Mass action kinetics

Chemical kinetics govern the transformation of species due to chemical reactions. In very dilute systems, the effect of reaction chemistry can be so minor that its influence on the fluid flow is negligible. At the other extreme, in the combustion of gases, chemical reactions and especially their heat release are a dominant aspect of the flow. Reacting streams of combusting gases are among the most important and difficult flow problems studied today. 

In all of these situations, homogeneous reactions in the gas phase provide source and sink terms in the species continuity equation. In addition the creation and destruction of species can be an important heat source or sink term in the energy equation. Therefore it is important to understand the factors that govern gas-phase chemical kinetics. 

This chapter sets out the basic formulation and governing equations of mass-action kinetics. These equations describe the time evolution of chemical species due to chemical reactions in the gas phase. Chapter 11 is an analogous treatment of heterogeneous chemical reactions at a gas-solid interface. A discussion of the underlying theories of gas-phase chemical reaction rates is given in Chapter 10. 

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Complex chemical mechanisms are written as sequences of elementary steps satisfying detailed balance where tire forward and reverse reaction rates are equal at equilibrium. The laws of mass action kinetics are applied to each reaction step to write tire overall rate law for tire reaction. The fonn of chemical kinetic rate laws constmcted in tliis manner ensures tliat tire system will relax to a unique equilibrium state which can be characterized using tire laws of tliennodynamics. 

In particular if the reaction rate depends only on Cj, which is the case, for example, if the reaction is irreversible with mass,-action kinetics, then these reduce further to a pair of equations, namely... 

Edsberg, L., "Numerical Methods for Mass Action Kinetics" in Numerical Methods for Differential Systems, Lapidus, L. and Schlesser W.E., Eds., Academic Press, New York, NY, 1976. 

Enzyme-catalyzed reactions can be described at least at two distinct levels. At the basic level, the interconversion of substrates by enzymes is governed by a set of elementary steps, including enzyme substrate binding, isomerization and dissociation steps, see Fig. 6 for a schematic depiction. Assuming the intracellular medium is an ideal solution, each elementary step is governed by mass-action kinetics, that is, the reaction rates are proportional to the probability of collision of the reactants. For a reaction of the type... 

It should be emphasized that Eq. (22) is already based on a number of preconditions. In particular, the intracellular medium may significantly deviate from a well-stirred ideal solution [141 143], While the use of Eq. (22) is often justified, several authors have suggested to allow noninteger exponents in the expression of elementary rate equations [96,142,144] corresponding to a more general form of mass-action kinetics. A related concept, the power-law formalism, developed by M. Savageau and others [145 147], is addressed in Section VII.C. 

Using mass-action kinetics for the elementary steps, the rates of change for the substrate and enzyme substrate complex concentrations are... 

The parameterization of the remaining reactions is less complicated. For simplicity, the rate v2(TP,ADP) is assumed to follow mass-action kinetics, giving rise to saturation parameters equal to one. Finally, the ATPase represents the overall ATP consumption within the cell and is modeled with a simple Michaelis Menten equation, corresponding to a saturation parameter 6 e [0,1], The saturation matrix is thus specified by four nonzero entries ... 

Evaluating the structural kinetic model, we first consider the possibility of sustained oscillations. Starting with the simplest scenario, all saturation parameters are set to unity, corresponding to bilinear mass-action kinetics and... 

The construction of the structural kinetic model proceeds as described in Section VIII.E. Note that in contrast to previous work [84], no simplifying assumptions were used the model is a full implementation of the model described in Refs. [113, 331]. The model consists of m = 18 metabolites and r = 20 reactions. The rank of the stoichiometric matrix is rank (N) = 16, owing to the conservation of ATP and total inorganic phosphate. The steady-state flux distribution is fully characterized by four parameters, chosen to be triosephosphate export reactions and starch synthesis. Following the models of Petterson and Ryde-Petterson [113] and Poolman et al. [124, 125, 331], 11 of the 20 reactions were modeled as rapid equilibrium reactions assuming bilinear mass-action kinetics (see Table VIII) and saturation parameters O1 1. 

F. J. M. Horn and R. Jackson, General mass action kinetics. Arch. Rational Mech. Anal. 47(2), 81 116(1972). 

I1J2 inputs to the system s substrate pools of Xi and X3, respectively. Simple mass action kinetics. Irreversible reactions. 

Coupled cyclic enzyme system Ii and I2 are inputs to the system s pools of substrate Xi and X3, respectively simple mass action kinetics irreversible reactions. 

The model followed mass action kinetics with Langmuir-Hinshelwood adsorption. 

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 ... 

We are now able to obtain the collision theory approximation to the bimolecular rate constant k (T). Recall that the mass-action kinetics expression for the reaction rate q is... 

In the Surface Chemkin formalism, surface processes are written as balanced chemical reactions governed by the law of mass-action kinetics. The framework was developed to provide a very general way to describe heterogeneous processes. In this section many of the standard surface rate expressions are introduced. The connection between these common forms and the explicit mass-action kinetics approach is shown in each case. 

An expression that is equivalent to the Langmuir adsorption isotherm is readily derived within mass-action kinetics form that we have adopted. Write the adsorption process as... 

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