Temperature dependence of the rate coefficient

These equations look innocuous, but they are highly nonlinear equations whose solution is almost always obtainable only numerically. The nonlinear terms are in the rate r (Ca, T), which contains polynomials in Ca, especially the very nonlinear temperature dependence of the rate coefficient k(T). For first-order kinetics this is... 

Boyd, A. A., and R. Lesclaux, The Temperature Dependence of the Rate Coefficients for /3-Hydroxyperoxy Radical Self Reactions, Int, J. Chem. Kinet., 29, 323-331 (1997). 

The modified thermal and phase space theories reproduce most three body association data equally well, including the inverse temperature dependence of the rate coefficient (Herbst 1981 Adams and Smith 1981), and are capable of reproducing experimental rate coefficients to within an order of magnitude (Bates 1983 Bass, Chesnavich, and Bowers 1979 Herbst 1985b). They should therefore be this accurate for radiative association rate coefficients if kr is treated correctly. 

FA and HPMS have provided much valuable data. However, the maximum temperature accessible to these techniques is limited and so variants of the DT technique have been used to study rate coefficients as a function of ion kinetic energy (up to several electron volts). The temperature dependences of the rate coefficient are then deduced (not without difficulty) from the data. The DT technique of Biondi and his co-workers 121 123) and the FDT technique, developed and carefully exploited by Albritton and others 124,125 which combines the versatility of the FA with the conventional DT technique, have proven to be especially useful (Sect. 3.2.2). The HPMS technique developed by Castleman and his co-workers 126, 27 is also providing valuable data of environmental interest. 

The temperature dependence of the rate coefficient was given by the following Arrhenius equation kx = 10(1394 02)exp [(-174,000 2000)/8.3147] s 1. The relative rate ratio isopropyl chloroformate ethyl chloroformate was 160 at 280 °C. The enhanced rate due to an a-substitution was associated with the degree of polarity of the alkyl halides7. Therefore, the transition state for chloroformate ester decomposition must also be polar. The mechanism was believed to involve a cyclic six-membered transition state in which formation of HC1 is assisted, as shown below. 

Activation energy was introduced in 1889 by -> Arrhenius in a paper [ii] which dealt with the temperature dependence of the - rate coefficient. The - Arrhenius expression (equation) in that a appears is valid over a finite temperature range. a is usually determined by plotting In k vs. l/T on the basis of the following expression [iii,iv]... 

In this chapter the aspects of model selection/discrimination and parameter estimation and the experimental acquisition of kinetic data are not dealt with, since they fall fell outside its scope. Moreover, in interpreting the observed temperature dependency of the rate coefficients in this chapter it was assumed that we are dealing with intrinsic kinetic data. As will be shown in a Chapter 7, other, parasitic, phenomena of mass and heat transfer may interfere, disguising the intrinsic kinetics. Criteria will be presented there, however, to avoid this experimental problem. 

The calculated rate coefficients at 298 K are 1.10 and 1.45 x 10 L/(cm s) for formaldehyde and acetaldehyde, respectively [27]. These values are in excellent agreement with the experimental data. The structure of the transition states are shown in Figure 12.4. Both are early transition states consistent with reactions with very low barriers. The transition state of OH hydrogen abstraction from acetaldehyde is earlier than the one of formaldehyde. Additionally, the possibility of the addition channel was excluded due to the large barrier associated to this process. The temperature dependence of the rate coefficient was not studied. In a more recent work [105] the level of the calculations was increased, the temperature dependence of the rate coefficient and the role of direct abstraction were studied. All the main conclusions from these articles are now accepted in recent works [106-108], and it is well known that the hydrogen abstraction is the main reaction channel if not unique [108,109]. 

Goy et have studied the reaction of CN radicals with hydrocarbons and hydrogen the CN radicals being produced by photolysis of ICN at 2537 A. Relative rate coefficients for H abstraction were obtained as a function of temperature for only C2H6-CH4 mixtures. For systems containing ethane-propane and propane alone no temperature dependence of the rate coefficient ratios were observed. For... 

In the work of Hynes et al. (1986) the temperature dependence of the rate coefficient for DMS + OH in 760 Torr air, together with temperature dependence of the branching ratio were determined. The authors obtained the following expression for bs for one atmosphere of air ... 

The kinetic data obtained in this work shows that, for all the temperatures studied, the rate coefficient for DMS + OH is dependent on the O2 partial pressure, increasing as the O2 partial pressure is increased from 0 to 500 mbar. At a fixed O2 partial pressure, the rate coefficient is observed to increase on decreasing the temperature from 299 to 250 K for 205 mbar and 500 mbar O2 partial pressure, the temperature dependence of the rate coefficient was found to be strongly. 

