michalowski [8] interpret this behavior as the thermal effect of adsorption being equal to the heat of condensation only after a multimolecular layer has been formed. 

Certain impurities such as aluminum in minute amounts not only reduce the rate of dissolution of silica, but by chemisorption on the surface of silica, even in amounts less than a monomolecular layer, reduce the solubility of silica at equilibrium. Jeph-cott and Johnston (179a) have shown that the apparent solubility of amorphous finely divided silica in water, which they find to be 0.017% at 37 C, is reduced to 0.003-0.0097% when aluminum oxide is added to the system and to less than 0.0001% when powdered aluminum is present. Since it was also shown that the addition of silica to a suspension of alumina depressed the solubility of alumina, it seems likely that a surface containing both SiOj and AljOa is formed on both the silica and alumina phases and has a lower solubility than either oxide. Earlier Denny. Robson, and Irwin (179b) had shown similar effects of iron and aluminum. 

When q > 1, the critical dimensions and the free energy for nucleation are all reduced relative to the homogeneous process. For the special case q =, i.e. CTk - CTh = ctu, these equations reduce to those for the coherent formation of a monomolecular layer nucleus on the face of an existing crystallite. This important special case will be treated in more detail shortly. 

Surfactants that are adsorbed at oil/water interfaces to form monomolecular films and reduce interfacial tension. 

The preceding equations can be used with appropriate experimental data to determine the kinetic parameters k, E, n, k , j , n i, Kw, and Kh. The pseudo-monomolecular form of Eq. (5) can be used to simplify the parameter estimation into a selectivity problem (determine K) and an activity problem (determine 0). This reduces the original highly nonlinear problem into two... 

The techniques of monomolecular rate theory easily transform measured reaction data into a form where we can analyze apparent kinetics and the effects of intracrystalline diffusion by the use of selectivity data. Time dependency has been eliminated. Since selectivity is extremely reproducible and is independent of short-term aging effects, the number of experimental runs is reduced while data reliability is maintained. For catalyst evaluation at any temperature, it is necessary to determine the equilibrium composition and the straight-line reaction path. With this information any catalyst can be evaluated at this temperature with simply the additional information from a curved-line reaction path. The approach used in the application of monomolecular rate theory to the xylene isomerization selectivity kinetics is as follows. Reference is made to the composition diagram, Figure 1. 

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