Quasi-stationary concentrations

In general, the assumption of quasi-stationarity is difficult to justify a priori. There may be several possible choices of intemiediates for which the assumption of quasi-stationary concentrations appears justified. It is possible to check for consistency, for example [A ]qj, [Pg.792]

J. G. Tolpin, G. S. John, and E. Field The Elucidation of Reaction Mechanisms by the Method of Intermediates in Quasi-Stationary Concentrations J. A. Christiansen... 

Quasiperiodic behavior, Pt, 37 240-242 Quasi-stationary concentrations, reaction mechanisms by intermediates in, 5 311... 

Europium also does not modify the mantle thermoluminescence perceptibly. There are no sharp emission lines in the red due to a conceivable luminescence of a quasi-stationary concentration of Uo built up by the flame, in contradistinction to cathodo-luminescence. It must be remembered that the Boltzmann population of this state is only 4.10 even at 2000 K. 

In flames, hydrogen seems to be more efficient than coal gas to produce candoluminescence, possibly because of appreciable quasi-stationary concentrations 62) of highly reactive H or OH. Hence, it might be true that selected mixed oxides would be particularly suitable for light emission in flames of pure hydrogen. 

The time t that must elapse before a supersaturated solution reaches a quasi-stationary concentration In dilute aqueous solutions, t is typically around 10 seconds, but for some solutes this period has proven to be much greater. For example, Dunning found that the relaxation period for concentrated sucrose solutions is about 100 hours. See Biomineralization... 

Some simulation results for trilobic particles (citral hydrogenation) are provided by Fig. 2. As the figure reveals, the process is heavily diffusion-limited, not only by hydrogen diffusion but also that of the organic educts and products. The effectiviness factor is typically within the range 0.03-1. In case of lower stirrer rates, the role of external diffusion limitation becomes more profound. Furthermore, the quasi-stationary concentration fronts move inside the catalyst pellet, as the catalyst deactivation proceeds. 

The increased temperature results in an increased rate of destruction of the branching intermediate (methyl hydroperoxide) with a consequent further increase of the rate, but also a decreased rate of formation of fresh hydroperoxide since Equilibrium 5 is displaced to the left, and the alternative reactions of methylperoxy increase in rate faster than that leading to formation of hydroperoxide. Consequently the quasi-stationary concentration of methyl hydroperoxide falls, and the rate of reaction declines since the new product of methyl oxidation—formaldehyde— cannot bring about branching at these temperatures. The temperature of the reaction mixture falls (because the rate has fallen), and when it has fallen sufficiently, provided sufficient of the reactants remain, the whole process may be repeated, and several further flames may be observed. 

The thermal and kinetic models discussed above are the basis for determining the processing conditions for reactive processing by ionic polymerization,29 addition polymerization, vulcanization of rubbers and radical polymerization, although in the latter case additional assumptions of a constant initiation rate and a quasi-stationary concentration of radicals are made.89 These models can also be used to solve optimization problems to improve the performance and properties of end-products. 

In former editions of this expert report, I have used the equations determined in chapter 6.7.4. to calculate the relative saturation of masonry cyclically exposed to hydrogen cyanide. However, after using several approaches on exactly how to do it, which lead to sometimes quite different results,482 1 decided to refer to this equation only in order to establish the time it takes for masonry to reach its maximum saturation or a quasi-constant concentration (20 days and 20 daily cycles, respectively). In this edition, the quasi-stationary concentration in masonry were calculated iteratively using Fick s law of diffusion 483... 

Table 13 Quasi-stationary concentrations of HCN in masonry in per-cent of saturation, as a function of daily exposure time to HCN...

I have emphasized the values of particular interest In case of homicidal gassings in the morgues 1 of crematoria II and III (without Zyklon B introduction columns), the walls will reach a quasi-stationary concentration of 8% of their saturation concentration. In case of disinfestation chambers, the value given for 6 hours of exposure to a constant HCN concentration—corresponding to a round-the-clock operation—leads to ca. 16% for the average value of the entire wall, and some 30% for the surface. 

The Elucidation of Reaction Mechanisms by the Method of Intermediates in Quasi-Stationary Concentrations... 

Let us assume that it has been shown analytically that the reaction is pure and let us further assume that it has been shown by kinetical experiments that the reaction does not follow the kinetics derived from its stoichiometrical equation in the well-known way. Obviously then we have to split up the overall reaction in a number of steps, each represented by a chemical equation, and thus we must assume n > 1. If for the time being we exclude the addition of foreign substances acting as catalysts, the number of elements is obviously constant. We must therefore increase the number of molecules occurring in the system by 1 for each added step and are thus compelled to destroy the stoichiometrical simplicity. To justify the addition of such reactions which are not evident from the stoichiometrical scheme a new theory was introduced in 1913. This may be called the theory of intermediates in stationary concentrations (or even better the theory of intermediates in quasi-stationary concentrations) and has since then shown to be of the greatest importance in reaction kinetics. 

Classifying variables into fast or slow is a typical approach in chemical kinetics to apply the method of (quasi)stationary concentrations, which allows the initial set of differential equations to be largely reduced. In the chemically reactive systems near thermodynamic equihbrium, this means that the subsystem of the intermediates reaches (owing to quickly changing variables) the stationary state with the minimal rate of entropy production (the Rayleigh Onsager functional). In other words, the subsys tern of the intermediates becomes here a subsystem of internal variables. 

These autocatalytic instabilities in reaction system which we have described are characterized by a rate of reaction which starts off from some very low value, increases during the entire course of the reaction (which is usually of the order of magnitude of seconds or less) and reaches a maximum only because of the depletion of reactants. This behavior differs from a normal, slow reaction in that the half-life of the reaction is remarkably short and of the order of magnitude of the time required to develop the quasi-stationary concentrations of intermediates or temperature. ... 

Finally, an efficiency r/par (which is less than one) due to parasitic losses composed of selfabsorption16, 17) of the fluorescence by the emitting centers, absorption and scattering by chemical and structural imperfections. As discussed below, a special case is absorption due to a quasi-stationary concentration of excited states (such as triplet states of organic dye-stuffs) maintained by the illumination. 

The average quasi-stationary concentration of AIH3 in the film can be estimated as... 

The following expression for the quasi-stationary concentration of the O atom is deduced ... 

This computer program carries out the reduction of detailed mechanisms using the Quasi- Stationary-State Approximation (QSSA). When the negligible species have been eliminated and the quasi-stationary species identified, the algorithm looks for a set of independent reactions allowing the quasi-stationary concentrations to be calculated by applying the QSSA. Lumped reactions are obtained by a linear combination of elementary reactions of the detailed mechanism. 

From some point set a quasi-stationary concentration of hydrofjeroxide,... 

Christiansen J. A. The elucidation of reaction mechanisms by the method of intermediate in quasi-stationary concentrations, Advan. Catalysis. N. Y. Acad. Press Inc., 1953 (5), p. 311. 

Under the approximation of the method of quasi-stationary concentration —= 0,... 

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