Rate coefficient, thermalized

Wahnstrom G and Metiu H 1988 Numerical study of the correlation function expressions for the thermal rate coefficients in quantum systems J. Phys. Chem. JPhCh 92 3240-52... 

Thachuk M and Schatz G C 1992 Time dependent methods for calculating thermal rate coefficients using flux correlation functions J. Chem. Phys. 97 7297-313... 

Rate constants for initiator decomjosition and radical reactions in aqueous laiase. The rate coefficient for KgSgOg thermal decoiposition has been calculated at the relevant teiperature according to Kolthoff and Hiller (W). The... 

Fig. 9. The thermal rate coefficient for H2 + OH - H + H2O on the WDSE, YZCL1, and YZCL2 surfaces are compared with experimental results.74...

We can calculate the thermal rate constants at low temperatures with the cross-sections for the HD and OH rotationally excited states, using Eqs. (34) and (35), and with the assumption that simultaneous OH and HD rotational excitation does not have a strong correlated effect on the dynamics as found in the previous quantum and classical trajectory calculations for the OH + H2 reaction on the WDSE PES.69,78 In Fig. 13, we compare the theoretical thermal rate coefficient with the experimental values from 248 to 418 K of Ravishankara et al.7A On average, the theoretical result... 

Fig. 15. Comparison of the theoretical thermal rate, fc(T), with experimental results.74 Also shown are the initial state selected rate coefficient for the (0,0) state, and an approximate theoretical thermal rate coefficient, fcest(T).

Ion-molecule radiative association reactions have been studied in the laboratory using an assortment of trapping and beam techniques.30,31,90 Many more radiative association rate coefficients have been deduced from studies of three-body association reactions plus estimates of the collisional and radiative stabilization rates.91 Radiative association rates have been studied theoretically via an assortment of statistical methods.31,90,96 Some theoretical approaches use the RRKM method to determine complex lifetimes others are based on microscopic reversibility between formation and destruction of the complex. The latter methods can be subdivided according to how rigorously they conserve angular momentum without such conservation the method reduces to a thermal approximation—with rigorous conservation, the term phase space is utilized. 

Even in J-type shock models, it is not appropriate to use thermal rate coefficients because the internal degrees of freedom will cool rapidly (via radiation) in the low density medium, whereas the translational degree of freedom will cool much more slowly. Appropriate rate coefficients are then those in which only translation is strongly excited such rate coefficients can be considerably lower than thermal rates for systems in which vibrational energy is the most efficient at inducing reaction. 

The ions or cluster ions are thermalized by collisions with an inert carrier gas (usually helium), although often argon or even nitrogen is employed. Neutral reactant gas is added through a reactant gas inlet at an appropriate location downstream in the flow tube, and allowed to react with the injected ions. Rate coefficients, k, are determined by establishing pseudo-first-order reaction conditions in which the reactant ion concentration is small compared to the reactant neutral concentration. Bimolecular rate coefficients, k, are obtained from the slope of the natural logarithm of the measured signal intensity, /, of the reactant ion versus the flow rate (2b of reactant gas 45,48-50... 

Some reactions of the type H+hydride - hydride radical+H2 have been studied, mainly at lower temperatures, with H atoms generated by an external source. There might be appreciable errors in extrapolation of these rate coefficients to temperatures where thermal decomposition takes place. In many cases only a lower or upper limit of the rate of consecutive reactions can be given, especially if the decomposition takes place at temperatures appreciably above 1000 °K. We will not discuss reaction mechanisms in detail which lead to untested rate phenomena nor those which are based upon product analysis without a well-defined time history. It is true, however, that no decomposition of a hydride consisting of more than two atoms has a mechanism which is fully understood and which can be completely described in terms of the kinetics of the elementary reactions. 

Table 8 gives expressions for the rate coefficients of secondary reactions in the thermal decompositions of N20, where these have been measured. To our knowledge no determination has been made of ks. 

RATE COEFFICIENTS FOR ELEMENTARY STEPS IN THE THERMAL DECOMPOSITION OF NO... 

Rate coefficients of elementary steps in the thermal decomposition of HN03 are summarized in Table 21. 

The thermal decomposition of F202 was studied by Schumacher and Frisch401 who found it to be a homogeneous, unimolecular reaction with the first-order rate coefficient given by... 

Shushunov and Pavlova158 have investigated the thermal decomposition of nitrogen trichloride at a concentration of 0.7 mole.l-1 in liquid carbon tetrachloride. In the absence of light and air the reaction was first order up to at least 50 % decomposition, and the rate coefficients fitted the Arrhenius expression... 

The cross-section for electron attachment shows an inverse dependence on electron velocity170, and for this reason there has been a marked inconsistency in the cross-sections obtained by different methods. Mahan and Young104 have reported a capture rate coefficient for thermal electrons of 2x 1014 l.mole-1.sec-1. This was obtained by a microwave technique in the presence of helium as a moderating gas. 

Laurie and Long59 studied the thermal decomposition of dimethyl cadmium in the absence of inhibitors. Rate coefficients were calculated on the basis of the undecomposed alkyl. A marked surface affect was noted. The homogeneous rate coefficient was obtained at 258 °C by studying the pyrolysis with various surface to volume ratios and extrapolating to zero surface. The mechanism proposed is... 

The thermal decomposition of this alkyl was studied in a static system over the temperature range 162-192.4 °C121. The surface of the reaction vessel was unintentionally activated before each run by rinsing with distilled water before baking out. Under these conditions the decomposition occurs by a chain mechanism with initiation and termination at the walls. The overall rate coefficient for the decomposition is 1.58 x 108 exp(—29,000/RT) sec-1. 

Over the temperature range 659-717 °C and above 100 torr the thermal decomposition of this alkyl is first-order and homogeneous126. The overall rate coefficient is 1.6x 1015 exp(—78,800/Hr) sec-1. The detailed mechanism is undoubtedly complex. The main gaseous products at high conversion are H2 and CH4. The following steps have been proposed127... 

The thermal decomposition is first-order and the rate coefficient is given by k = 1.7 x 1014 exp(—51,000/i T) sec-1. The mean metal-carbon bond dissociation energy in this alkyl is 58.0 kcal.mole-1. In view of the normal frequency factor, it might seem reasonable to relate the observed activation energy to... 

The rate constant is measured in units of moles dnr3 sec /(moles dnr3)", where n = a + b. Time may also be in minutes or hours. It should be noted that in case where the reaction is slow enough, the thermal equilibrium will be maintained due to constant collisions between the molecules and k remains constant at a given temperature. However, if the reaction is very fast the tail part of the Maxwell-Boltzmann distribution will be depleted so rapidly that thermal equilibrium will not be re-established. In such cases rate constant will not truly be constant and it should be called a rate coefficient. 

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