The electron exchange rate k (Eq. 10.5) is a function of the transmission coefficient k (approximately 1 for reactions with substantial electronic coupling (>4 kJ), i.e., for adiabatic reactions), the effective collision frequency in solution (Z 1011 M 1 s 1 Ar2) and the free energy term AG. [Pg.112]

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. [Pg.653]

Knock resistance has also been correlated with other preflame reaction properties such as the rate of pressure development during adiabatic compression (17), the temperature coefficient of preflame reactions (202), and the pressure developed prior to firing (34). Estrad re (59) made a correlation between the temperature of initial exothermic oxidation in a tube and knock. No quantitative connection exists between apparent activation energy (160) or the total heat (179) of the precombustion reactions and knock. [Pg.191]

These two possibilities of reaction processes make much difference in calculating the rate of any chemical reaction. According to the transition state theory formalism, these two types of reactions (i.e., adiabatic and nonadiabatic) influence the value of the transmission coefficient, k, which is a preexponential term in the absolute rate expression. The value of k is considered unity for the adiabatic reaction and less than unity for a nonadiabatic reaction. [Pg.76]

The reaction O -I- N2 NO -I- N (6-2), hmiting the Zeldovich mechanism of NO synthesis in air plasma, proceeds in non-equihbrium conditions mostly through the non-adiabatic chaimel (Fig. 6-6) with probability (6-32). To find out the rate coefficient of the reaction under non-equilibrium conditions (F > To) as a function of vibrational (T ) and translational (To) temperatures, probabihty (6-32) should be averaged over the vibrational [Pg.367]

The determination of the microcanonical rate coefficient k E) is the subject of active research. A number of techniques have been proposed, and include RRKM theory (discussed in more detail in Section 2.4.4) and the derivatives of this such as Flexible Transition State theory. Phase Space Theory and the Statistical Adiabatic Channel Model. All of these techniques require a detailed knowledge of the potential energy surface (PES) on which the reaction takes place, which for most reactions is not known. As a consequence much effort has been devoted to more approximate techniques which depend only on specific PES features such as reaction threshold energies. These techniques often have a number of parameters whose values are determined by calibration with experimental data. Thus the analysis of the experimental data then becomes an exercise in the optimization of these parameters so as to reproduce the experimental data as closely as possible. One such technique is based on Inverse Laplace Transforms (ILT). [Pg.166]

This is the reverse process with respect to the dissociative attachment (2-66) and therefore it can also be illnstrated by Fig. 2-7. The associative detachment is a non-adiabatic process, which occnrs via intersection of electroiuc terms of a complex negative ion A -B and corresponding molecnle AB. Rate coefficients of the non-adiabatic reactions are qnite high, typically kd = 10 °-10 cm /s. The kinetic data and enthalpy of some associative detachment processes are presented in Table 2-7. [Pg.35]

Relatively little attention has been given in the literature to the electronic transmission coefficient for electrochemical reactions. On the basis of the conventional collisional treatment of the pre-exponential factor for outer-sphere reactions, Kel has commonly been assumed to equal unity, i.e. adiabatic reaction pathways are followed. Nevertheless, as noted above, the dependence of xei upon the spatial position of the transition state is of key significance in the "encounter pre-equilibrium treatment embodied in eqns. (13) and (14). Thus, the manner in which Kel varies with the reactant-electrode separation for outer-sphere reactions will influence the integral of reaction sites that effectively contribute to the overall measured rate constant and hence the effective electron-tunneling distance, Srx, in eqn. (14). [Pg.23]

In electrochemical kinetics, this model corresponds to the Butler-Vohner equation widely used for the electrode reaction rate. The latter postulates an exponential (Tafel) dependence of both partial faradaic currents, anodic and cathodic, on the overall interfacial potential difference. This assumption can be rationalized if the electron transfer (ET) takes place between the electrode and the reactant separated by the above-mentioned compact layer, that is, across the whole area of the potential variation within the framework of the Helmholtz model. An additional hypothesis is the absence of a strong variation of the electronic transmission coefficient", for example, in the case of adiabatic reactions. [Pg.42]

The idea that the vibrational enhancement of the rate is due to the attractive potential for excited vibrational states of the reactant is closely related to the observation made long ago based on transition state theory [25,26]. Poliak [25] found that for vibrationally highly excited reactants the repulsive pods (periodic orbit dividing snrface) is way out in the reactant valley, and the corresponding adiabatic barrier is shallow Based on this theory one can explain why dynamical thresholds are observed in reactions with vibrationally excited reactants. The simplicity of the theory and its snccess for mostly collinear reactions has a real appeal. However, to reconcile the existence of a vibrationally adiabatic barrier with the captnre-type behavior - which seems to be supported by the agreement of the calculated and experimental rate coefficients [23] -needs further study. [Pg.359]

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