Pseudo-monomolecular reactions

In the first case (pseudo-monomolecular reactions) the application of a... 

This is a general fact. For monomolecular (or pseudo-monomolecular) reactions the graphs corresponding to compartments are acyclic. A similar property for the systems having either bi- or termolecular reactions is more complex. It can be formulated as follows. If every edge in the graph of predominant reaction directions for some compartment is ascribed to a positive "rate constant k and chemical kinetic equations are written with... 

In spite of the complexity of real processes most cases of interest may be effectively described by a heterogeneous pseudo-monomolecular reaction of the type... 

With high concentrations of starting materials, the mode MIX is selected. This mode ensures that all combinations of starting materials are considered in the generation of reactions. For instance, if three starting materials. A, B, and C are given, nine reactions will be considered three for monomolecular or pseudo-monomolecular reactions of the reactants (decomposition) three for the combinations A + B, A + C, and B + C and three for potential dimerization or polymerization of the reactants. 

At very low concentration levels, the mode MONOMOLEC is used, which additionally eliminates the intermolecular reactions and considers only monomolecular or pseudo-monomolecular reactions of the starting materials. 

The chain-breaking reactions consist of the monomolecular reaction (3.6a), the pseudo-monomolecular reaction (3.6b) and the bimolecular reaction (3.7). They show the decomposition of hydroperoxide groups. The pure thermal decomposition of hydroperoxide involves high activation energies, especially the monomolecular reaction (3.6a). In the case of molten PET, the temperature is more than sufficient to bring such reactions into play. Decomposition of hydroperoxide is efficiently catalysed by various metal ions which may be present in the polymer as catalyst residues, or as part of additive packages. This is especially the case with metal ions that exhibit more than one stable oxidation state. Such catalysed reactions are equivalent to reaction (3.7) but are much faster. 

The mean squared displacement and the diffusion coefficient are not always the most useful parameters to calculate. For instance, in cases where we are interested in a chemical reaction. Suppose we wish to calculate the time development of the concentration of a molecule A, free to move within a fractal space in which a great number of fixed molecules B have been scattered at random. Although they do not move, the B molecules can react with the A molecules. In chemical kinetics, this constitutes a pseudo-monomolecular reaction. In more simple terms, we are dealing with a survival problem in the presence of traps. What is the survival probability u N) for an A molecule after N steps If p is the probability that a site is occupied by a trap (so p is the number of traps divided by the number of sites) and if A reacts instantaneously with B as soon as they are juxtaposed on the same site,... 

The results obtained by Wei and Prater gave rise to a question How do we lump components into suitable pseudocomponents with proper accuracy Wei and Kuo determined conditions for exact (Wei and Kuo, 1969) and approximate (Kuo and Wei, 1969) lumping for monomolecular and pseudo-monomolecular reaction systems. They showed that under certain conditions, a large monomolecular system could be modeled well by a lower-order system. 

Aspects of the sono-chemical degradation mechanism After the establish of the ultrasound waves physical and chemical components, the mechanisms of sono-chemical destruction have dominantly been interpreted on this basis. Thus, in the cavitation bubble collapse moment, N.Sata and H. Okuyama defined four types of possible reactions, namely 1) collision of the polymer - polymer molecules, occurring by a bimolecular reaction 2) collision of the polymer-solvent molecules, which proceeds by a pseudo-monomolecular reaction 3) intramolecular collision that occurs by a monomolecular reaction and 4) tearing resulting from the entanglement points that gives a monomolecular reaction. The authors accepted that the active centres of this type of reaction are free radicals and that about 30% from the efficiency of this process is assured by the subsequent reactions of the formed macroradicals with the polymer chains [1130, 1139]. 

Usual elementary reactions are not so simple and Eq. (6.126) is only vahd sufficiently close to equilibrium . Nonetheless the range of applicability may be wider than assumed, since many reactions behave as if they were monomolecular under certain conditions (so-called pseudo-monomolecular reactions). In addition, relevant processes are usually not just single step reactions, in which B only increases at the expense of A and vice versa. The relations between k and k, k are then more involved. Even under those conditions the exchange rate remains the decisive permeability parameter [452] containing k and k of the rate determing step in a symmetrical way. 

Since chlorine is always in more than a hundred-fold excess compared to bromine the reaction is occurring by pseudo monomolecular kinetics. The reaction occurs via nucleophilic aromatic substitution by an addition-elimination mechanism, the so-called SjsfAr mechanism (ref. 24). 

On the other hand, when the pure anhydride (XXXIV) was heated on a steam bath, without hydrochloric acid, analyses with periodic acid at room temperature showed that the reaction is reversible and that an equilibrium is reached when the solution contains approximately 92 % of compound XXXIV. The investigators deduce from their experimental data that the dehydration reaction is reversible and pseudo-monomolecular. The data fit the following equation. 

If radicals are produced in the reactions of unimolecular hydroperoxide decomposition and the reaction of ROOH with hydrocarbon whose concentration at the initial stages of oxidation is virtually constant, the production of radicals from ROOH can be regarded as a pseudo-monomolecular process occurring at the rate V = [ROOH] = + iRH[RH]). The... 

The usual kinetic law for S/v Ar reactions is the second-order kinetic law, as required for a bimolecular process. This is generally the case where anionic or neutral nucleophiles react in usual polar solvents (methanol, DMSO, formamide and so on). When nucleophilic aromatic substitutions between nitrohalogenobenzenes (mainly 2,4-dinitrohalogenobenzenes) and neutral nucleophiles (amines) are carried out in poorly polar solvents (benzene, hexane, carbon tetrachloride etc.) anomalous kinetic behaviour may be observed263. Under pseudo-monomolecular experimental conditions (in the presence of large excess of nucleophile with respect to the substrate) each run follows a first-order kinetic law, but the rate constants (kQbs in s 1 ruol 1 dm3) were not independent of the initial concentration value of the used amine. In apolar solvents the most usual kinetic feature is the increase of the kabs value on increasing the [amine]o values [amine]o indicates the initial concentration value of the amine. 

