Arrhenius curvature

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... 

The Arrhenius curvature could be attributed to the occurrence of two competing reactions with different activation energies. However, photolysis of 9a at —80°C afforded only p-chlorostyrenes 11a and 12a no carbene-solvent insertion product was detected, and reaction of the carbene with diazirine to give azine was considered unimportant at the diazirine concentrations employed. 

Of course carbene C-H insertion reactions are well known absolute kinetics have been reported for the insertions of ArCCl into isooctane, cyclohexane, and n-hexane,67 and of PhCCl into Si-H, Sn-H, and C-H bonds.68 More recently, detailed studies have appeared of PhCCl insertions into a variety of substrates bearing tertiary C-H bonds, especially adamantane derivatives.69 Nevertheless, because QMT is considered important in the low temperature solution reactions of MeCCl,60,63 and is almost certainly involved in the cryogenic matrix reactions of benzylchlorocarbene,59 its possible intervention in the low temperature solution reactions of the latter is a real possibility. We are therefore faced with two alternative explanations for the Arrhenius curvature exhibited by benzylchlorocarbene in solution at temperatures < 0°C either other classical reactions (besides 1,2-H shift) become competitive (e.g., solvent insertion, azine formation), or QMT becomes significant.7,59,66... 

The possible intervention of classical, competitive reactions in the low temperature solution chemistry of benzylchlorocarbene (10a) requires careful investigation. There are reasons to suspect azine (48) formation Goodman reported minor yields of azine in analogous MeCCl experiments,60 and Liu et al. found 40% of 48 in the photolysis of neat diazirine 9a.65 Perhaps azine formation is also significant at low temperature in hydrocarbon solvents. If so, the intervention of bimolecular azine formation, in competition with the unimolecular carbene 1,2-H shift, could lead to a nonlinear temperature dependence for the disappearance of 10a. Arrhenius curvature could then be explained without invoking QMT. 

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 value of B/ depends on the type of elementary process concerned. This relationship may account for the so-called Arrhenius curvature, which is exhibited by the rate coefficients of metathetical processes. 

The rearrangement of dimethylcarbene to propene has been studied " by laser flash photolysis and ab initio MO theory, and substituent effects at the migration origin on the rate of rearrangement of several alkylchlorocarbenes have been studied. It has been shown that the Arrhenius curvature observed for the rate constants of the... 

State-specific and thermal rate coefficients for this reaction are shown in Fig. 7. Substantial Arrhenius curvature is predicted above 1500 K, although the curvature predicted on the basis of the vibrational rate enhancement is insufficient to account for all of the experimentally observed behavior (see also Section 4). 

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. 

A more interesting possibility, one that has attracted much attention, is that the activation parameters may be temperature dependent. In Chapter 5 we saw that theoiy predicts that the preexponential factor contains the quantity T", where n = 5 according to collision theory, and n = 1 according to the transition state theory. In view of the uncertainty associated with estimation of the preexponential factor, it is not possible to distinguish between these theories on the basis of the observed temperature dependence, yet we have the possibility of a source of curvature. Nevertheless, the exponential term in the Arrhenius equation dominates the temperature behavior. From Eq. (6-4), we may examine this in terms either of or A//. By analogy with equilibrium thermodynamics, we write... 

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... 

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.)... 

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