Pseudomonomolecular systems

Our discussion of monomolecular systems will also provide structural information about an important class of nonlinear reaction systems, which we shall call pseudomonomolecular systems. Pseudomonomolecular systems are reaction systems in which the rates of change of the various species are given by first order mass action terms, each multiplied by the same function of composition and time. For example, the rate equations for a typical three component reversible pseudomonomolecular system are... 

Pseudomonomolecular systems and pseudo-mass-action systems may arise when the reaction system contains quantities of intermediate species that are not directly measured and that consequently, do not appear... 

In this section, we shall establish some sufficiency condition for the origin of some pseudo-mass-action systems with particular emphasis on pseudomonomolecular systems. This discussion will not, however, lead to the establishment of necessary conditions for the origin of such systems. 

The steady state matrix for pseudomonomolecular systems The element in the fth row and jth column of the matrix G The matrix formed by replacing the jth row of the matrix... 

The discriminant of the three component system A matrix for the pseudomonomolecular system The determinant of the matrix A... 

Some reactions have to be "pseudomonomolecular". Their constants depend on concentrations of outer components, and are constant only under condition that these outer components are present in constant concentrations, or change sufficiently slow. For example, the simplest Michaelis-Menten enzymatic reaction is E+S ES->E+P (E here stands for enzyme, S for substrate and P for product), and the linear catalytic cycle here is S ES S. Hence, in general we must consider nonlinear systems. 

A. Some Classes of Heterogeneous Catalytic Reaction Systems with Rate Equations of the Pseudomonomolecular and Pseudo-Mass-Action Form. 313... 

A. Some Classes op Heterogeneous Catalytic Reaction Systems WITH Rate Equations op the Pseudomonomolecular and Pseudo-mass-action Form... 

A Class of Heterogeneous Catalytic Systems with Rale Equations of the Pseudomonomolecular Form... 

In the discussion to follow, we shall always assume that the amounts of adsorbed species are not measured. We shall show that, when the above conditions apply, the amounts of adsorbed species can be eliminated from the rate equation and that a pseudomonomolecular reaction system is always obtained. Hence, conditions (1) through (6) are sufficient to insure that the rate equations for the reaction systems are pseudomonomolecular. We shall first discuss systems satisfying the above conditions and then examine some systems in which some of the conditions are not satisfied. 

Since the matrices U and G do not contain the amounts of any species in the system, Eqs. (331) and (319) show that systems with the properties (1) through (6) give pseudomonomolecular rate equations for steady state conditions. 

It is desirable to make one of the pseudomonomolecular rate constants unity by dividing each element of the n X n matrix of Eq. (332) by one of the determinants fcai G , I m and multiplying the general function by fco/ G ). Let the zjth pseudo-rate-constant for this normalized system be designated d a and the rate constant matrix by . Then... 

Equation (379) resembles the matrix Eq. (318). The most important change is that the rate constant kn has been replaced by ka i and, therefore, all amounts a,- do not occur in the same column of the matrix A. Hence, we shall obtain terms containing the products of amounts and the system will not be pseudomonomolecular but will, in this case, contain second order mass action terms. Equation (379) gives... 

Therefore, if free molecular species interact with adsorbed molecular species and the other conditions (1) through (6) hold, we may infer that the reaction will be pseudo-mass-action but not pseudomonomolecular and that conditions (1), (2), (3), (5), and (6) are sufficient conditions for the system to have pseudo-mass-action rate equations in terms of the free molecular species. 

In addition, at constant hydrogen partial pressure the system should appear to be pseudomonomolecular and the reaction paths for all initial compositions should be identical with those obtained from the scheme... 

In the preceding sections we confined our discussion almost exclusively to systems with monomolecular and pseudomonomolecular rate equations. 

We have studied the kinetics of ozone reaction with a series of paraffins of different structure [47, 59], The rates of the reactions (W) have been determined in a close and open system. By following the change of [O ] in time (t) in static conditions we have determined the rate constant of the pseudomonomolecular reaction k =k [RH] and the bimolecular constant k. 

Vas (1949) studied the kinetics of the addition of glucose and bisulfite under controlled conditions probably best suited for conclusions in fruit juice treatments with sulfur dioxide, using concentrations of glucose far in excess of the sulfur dioxide contents. For such conditions the system would be expected to behave in a pseudomonomolecular manner, since the proportion of change of glucose from beginning to end of the reaction would be very small. However, values for ki at 20° C. and ki at 20 C. 

The strategy for predicting the temporal evolution of a complex chemical reaction described in this section is based on the application of mass balances and symmetry relations between concentration dependences, starting from extreme initial values of the concentrations. The results obtained may be very useful for advanced analysis of complex chemical reactions and can be applied to the analysis of linear models of reversible reactions in plug-flow reactors and in the linear vicinity of nonlinear complex reversible reactions both in batch reactors (closed systems) and in plug-flow reactors. They can also be applied to the analysis of pseudomonomolecular models of the Langmuir-Hinshelwood-Hougen-Watson type for reversible reactions. 

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