Reaction rates for the start-of-cycle reforming system are described by pseudo-monomolecular rates of change of the 13 kinetic lumps. That is, the rates of change of the lumps are represented by first-order mass action kinetics with the same adsorption isotherm applicable to each reaction step. Following the same format as Eq. (4), steady-state material balances for the hydrocarbon lumps are derived for a plug-flow, fixed bed catalytic reformer. A nondissociation, Langmuir-Hinshelwood adsorption model is employed. Steady-state material balances written over a differential fractional catalyst volume dv are the following ... 

The stoichiometric (brutto) equations for the conversion of gas-phase substances are considered. According to them, linear kinetic equations can be obtained, apparently, if only the time scale is changed. These reactions are pseudo-monomolecular and comprehensively treated by Wei and Prater [11]. An example is the familiar reaction of butene isomerization. 

The assumption of uniformity is in fact justified for some realistic kinetic schemes, such as Langmuir isotherm catalyzed reactions, Michaelis-Menten kinetics, and others (Aris, 1989 Cicarelli et al, 1992). The assumption bears a more than superficial analogy with those systems termed pseudo-monomolecular by Wei and Prater (1962). Mathematically, it is a very powerful assumption By crossing out the dependence of F[ ] on x, its value has been reduced from an infinite-dimensional vector (a function of x) to a scalar. This simplification makes Eq. (102) a quasilinear one, and it can be integrated explicitly by introducing a warped time scale t(0. (0) = 0. The solution, as can be verified by inspection, is... 

Such reactions are called pseudo-monomolecular or pseudo-first-order. 

The reaction kinetics studied using UV spectroscopy is formally identical to that of acid-catalyzed hydrolysis of l-alkoxybut-l-en-3-ynes (a first-order reaction with respect to the substrate and acid) (75IZV1975 78IZV153). At a constant acid concentration the reaction proceeds as a pseudo-monomolecular process. 

In their classical paper, Wei and Prater (1962) introduced a so-called lumping procedure. They showed that for systems in which only monomolecular or pseudo-nionomolecular reactions occur, a linear combination exists of concentrations that change in time independently. These linear combinations or pseudocomponents correspond to the left eigenvectors (row vectors) I of a kinetic matrix K as follows. If lK=il, then... 

Ardagh and Rutherford (207) find the reaction to be of second-order, whereas Compton and Wolfrom (209) report it to be pseudo-monomolecular when a hydrazine hydrochloride solution buffered with acetate ions is used. 

This is the equation expressing the kinetics of a first-order reaction, a theoretical monomolecular reaction, and defining the first-order velocity constant, Ki. In this case, however, it has been called a pseudo mono-molecular reaction, since there is actually a second molecule, water, entering the reaction. The decrease in the concentration of the water is so slight relative to the amount present as to have no influence ordinarily. 

Reaction scheme (6) is typical in the oxidation of hydrocarbons (A, R, and S) in the presence of a large amount of oxygen. Therefore, the reactions become pseudo-first-order from the viewpoint of hydrocarbons, and the practically constant oxygen partial pressure can be included in the rate constants. The intermediate product, R, represents a partial oxidation product (such as phthalic anhydride in the oxidation of o-xylene or maleic anhydride in the oxidation of benzene), whereas S represents the undesirable byproducts (CO2, H2O). The triangle system (7) represents monomolecular reactions such as isomerizations A, for instance, can be 1-butene, which is subject to an isomerization to ds-2-butene and trflns-2-butene. 

The start-of-cycle (fresh catalyst) kinetics for a pseudo-monomolecular reforming reaction system may be determined In two steps (IJ ... 

The kinetics become practically first-order. The reaction is said to be pseudo-monomolecular. Hydrolysis reactions are examples of such reactions since the concentration of water does not change in a measurable way. 

The second reaction is pseudo-monomolecular the reverse reaction is bi-molecular and in their cases are assumed to be neglig-... 

Ible As long as we are far from equilibrium, we can model the backward reaction as pseudo-monomolecular with a small mistake The paper is a fine example of how to simplify and decouple in order to simplify the estimation of the rate matrix Using methods derived in (, 24) it also reveals some other problems We can write the whole reaction as a single pseudo-monomolecular rate matrix ... 

Pulse radiolysis of some scavenger solutions in water, intermediates spectra, and kinetics of their decay in liquid ammonia are investigated. Rate constant and activation energy are calculated for the latter. The dependence of the disappearance of intermediates on concentration is analyzed. It is shown that rate constant of reactions of pseudo-first order is not proportional to acceptors concentration. One of the possible reasons is that first order reaction was not taken into consideration. On this basis, rate constants of reactions with acceptors and these of monomolecular decay are calculated. It is revealed the decay of intermediates in 10 5-10 3M perchloric acid solutions does not depend upon HsO+ ion concentration. This fact is contrary to the present day theories about the nature of intermediates. 

The experimental results in aqueous and ammonium solutions show that the process of intermediates decay in the presence of acceptors follows a first-order law. However, a proportionality between the calculated rate constant of the pseudo-first order reaction and the concentration is not observed. Under these conditions no influence of dose rate on the kinetics of intermediates decay is found, so recombination interactions play a rather small role. By kinetic treatment of the results, satisfactory agreement with experimental data can be obtained by supposing that the intermediates disappear in a monomolecular decay which simultaneously proceeds with scavenger reactions. 

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