Temperature Dependence of Rate Coefficients

Ciary D C, Smith D and Adams N G 1985 Temperature dependence of rate coefficients for reactions of ions with dipolar molecules Chem. Phys. Lett. 119 320-6... 

The temperature dependence of reactions comes from dependences in properties such as concentration (Cj = PjfRT for ideal gases) but especially because of the temperature dependence of rate coefficients. As noted previously, the rate coefficient usually has the Arrhenius form... 

This chapter and chapter 5 study the prototypical thermokinetic oscillator. Thermal feedback replaces autocatalysis, and the Arrhenius temperature dependence of rate coefficients supplies non-linearity in the scheme P - A - B + heat. After careful study of this chapter the reader should be able to ... 

Rate equations state rates of formation (if positive) or consumption (if negative) of species in terms of moles per unit volume and unit time as functions of the local and momentary concentrations of the participants. For gas-phase reactions, partial pressures may be substituted for molar concentrations. Where necessary, rate coefficients are identified by double indices, the first member for the reactant, the second for the product (co-reactants and co-products are disregarded). The temperature dependence of rate coefficients is characterized by Arrhenius activation energies. 

The temperature dependence of rate coefficients of elementary steps generally follows the Arrhenius equation in good approximation. That of apparent rate coefficients of empirical rate equations of multistep reactions, however, may deviate in several ways The activation energy may be negative (slower rate at higher temperature) or have different values in different temperature regions. 

The reaction of OH radicals with alkenes differs from that with alkanes in that OH has a choice of attaching to the C=C double bond versus abstracting a hydrogen atom. Measurements of the temperature dependence of rate coefficients in addition to the observed product distributions have provided ample evidence for the preponderance of OH addition, at least for the smaller alkenes and alkadienes. The preference for addition is due to the fact that hydrogen abstraction reactions require an activation energy in contrast to the process of OH addition. Atkinson et al. (1979) have reviewed reactions of OH radicals with a number of alkenes. The large rate coefficients associated with addition reactions leave little doubt that longer side chains are necessary before H-atom abstraction can become competitive. An exception may be the more weakly bonded allylic H atom adjacent to the C=C double bond, as Atkinson et al. (1977) have pointed out. The present discussion will concentrate on ethene and propene as suitable examples for the oxidation of alkenes. 

The relative migration ability of CH3, C2H5 and CgHj groups is 1 36 10 (a detailed analysis of rearrangement kinetics and the temperature dependence of rate coefficients see... 

Chemical symbol for generic collision partner Initial mean molecular weight Exponent describing temperature dependence of rate coefficient kf ... 

The adsorber model comprises a system of (i) three parabolic partial differential equations for the mass transport of each single component coupled by both sorption isotherm equations and an expression for the temperature dependence of rate coefficients (ii) two differential equations for chemical reaction and (iii) two parabolic partial differential equations for heat transfer. Beside time, the model contains three spatial coordinates that refer to the interstitial column volume, the macropore volume and the micropore volume and that may be of different geometry. The solution of the problem for which a module-wise algorithm was developed, is described in detail in refs. [103,104]. 

Now we switch attention from the concentration dependence of reaction rates to the temperature dependence of rate coefficients. This, too, can give insights into the mechanism of the reaction. 

Table I. Temperature dependencies of rate coefficients from -R ...

The lack of experimental results at very tow temperature necessitated the extrapolation of rate coefficients from higher temperatures. At the same time, important theoretical efforts were made to predict the temperature dependence of rate coefficients. Several calculations are restricted to this part of the potential surface corresponding to tong range intermolecular forces (ca ure theories). They are generally performed from a classical or semiclassical viewpoint (Su and Bowers,... 

As an example consider a second-order reaction Here the suitable coupling between pex and V, over and above the couphng due to the compressibility of the system (the equation of state triangle in Fig. 15.3), comes from the fact that on decreasing V the number of reactions per unit time increases as V for fixed total number of particles. For an exothermic (endothermic) reaction this effect leads to increased (decreased) production of heat as V decreases, and consequently to temperature and pressure changes, in addition to those due to compression. For first-order reactions coupling can be achieved through the temperature dependence of rate coefficients. 

As explained in Ref. 44, the temperature dependence of rate coefficients can be measured rather quickly during the cooling of the trap, which typically takes 1 hr. Fitting experimental results measured for n-H2 and P-H2 has resulted in temperature dependent rate coefficients. 

An important part of specifying a chemical reaction mechanism is providing accurate parameterisations of the rate coefficients. In liquid phase and in atmospheric kinetics, the temperature dependence of rate coefficient k is usually described by the Arrhenius equation ... 

Arrhenius plots (graphs of log/c versus /T) showing the temperature dependence of rate coefficients are given for reactions if the data are too numerous or too scattered to be understood from the representations in the tables alone. In these graphs the data are marked by the initials of the authors. 

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