Chemical kinetics monomolecular reaction

In chemical kinetics, the reaction rates are proportional to concentrations or to some power of the concentrations. Phenomenological equations, however, require that the reaction velocities are proportional to the thermodynamic force or affinity. Affinity, in turn, is proportional to the logarithms of concentrations. Consider a monomolecular... 

For a given kinetics of the chemical reaction, the relation between the concentrations at entry and exit (i.e., before and after the chemical reaction) depends only on the time t. However, the form of the dependence, obtained by solution of equation (4), is itself substantially different from the integral of equation (1) for identical chemical kinetic laws [identical functions /(c)]. So, for a monomolecular reaction, instead of (3) we find... 

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... 

Because the general principles of chemical kinetics apply to enzyme-catalyzed reactions, a brief discussion of basic chemical kinetics is useful at this point. Chemical reactions may be classified on the basis of the number of molecules that react to form the products. Monomolecular, bimolecular, and termolecular reactions are reactions involving one, two, or three molecules, respectively. 

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. 

The major part of this article will be devoted to a particular class of reaction systems—namely, monomolecular systems. A reaction system of (n) molecular species is called monomolecular if the coupling between each pair of species is by first order reactions only. These linear systems are satisfactory representations for many rate processes over the entire range of reaction and are linear approximations for most systems in a sufficiently small range. They play a role in the chemical kinetics of complex systems somewhat analogous to the role played by the equation of state of a perfect gas in classical thermodynamics. Consequently, an understanding of their behavior is a prerequisite for the study of more general systems. 

The monomolecular reaction systems of chemical kinetics are examples of linear coupled systems. Since linear coupled systems are the simplest systems with many degrees of freedom, their importance extends far beyond chemical kinetics. The linear coupled systems in which we are interested may be characterized, in general terms, as arising from stochastic or Markov processes that are continuous in time and discrete in an appropriate space. In addition, the principle of detailed balancing is observed and the total amount of material in the system is conserved. The system is characterized by discrete compartments or states and material passes between these compartments by first order processes. Such linear systems are good models for a large number of processes. 

Most of the literature on coupled reaction systems in chemical kinetics has been concerned with the solution of special cases of the monomolecular reaction systems that almost always contain no more than three components and with only a few of the rate constants nonzero. The solutions are obtained in a closed form with the values of the constants cy,- and X, of Eq. (6) expressed as functions of the rate constants fcy,. As examples we may mention the work of Rakowski (43), Alberty and Miller (44), de Boer and van der Eorg (45), and Jungers et al. (46). This type of approach, however, can be used only for certain special cases. 

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,... 

In terms of chemical kinetics, the loss of nutrient can be visualized as the decomposition of a particular chemical compound. This decomposition for a single monomolecular reaction may be expressed by... 

We want to illustrate here the behavior of the open systems using the simplest examples of monomolecular chemical reactions. For quantitative analysis, in this section we will consider thermodynamic and kinetic relations for coupled monomolecular reactions AoB and BoC), Analysis of the behavior of this reaction in an open system gives explicit and simple relationships, between the kinetic and thermodynamic characteristics of the reaction mixture on one hand, and the flux through the system on the other. However, for didactic reasons we start our analysis with a consideration of the simplest monomolecular reaction, the transformation of S into P. 

The first quantum-chemical investigation of the mechanism of olefin epoxidation in flnoroalcohols was carried out by Shaik et al. [54], In the absence of kinetic data, a monomolecular mode of activation by the fluorinated alcohols for aU reaction pathways was assnmed [54],... 

Since the concentration of water in this reaction is virtually constant (55.5 M), an essentially bimolecular chemical reaction can be treated kineticaUy as a monomolecular, which simplifies considerably the kinetic treatment. 

Medvedevskikh Yu., Kytsya A., Bazylyak L., Bratus., Turovskij A., Zaikov G. Monomolecular chain termination in kinetics of dimethacrylates postpolymerization /In Chemical reactions in liquid and solid phase Kinetics Thermodynamics, Nova Science Publishers, New York, NY, 2003, p. 117. 

Another example requiring the solution of linear algebraic equations comes from the analysis of complex reaction systems that have monomolecular kinetics. Fig. 2.2 considers a chemical reaction between the three species, whose concentrations are designated by Fj, Fj, taking place in a batch reactor. 

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