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Mass action rate law

For a closed chemical system witli a mass action rate law satisfying detailed balance tliese kinetic equations have a unique stable (tliennodynamic) equilibrium, In general, however, we shall be concerned witli... [Pg.3055]

The macroscopic mass action rate law, which holds for a well-mixed system on sufficiently long time scales, may be written... [Pg.128]

The numerator of Eq (1) is that of a homogeneous mass action rate law. The denominator seems to have been added to account for adsorption of some of the participants. [Pg.700]

Despite its limitations, the reversible Random Bi-Bi Mechanism Eq. (46) will serve as a proxy for more complex rate equations in the following. In particular, we assume that most rate functions of complex enzyme-kinetic mechanisms can be expressed by a generalized mass-action rate law of the form... [Pg.136]

The mass-action assumption that j + and j do not depend on reactant concentrations can be applied to reactions other than the uni-unimolecular reaction A B. For example, the mass-action rate laws for the reaction... [Pg.48]

For a closed chemical system with a mass action rate law satisfying detailed balance these kinetic equations have a unique stable (thermodynamic) equilibrium, lim c( )=Cgq. In general, however, we shall be concerned with chemical reactions that are maintained far from chemical equilibrium by flows of reagents intoand out of a continuously stirred tank reactor (CSTR). In this case the chemical kinetic equation (C3.6.1) must be supplemented with flow terms... [Pg.3055]

Thus, we find the macroscopic chemical rate law for the Schlogl model. Mesoscopic simulations of the Schlogl model have been carried out using a Markov chain model.Figure 3 shows the results for the steady-state concentrations derived from such a mesoscopic simulation along with the deterministic steady-state concentrations discussed earlier. The stochastic model yields results that are close to those of the mass action rate law. However, in the vicinities of points where the deterministic stable and unstable fixed points meet, so that one of the stable states loses its stability, fluctuations play an important role. [Pg.240]

Several features of the automation dynamics are worth noting. First, a series of automaton models can be constructed whose mean field limit is a particular mass-action rate law. Thus, since the parameters in the rate law can be tuned to investigate a series of bifurcation structures, so too a series... [Pg.616]

The automaton dynamics provides an ideal way to investigate such a possible breakdown since the mean-field limit of the automaton dynamics is the mass-action rate law and the full automaton dynamics incorporates correlations and fluctuations thus, the automaton dynamics can be compared with the mean field-limit to assess its range of validity. Such a comparison is very difficult to make in real systems since any real system is subject to both external and internal noise. Also, in physical systems the reaction mechanism is usually imperfectly known, which in turn can lead to uncertainties in the form of the rate law. In the automaton one can control the interplay between internal and external noise as well as noise arising from spatial inhomogeneities and reaction kinetics. [Pg.623]

The higher the concentrations of the reacting molecules, the faster the reaction will proceed. Since the rate in either direction is proportional to the concentrations of each of the reactant molecules, a mass action rate law connects the rate of reaction to the reactant concentrations. Thus for the H + O2 OH + O elementary reaction we have... [Pg.4]

The law of mass action, the laws of kinetics, and the laws of distillation all operate simultaneously in a process of this type. Esterification can occur only when the concentrations of the acid and alcohol are in excess of equiUbrium values otherwise, hydrolysis must occur. The equations governing the rate of the reaction and the variation of the rate constant (as a function of such variables as temperature, catalyst strength, and proportion of reactants) describe the kinetics of the Hquid-phase reaction. The usual distillation laws must be modified, since most esterifications are somewhat exothermic and reaction is occurring on each plate. Since these kinetic considerations are superimposed on distillation operations, each plate must be treated separately by successive calculations after the extent of conversion has been deterrnined (see Distillation). [Pg.378]

Mass action, this law states that the rate of a chemical reaction is proportional to the concentration (mass) of the reactants. [Pg.280]

Chemical kinetics govern the rate at which chemical species are created or destroyed via reactions. Chapter 9 discussed chemical kinetics of reactions in the gas phase. Reactions were assumed to follow the law of mass action. Rates are determined by the concentrations of the chemical species involved in the reaction and an experimentally determined rate coefficient (or rate constant) k. [Pg.401]

A difference between "elementary (e.g., H + 02 OH + O) and non-elementary (e.g. 02 + 2H2 - 2H20) reactions is in the form of the w dependence on the reactant concentrations. For elementary reactions the law of mass action (the law of acting surfaces) is assumed to hold. According to these laws, the rates for direct and inverse elementary reactions... [Pg.105]

Reaction rates r,- are functions of the concentrations and of the temperature. For elementary processes in the gaseous phase, a mass action kinetic law holds... [Pg.266]

