Arrhenius behavior

The temperature dependence of chemical kinetics was observed before the detailed molecular viewpoint of modern chemistry was developed. An empirical relationship, called the Arrhenius equation, was proposed to describe the temperature dependence of the rate constant, k  

Here is the activation energy, R is the universal gas constant, T is the temperature (in kelvins), and is a proportionality constant called the frequency factor or preexponential factor. We noted earlier that a large activation energy should hinder a reaction. Equation 11.9 shows this effect As increases, k will be smaller, and smaller rate constants correspond to slower reactions. Note that because the temperature and activation energy appear in the exponent, the rate constant will be very sensitive to these parameters. That s why fairly small changes in temperature can have drastic effects on the rate of a reaction. 

The Arrhenius equation can be used to determine activation energy experimentally. Temperature is a parameter that we can usually control in an experiment, so it may help to remove it from the exponent. We can do this by taking the natural log of both sides of Equation 11.9  

Svante Arrhenius also studied acids and bases. The notion that acids form hT and bases form OH in water is attributed to him. 

In the troposphere, ozone can be converted to O2 by the following reaction with hydrogen oxide radicals  

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Linderoth T R, Florsch S, Laesgaard E, Stensgaard i and Besenbacher F 1997 Surface diffusion of Pt on Pt(110) Arrhenius behavior of iong ]umps Phys. Rev. Lett. 78 4978... 

Exploration of the region 0 < T < requires numerical calculations using eqs. (2.5)-(2.7). Since the change in /cq is small compared to that in the leading exponential term [cf. (2.14) and (2.18)], the Arrhenius plot k(P) is often drawn simply by setting ko = coo/ln (fig. 5). Typical behavior of the prefactor k and activation energy E versus temperature is presented in fig. 6. The narrow intermediate region between the Arrhenius behavior and the low-temperature limit has width... 

The PES found by Smedarchina et al. [1989] has two cis-form local minima, separated by four saddle-points from the main trans-form minima. The step-wise transfer (trans-cis, cis-trans) - because of endoergicity of the first stage - displays Arrhenius behavior even at T < T. . The concerted transfer of two hydrogen atoms was supposed to become prevalent at sufficiently low temperatures. However, because of too high a barrier for the concerted trans-trans transition, this... 

The diffusion coefficient corresponding to the measured values of /ch (D = kn/4nRn, is the reaction diameter, supposed to be equal to 2 A) equals 2.7 x 10 cm s at 4.2K and 1.9K. The self-diffusion in H2 crystals at 11-14 K is thermally activated with = 0.4 kcal/mol [Weinhaus and Meyer 1972]. At T < 11 K self-diffusion in the H2 crystal involves tunneling of a molecule from the lattice node to the vacancy, formation of the latter requiring 0.22 kcal/mol [Silvera 1980], so that the Arrhenius behavior is preserved. Were the mechanism of diffusion of the H atom the same, the diffusion coefficient at 1.9 K would be ten orders smaller than that at 4.2 K, while the measured values coincide. The diffusion coefficient of the D atoms in the D2 crystal is also the same for 1.9 and 4.2 K. It is 4 orders of magnitude smaller (3 x 10 cm /s) than the diffusion coefficient for H in H2 [Lee et al. 1987]. 

It is noteworthy that the above rule connects two quite different values, because the temperature dependence of is governed by the rate constant of incoherent processes, while A characterizes coherent tunneling. In actual fact, A is not measured directly, but it is calculated from the barrier height, extracted from the Arrhenius dependence k T). This dependence should level off to a low-temperature plateau at 7 < This non-Arrhenius behavior of has actually been observed by Punnkinen [1980] in methane crystals (see fig. 1). A similar dependence, also depicted in fig. 1, has been observed by Geoffroy et al. [1979] for the radical... 

The non-Arrhenius behavior of the inversion rate constant has been detected by [Deycard et al. 1988] for the oxyranyl radical,... 