Figure 2 shows the temperature dependence of the rate coefficient for OH + DMS obtained in this work in 1000 mbar air and at an oxygen partial pressure of 500 mbar. For comparison this figure includes the fit of Hynes et al. (1986) in 1 atm of air and the values calculated for 205 mbar oxygen partial pressure and 500 mbar oxygen partial pressure using the new preferred expressions from the review of Atkinson et al. (2004). 

An approximate formula for the temperature dependence of the rate coefficient, k, is given by the Arrhenius equation... 

Recombination reactions differ from bimolecular and thermal decomposition reactions also by their weak and usually negative dependence on temperature. Recombination reactions do not require an activation energy. Rather, the excess energy has to be dissipated. If the temperature dependence of the rate coefficient is expressed nonetheless by an exponential factor, the exponent -Er/RsT is positive and R constitutes just a parameter... 

Some VT-relaxation rate coefficients at room temperature are shown in Table 2-19. Temperature dependencies of the rate coefficients are given in Table 2-20 most of them follow the Landau-Teller functionality. 

The exponential temperature dependency of the rate coefficient can cause enormous variations in its magnitude over reasonable temperature ranges. 

In a kinetic study the activation energy is generally not known a priori, or only with insufficient accuracy. The use of the equivalent reactor volume concept therefore leads to a trial-and-error procedure a value of is guessed and with this value and the measured temperature profile Vp is calculated by graphical or numerical integration. Then, for the rate model chosen, the kinetic constant is derived. This procedure is carried out at several temperature levels and from the temperature dependence of the rate coefficient, expressed by Arrhenius formula, a value of is obtained. If this value is not in accordance with that used in the calculation of Vp the whole procedure has to be repeated with a better approximation for . 

There are additional kinetic effects in the high-temperature chain reaction regime, besides the much higher and nonsteady gross reaction rate, which arise from the Arrhenius temperature dependence of the rate coefficients of most of the initiation and propagation (including... 

Further studies of the temperature dependence of the rate coefficients for the reactions of OH with a series of ethers under simulated atmospheric conditions,... 

Eor ferrocene sites at the end of long alkanethiols self-organized at gold electrodes and diluted with unsubstituted thiols with the redox moiety in contact with the electrolyte (Fig. 4a), Chidsey has reported [34] curved Tafel plots (Fig. 4b), which could be fitted by equations derived from Marcus theory with values of k = 0.85 eV and Z = 6.73 x 10 s"l eV" for a reaction rate of A = 2.5 s at in Fig. 4(b). Similar curvature in Tafel plots has been reported by Faulkner and coworkers [35] for adsorbed osmium complexes at ultramicro-electrodes (UME). The temperature dependence of the rate coefficient could also be fitted from Marcus equation and electron states in the metal and coupling factors given by quantum mechanics. 

Quantum caleulations of rotational relaxation of CO in cold and ultracold collisions with H2 have recently been performed by Yang and colleagues [132,133]. They reported quenching rate coefficients for y = 1 to 3 of the CO molecule in collisions with both ortho- and para-H2 [132]. Due to the relatively deep van der Waals interaction potential for the H2-CO system the cross-sections exhibit a number of narrow resonances for collision energies between 1.0 and 40.0 cm . The signatures of these resonances are present in the temperature dependence of the rate coefficient, which shows broad oscillatory features in the temperature range of 10 to 50 K [132]. 

Fig. 3.23. Temperature dependence of the rate coefficient for the reaction C2HJ+H2 —> C2H + H. As discussed by Gerlich, there is some disagreement between the free jet and the ion trap experiments. While, at low temperatures, the high pressure experiments seems to indicate an increasing rate coefficient, the 10 K ion trap results proof that the rate coefficient for the abstraction reaction is much smaller than 10 cm s . A possible explanation is the fast radiative association process (fcr(p-H2) = 5 X 10 cm s ), which has been observed in the ion trap experiment (open circle and triangle). The phase space calculations (solid line) have used adjusted parameters for getting the low temperature behavior.

Le Picard SD, Canosa A, Geppert W, Stoecklin T. (2004) Experimental and theoretical temperature dependence of the rate coefficient of the... 

This equation and slight variants of it are frequently referred to as the modified Arrhenius equation and sometimes as the Kooij equation, and are often used to express the temperature dependence of the rate coefficients in kinetic databases compiled for use in modelling atmospheric, combustion and astrochemical environments. For example, in KIDA (a Kinetic Database for Astrochemistry [29]), rate coefficients and their temperature dependences are expressed by the equation ... 

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