While the majority of these concepts are introduced and illustrated based on single-substrate single-product Michaelis-Menten-like reaction mechanisms, the final section details examples of mechanisms for multi-substrate multi-product reactions. Such mechanisms are the backbone for the simulation and analysis of biochemical systems, from small-scale systems of Chapter 5 to the large-scale simulations considered in Chapter 6. Hence we are about to embark on an entire chapter devoted to the theory of enzyme kinetics. Yet before delving into the subject, it is worthwhile to point out that the entire theory of enzymes is based on the simplification that proteins acting as enzymes may be effectively represented as existing in a finite number of discrete states (substrate-bound states and/or distinct conformational states). These states are assumed to inter-convert based on the law of mass action. The set of states for an enzyme and associated biochemical reaction is known as an enzyme mechanism. In this chapter we will explore how the kinetics of a given enzyme mechanism depend on the concentrations of reactants and enzyme states and the values of the mass action rate constants associated with the mechanism. [Pg.69]

Often the key entity one is interested in obtaining in modeling enzyme kinetics is the analytical expression for the turnover flux in quasi-steady state. Equations (4.12) and (4.38) are examples. These expressions are sometimes called Michaelis-Menten rate laws. Such expressions can be used in simulation of cellular biochemical systems, as is the subject of Chapters 5, 6, and 7 of this book. However, one must keep in mind that, as we have seen, these rates represent approximations that result from simplifications of the kinetic mechanisms. We typically use the approximate Michaelis-Menten-type flux expressions rather than the full system of equations in simulations for several reasons. First, often the quasi-steady rate constants (such as Ks and K in Equation (4.38)) are available from experimental data while the mass-action rate constants (k+i, k-i, etc.) are not. In fact, it is possible for different enzymes with different detailed mechanisms to yield the same Michaelis-Menten rate expression, as we shall see below. Second, in metabolic reaction networks (for example), reactions operate near steady state in vivo. Kinetic transitions from one in vivo steady state to another may not involve the sort of extreme shifts in enzyme binding that have been illustrated in Figure 4.7. Therefore the quasi-steady approximation (or equivalently the approximation of rapid enzyme turnover) tends to be reasonable for the simulation of in vivo systems. [Pg.87]

Thus, the form of mass action law of chemical kinetics was recovered where feoi and k(, /Ki may be interpreted as the rate constants in the forward and reversed directions of reaction (4.476) respectively moreover, these constants depend only on temperature and fulfil the known relation (4.486) with the equilibrium constant. Further, this form of mass action rate equation automatically satisfies the principle of detailed balance which is used as a thermodynamic restriction on chemical kinetics and which, in turn, seems to be a result of permanence of atoms [140] stated in Sect.4.2. Conditions when this form transforms to traditional and experimentally supported mass action rate equations are discussed in Ref. [163]. In practice rate constants in the two directions often differ essentially (usually by extremely high or low values of equilibrium constants, cf (4.486)) and we obtain the classical form of the chemical kinetic law for an irreversible one-directional reaction. From (4.487) and (4.478) (and this is valid by (4.44) more generally) the constitutive equations for... [Pg.252]

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... [Pg.722]

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. [Pg.3054]

Law of Mass Action The effect of concentration on the rate is isolated as... [Pg.685]

The rates of many reactions are not represented by application of the law of mass action on the basis of their overall stoichiometric relations. They appear, rather, to proceed by a sequence of first- and second-order processes involving short-lived intermediates which may be new species or even unstable combinations of the reaclants for 2A -1- B C, the sequence could be A -1- B AB followed by A -1- AB C. [Pg.690]

The two basic laws of kinetics are the law of mass action for the rate of a reac tion and the Arrhenius equation for its dependence on temperature. Both of these are strictly empirical. They depend on the structures of the molecules, but at present the constants of the equations cannot be derived from the structures of reac ting molecules. For a reaction, aA + hE Products, the combined law is... [Pg.2071]

The interpretation of kinetic data is largely based on an empirical finding called the Law of Mass Action In dilute solution the rate of an elementary reaction is... [Pg.11]


See other pages where Mass action rate law is mentioned: [Pg.3056]    [Pg.3056]    [Pg.249]    [Pg.13]    [Pg.743]    [Pg.508]    [Pg.45]    [Pg.47]    [Pg.49]    [Pg.51]    [Pg.53]    [Pg.251]    [Pg.2062]    [Pg.2815]    [Pg.197]    [Pg.277]    [Pg.685]    [Pg.701]   
See also in sourсe #XX -- [ Pg.3 ]




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