Arrhenius plot curvature

Usually the Arrhenius plot of In k vs. IIT is linear, or at any rate there is usually no sound basis for coneluding that it is not linear. This behavior is consistent with the conclusion that the activation parameters are constants, independent of temperature, over the experimental temperature range. For some reactions, however, definite curvature is detectable in Arrhenius plots. There seem to be three possible reasons for this curvature. 

Thus curvature in an Arrhenius plot is sometimes ascribed to a nonzero value of ACp, the heat capacity of activation. As can be imagined, the experimental problem is very difficult, requiring rate constant measurements of high accuracy and precision. Figure 6-2 shows a curved Arrhenius plot for the neutral hydrolysis of methyl trifluoroacetate in aqueous dimethysulfoxide. The rate constants were measured by conductometry, their relative standard deviations being 0.014 to 0.076%. The value of ACp was estimated to be about — 200 J mol K, with an uncertainty of less than 10 J moE K. ... 

AC is interpreted as the difference in heat capacities between the transition state and the reactants, and it may be a valuable mechanistic tool. Most reported ACp values are for reactions of neutral reactants to products, as in solvolysis reactions of neutral esters or aliphatic halides. " Because of the slight curvature seen in the Arrhenius plots, as exemplified by Fig. 6-2, the interpretation, and even the existence, of AC is a matter of debate. The subject is rather specialized, so we will not explore it deeply, but will outline methods for the estimation of ACp. 

Fig. 7.1 Arrhenius plot for the oxidation of mild steel and low-alloy steels in air showing a sharp break it the slope at d curvature due to the appearance of FeO in the scale above...

Above 570°C, a distinct break occurs in the Arrhenius plot for iron, corresponding to the appearance of FeO in the scale. The Arrhenius plot is then non-linear at higher temperatures. This curvature is due to the wide stoichiometry limits of FeO limits which diverge progressively with increasing temperature. Diffraction studies have shown that complex clusters of vacancies exist in Fe, , 0 Such defect clustering is more prevalent in oxides... 

Three possibilities were considered to account for the curved Arrhenius plots and unusual KIEs (a) the 1,2-H shift might feature a variational transition state due to the low activation energy (4.9 kcal/mol60) and quite negative activation entropy (b) MeCCl could react by two or more competing pathways, each with a different activation energy (e.g., 1,2-H shift and azine formation by reaction with the diazirine precursor) (c) QMT could occur.60 The first possibility was discounted because calculations by Storer and Houk indicated that the 1,2-H shift was adequately described by conventional transition state theory.63 Option (b) was excluded because the Arrhenius curvature persisted after correction of the 1,2-H shift rate constants for the formation of minor side products (azine).60... 

FIG U RE 1.4 Arrhenius plots for three Y203-Zr02 compositions showing different curvatures with increasing temperatures. (Data from Badwal, S.P.S., Solid State Ionics, 52, 23, 1992.)... 

The very important reaction (3.44) actually proceeds through a four-atom activated complex [10, 11] and is not a simple reaction step like reaction (3.17). As shown in Fig. 3.6, the Arrhenius plot exhibits curvature [10]. And because the reaction proceeds through an activated complex, the reaction rate exhibits some pressure dependence [12],... 

Recently, transition state theory calculations were applied to a class of reactions involving OH radicals and haloalkanes, again to account systematically for the expected curvature in Arrhenius plots for these reactions (Cohen and Benson, 1987a). Subsequently, empirical relationships were also derived for the a priori determination of pre-exponential factors (A) and activation energies ( ) based on an assumed T dependency of the pre-exponential factor (Cohen and Benson, 1987b). This and related studies clearly illustrate the broad utility of transition state theory in the systematic development of detailed chemical kinetic mechanisms. 

Borders R.A. and Birks J.W. (1982) High-precision measurements of activation energies over small temperature intervals curvature in the Arrhenius plot for the reaction NO + O3 = NO2 + O2. /. Phys. Chem. 86, 3295-3302. 

The temperature dependence is given in the form k = BT"e c /1, where n is usually taken as 2, except for CH4. This fit procedure provides curvature in the Arrhenius plot similar to that which is observed. Donahue et al. (1998a) propose an alternate form of the... 

Note that energies ED0 and EA0 are both referenced to the conduction band. Significant curvature in Arrhenius plot probably inhomogeneous sample. 

We now turn to the Cr-doped GaAs samples. If we ignore sample MOR 56/76, which showed curvature in the Arrhenius plot, the following mean values are obtained A0 a 0.78 eV and QA a 45. There is more variation in the E0 for Cr-doped samples than for -doped samples, possibly because of contamination in some of the Cr-doped samples. For the Cr acceptor, QK is defined somewhat differently than for the donor case (Eq. 23). Thus, if ND, = 0 in Eq. (21), we get... 

By preparing an Arrhenius plot (i.e., In kK versus 7 -1), estimate a pre-exponential factor A and an activation energy E for the surface reaction. Assume that the reaction is first order in CH4. Is there observable curvature in the Arrhenius plot ... 

The isomerizations of n-butenes and n-pentenes over a purified Na-Y-zeolite are first-order reactions in conversion as well as time. Arrhenius plots for the absolute values of the rate constants are linear (Figure 2). Similar plots for the ratio of rate constants (Figure 1), however, are linear at low temperatures but in all cases except one became curved at higher temperatures. This problem has been investigated before (4), and it was concluded that there were no diffusion limitations involved. The curvature could be the result of redistribution of the Ca2+ ions between the Si and Sn positions, or it could be caused by an increase in the number of de-cationated sites by hydrolysis (6). In any case the process appears to be reversible, and it is affected by the nature of the olefin involved. In view of this, the following discussion concerning the mechanism is limited to the low temperature region where the behavior is completely consistent with the Arrhenius law. 

Figure 9.1 presents self-diffusivity data for DD(dissoc), DD(undissoc), DB, DS, DXL, and DL, for f.c.c. metals on a single Arrhenius plot. With the exception of the surface diffusion data, the data are represented by ideal straight-line Arrhenius plots, which would be realistic if the various activation energies were constants (independent of temperature). However, the data are not sufficiently accurate or extensive to rule out some possible curvature, at least for the grain boundary and dislocation curves, as discussed in Section 9.2.3. 

The rate constant, k, for most elementary chemical reactions follows the Arrhenius equation, k = A exp(— EJRT), where A is a reaction-specific quantity and Ea the activation energy. Because EA is always positive, the rate constant increases with temperature and gives linear plots of In k versus 1 IT. Kinks or curvature are often found in Arrhenius plots for enzymatic reactions and are usually interpreted as resulting from complex kinetics in which there is a change in rate-determining step with temperature or a change in the structure of the protein. The Arrhenius equation is recast by transition state theory (Chapter 3, section A) to... 

Although it is difficult to detect curvature in the Arrhenius plots of the rate constant for unfolding, ACp D) can be determined by the same trick used for measuring ACp(N D) in equilibrium unfolding (Chapter 17, section A1F) measure AHiD at various values of acid pH and plot log Aversus , the average temperature range for the experiments (Figure 18.3).27... 

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