If the reaction products are irreversibly adsorbed on the surface of the catalyst they may act as very effective poisons by blocking the active centers for the forward reaction. In this case Roginskil found that the kinetic equation obtained had a form which was characteristic of an activated adsorption process. [Pg.254]

It is of interest to compare the pressure for the first and second limits of explosion derived from the same reaction model with those derived from equations for the one-centered kinetics of the branching-chain reactions [1] [Pg.110]

In a recent papet the chronoamperometry has been used to smdy the competitive occurrence of an electrochemical reaction of the mediators at the electrode and their chemical reaction with the cofectors of the Reaction Center of the photosyntheric bacterium Rhodobacter Sphaeroides. The overall process is modeled by a set of differential equations that allow the calculation of the kinetic constants of the chemical and elearochemical reactions respeaively. [Pg.102]

In this case, the reaction mixture permeates easily into the resin porous and there are more accessible active centers. As an opposite effect, when 5m and 5p are similar, the medium is highly polar, and the kinetic mechanism tends to a pseudo-homogeneous one, that usually shows a lower reaction rate. The modification of the kinetic equation should take into account both effects. [Pg.544]

Leaving aside individual reactions, mention will be made here only of one of the methods commonly used at present. This method involves elimination of time from the kinetic equations and attempts at finding stable solutions in terms of the Lyapunov stability theory. In the simple case of two variables X and Y (e.g. of two active centers, or of one active center and temperature), from the kinetic equations dx/dt = y) dy/dt = y(x, y) (x and y are either [Pg.202]

The kernel (26) and the absorbing probability (27) are controlled by the rate constants of the elementary reactions of chain propagation kap and monomer concentrations Ma(x) at the moment r. These latter are obtainable by solving the set of kinetic equations describing in terms of the ideal kinetic model the alteration with time of concentrations of monomers Ma and reactive centers Ra. [Pg.186]

The Flory principle allows a simple relationship between the rate constants of macromolecular reactions (whose number is infinite) with the corresponding rate constants of elementary reactions. According to this principle all chemically identical reactive centers are kinetically indistinguishable, so that the rate constant of the reaction between any two molecules is proportional to that of the elementary reaction between their reactive centers and to the numbers of these centers in reacting molecules. Therefore, the material balance equations will comprise as kinetic parameters the rate constants of only elementary reactions whose number is normally rather small. [Pg.170]

The thermodynamic form of kinetic equations is helpful for providing the kinetic thermodynamic analysis of the effect of various thermodynamic parameters on the stationary rate of complex stepwise processes. Following are a few examples of such analyses in application to the noncatalytic reac tions. The analysis of the occurrence of catalytic transformations is more specific because the concentrations and, therefore, the chemical potentials and thermodynamic rushes of the intermediates are usually related to one another in the total concentrations of the catalyticaUy active centers. (Catalytic reactions are discussed in more detail in Chapter 4.) [Pg.40]

Some authors have described the time evolution of the system by more general methods than time-dependent perturbation theory. For example, War-shel and co-workers have attempted to calculate the evolution of the function /(r, Q, t) defined by Eq. (3) by a semi-classical method [44, 96] the probability for the system to occupy state v]/, is obtained by considering the fluctuations of the energy gap between and 11, which are induced by the trajectories of all the atoms of the system. These trajectories are generated through molecular dynamics models based on classical equations of motion. This method was in particular applied to simulate the kinetics of the primary electron transfer process in the bacterial reaction center [97]. Mikkelsen and Ratner have recently proposed a very different approach to the electron transfer problem, in which the time evolution of the system is described by a time-dependent statistical density operator [98, 99]. [Pg.22]

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