Pseudo-mass-action systems

VI. Pseudo-Mass-Action Systems in Heterogeneous Catalysis. 313... 

C. The Hydrogenation-dehydrogenation of Ce-Cyclics over Supported Platinum Catalyst as a Pseudo-Mass-Action System. 334... 

In Eq. (2), a< is the amount of the species A<, 0<, is the pseudo-rate-constant for the reaction from the jth to the fth species and is independent of the amounts of the various species, and is some unspecified function of the amounts of the various species and time. This concept may be further generalized to give pseudo-mass-action systems. These are defined as systems in which all rates of change of the various species are given by mass action terms of various integral order each multiplied by the same function of composition and time. 

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. 

A rate constant in the pseudo-mass-action system A relative rate constant in a pseudo-mass-action system The non-negative forward and backward stoichiometric coefficients... 

A new time scale for pseudo-monomolecular systems An unspecified function of the amounts of the various species and time in pseudo-mass-action 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... 

Thus, the system is pseudo-mass-action. Evaluating the determinants in the mass action polynomial of Eq. (380), we have... 

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. 

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 ... 

Ion-exchange equilibrium can be considered to be analogous to chemical equilibrium. From that point of view, the mass-action law can be used to express the state of equilibrium despite the fact that this law is defined exclusively for homogeneous systems. Derived this way, the so-called pseudo-equilibrium constant Ke is not really a constant, since it depends on the total concentration ... 

The analysis of non-linear mechanisms and corresponding kinetic models are much more difficult than that of linear ones. The obvious difficulty in this case is the follows an explicit solution for steady-state reaction rate R can be obtained only for special non-linear algebraic systems of steady-state (or pseudo-steady-state) equations. In general case it is impossible to solve explicitly a system of non-linear steady-state (or pseudo-steady-state) equations. However, in the case of mass-action-law-model it is always possible to apply to this system a method of elimination of variables and reduce it to a polynomial in one variable [4], i.e., a polynomial in terms of the steady-state reaction rate. We refer a polynomial in the steady-state reaction as a kinetic polynomial. The idea of this polynomial was firstly emphasized in [5]. 

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