The effect of including attractive interactions with the walls is essentially to reduce the acceptance rate of the algorithm as more monomers get adsorbed on the walls. The relaxation times show an Arrhenius behavior, similar to the result on Fig. 9 in Sec. III. 

The conductivity of ionic liquids often exhibits classical linear Arrhenius behavior above room temperature. However, as the temperatures of these ionic liquids approach their glass transition temperatures (T s), the conductivity displays signif-... 

FIGURE 13.23 An Arrhenius plot is a graph of In A against 11T. If, as here, the line is straight, then the reaction is said to show Arrhenius behavior in the temperature range studied. This plot has been constructed from the data in Example 13.8. 

FIGURE 5.1 Arrhenius behavior over a large temperature range. (Data from Monat, J. P., Hanson, R. K., and Kruger, C. H., Shock tube determination of the rate coefficient for the reaction N2 + O- NO + N, Seventeenth Symposium (International) on Combustion, Gerard Faeth, Ed., The Combustion Institute, Pittsburgh, 1979, pp. 543-552.)... 

A good model is consistent with physical phenomena (i.e., 01 has a physically plausible form) and reduces crresidual to experimental error using as few adjustable parameters as possible. There is a philosophical principle known as Occam s razor that is particularly appropriate to statistical data analysis when two theories can explain the data, the simpler theory is preferred. In complex reactions, particularly heterogeneous reactions, several models may fit the data equally well. As seen in Section 5.1 on the various forms of Arrhenius temperature dependence, it is usually impossible to distinguish between mechanisms based on goodness of fit. The choice of the simplest form of Arrhenius behavior (m = 0) is based on Occam s razor. 

A plot of the adatom density versus T is shown in Fig. 4. An anomalous increase in the density is observed at high temperatures. The dashed line represents the adatom population that would be predicted if there were no lateral interactions. However, the LJ potential between adatoms tends to stabilize them at the higher coverages, and it is this effect that causes the deviation from Arrhenius behavior at high temperatures. A similar temperature dependence is observed in the rate of mass transport on some metal surfaces (8,9), and it is possible that it is caused by the enhanced population of the superlayer at high temperatures. 

M. Sponsler, R. Jain, F. Corns, and D. A. Dougherty, Matrix-isolation decay kinetics of triplet cyclobutanediyls. Ohservation of both Arrhenius behavior and heavy-atom tunneling in C-C bond-forming reactions, J. Am. Chem. Soc. 1989, 111, 2240. 

A method is described for fitting the Cole-Cole phenomenological equation to isochronal mechanical relaxation scans. The basic parameters in the equation are the unrelaxed and relaxed moduli, a width parameter and the central relaxation time. The first three are given linear temperature coefficients and the latter can have WLF or Arrhenius behavior. A set of these parameters is determined for each relaxation in the specimen by means of nonlinear least squares optimization of the fit of the equation to the data. An interactive front-end is present in the fitting routine to aid in initial parameter estimation for the iterative fitting process. The use of the determined parameters in assisting in the interpretation of relaxation processes is discussed. 

These results support the idea that Arrhenius curvature in the rearrangements of MeCCl60 (and MeCBr61) may be associated with QMT, although the theoretical analysis found that QMT dominated the 1,2-H(D) shift only below —73°C at higher temperatures, the classical process became more important.63 The benzylchlorocarbene case is less clear. QMT is clearly important in matrices at 10-34 K, where the KIE for 1,2-H(D) shift is 2000 59 cf. Section IV.A. However, the nonlinear Arrhenius behavior exhibited by 10a or 10b in solution is largely due to the intervention of intermolecular reactions (Section IV.C) which obscure any contribution of QMT.71... 

The temperature dependence of the reaction rate constant closely (but not exactly) obeys the Arrhenius equation. Both theories, however, predict non-Arrhenius behavior. The deviation from Arrhenius behavior can usually be ignored over a small temperature range. However, non-Arrhenius behavior is common (Steinfeld et al., 1989, p. 321). As a consequence, rate constants are often fitted to the more general expression k = BTnexp( —E/RT), where B, n, and E are empirical constants. 

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