Arrhenius activation parameters, for

The Brook silene 28, produced photochemically as shown in equation 18, dimerizes to yield a mixture of the 1,2-disilacyclobutane 29 and the acyclic ene-dimer 3064, the common mode of dimerization for the large majority of l,l-bis(trialkylsilyl)silenes that have been studied to date12. Conlin and coworkers determined the absolute rate constant for dimerization of 28 in cyclohexane solution, k, tm = 1.3 x 107 M 1 s 1 at 23 °C65. Arrhenius activation parameters for the reaction were determined over the 0-60 °C temperature range. The values obtained, a = 0.9 0.4 kJmol 1 and log(A/M 1 s 1) = 7 1, are consistent with the stepwise mechanism for head-to-head dimerization originally proposed by Baines and Brook (equation 19)64, provided that the rate of reversion of the... 

Arrhenius activation parameters for cleavage reactions of aryl halide radical anions"... 

Table 1. Arrhenius activation parameters for gas phase pyrolysis of alkyl...

Observed Arrhenius activation parameters for allylic alcohol isomerizations are also consistent with a unimolecular rate-limiting step. In aqueous ethanol and aqueous dioxane, differences in reactivity due to structural changes in the allylic system are reflected primarily in the energy of activation. Values of entropy of activation are generally near Harris... 

From the temperatures for the one- and ten-hour half lives, calculated using equation 6, Arrhenius activation parameters can be calculated for each initiator and compared to the experimental values. This comparison is made for some of the entries of reactions 1-4 in Table V. At least five entries were chosen for each reaction, spanning a wide range of reactivity, using common entries as much as possible for the four reactions. 

Table 1 Arrhenius and Eyring activation parameters for the reductive elimination of halogens from chalcogenopyrylium dyes containing tellurium(IV) dihalide groups...

Table 2 Arrhenius and Eyring activation parameters for the second, Slow reaction observed by stopped-flow spectroscopy in the oxidative addition of halogens to diorgano tellurides 17, 20, and 23-25...

The second, slow reaction was followed for 17 and 23-25 in several solvents at several different reaction temperatures. Arrhenius and Eyring activation parameters for the second, slow reaction observed in the addition of iodine to 17 and 23-25 along with those for the addition of bromine to compound 20 are compiled in Table 2. In the examples of Table 2, the rate of reaction increases as the polarity of the solvent increases from CCI4 to EtOAc to CH3CN. The slow reaction remains first-order in all three solvents. For di-4-methoxyphenyltelluride (24), values of and A// in CH3CN are 20-40 kJ moP lower than in CCI4 or EtOAc. Again, the data from the kinetics studies are consistent with the formation of an ionic intermediate via a dissociative process. 

Table 3 Arrhenius and Eyring activation parameters for the debrominations of 2,3-dibromo-2-methylpentane (27) and 1,2-dibromodecane (29) with di-n-hexyltelluride (26) and tetra-n-butylammonium iodide...

In order to find out whether captodative substitution of a methyl radical can lead to persistency, the rate of disappearance by bimolecular selfreaction was measured for typical sterically unhindered captodative radicals (Korth et al., 1983). The t-butoxy(cyano)methyl radical, t-butylthio(cyano)-methyl radical and methoxy(methoxycarbonyl)methyl radical have rate constants for bimolecular self-reactions between 1.0 x 10 and 1.5 X 10 1 mol s Mn the temperature range —60 to - -60°C. The dilTusion-controlled nature of these dimerizations is supported by the Arrhenius activation parameters. Thus, it has to be concluded that there is no kinetic stabilization for captodative-substituted methyl radicals. On the other hand, if captodative-substituted radicals are encountered which are kinetically stabilized (persistent) or which exist in equilibrium with their dimers, then other influences than the captodative substitution pattern alone must be added to account for this phenomenon. 

Table 12 gives Arrhenius activation parameters and rate constants for thermal decomposition of A,A-dimethoxybenzamides 194a-d. AS values are low when compared to homolysis of diacyl peroxides and peroxides, for which values are typically around 8-11 cal K moG. This has been attributed to significant ji stabilization and restricted... 

Activation parameters for template polymerization were computed from Arrhenius relationship ... 

From the Arrhenius plots (Fig.2) the activation parameters for propagation on macroions and on macroion-pairs were evaluated. They are given in Table 3. 

Head-to-tail dimerization of 1,1-diphenylsilene (19a), produced by laser flash photolysis of 1,1-diphenylsilacyclobutane (17a), yields the 1,3-disilacyclobutane 2761,62 with a rate constant fcdim = (1-3 0.3) x 1010 M 1 s 1 in hexane solution at 25 °C (equation 17)46. This value is within a factor of two of the diffusional rate constant in hexane at this temperature, indicating that dimerization of this silene is faster than reaction with even the most potent of nucleophilic trapping reagents (see Table 3). More recently, the temperature dependence of the rate constant for dimerization of 19a has been studied63. The results of these experiments are shown in Figure 1, and lead to Arrhenius activation parameters of a = -4 2 Id moD1 and log(A/M 1 s"1) = 9.2 0.4. 

The activation parameters for the acid-catalyzed hydrolysis of long chain alkyl sulfates compared to those for non-micellar ethyl sulfate calculated from potentiometric data indicate that the rate acceleration accompanying micellization is primarily a consequence of a decrease in the enthalpy of activation rather than an increase in the entropy (Kurz, 1962). However, the activation energies for the acid-catalyzed hydrolysis of sodium dodecyl sulfate calculated from spectrophotometric data have been reported to be identical (Table 8) for micellar and non-micellar solutions, but the entropy of activation for the hydrolysis of the micellar sulfate was found to be 6 9 e.u. greater than that for the non-micellar system (Motsavage and Kostenbauder, 1963). This apparent discrepancy may be due to the choice of the non-micellar state as the basis of comparison, i.e. ethyl sulfate and non-micellar dodecyl sulfate, to temperature dependent errors in the values of the acid catalyzed rate constant determined potentiometrically, or to deviations in the rate constants from the Arrhenius equation. 

With the assumptions that (2) represents the slow step and that kj = Ogg calculated Arrhenius parameters for the concurrent bimolecular (1) and unimolec-ular (2) processes. The Arrhenius activation energy for step (2) was calculated to be 43 kcal.mole for each of the alkyl iodides, and, assuming Ogg s mechanism, this value should equal the carbon-iodine bond dissociation energy in each of these molecules. Modern studies show that the D(R—I) values are in the range 50-55 kcal.mole" and for this and other reasons Ogg s mechanism is now considered unsatisfactory. 

The important point that arises from the Rodger-Sceats reduction is that the dynamics can take place on an effective potential P defined by Eq. (2.19). The origin of the potential can be traced back to the requirement that at long times the system must achieve a thermal distribution which is consistent with a Boltzmann distribution on the full potential and the use of P simply ensures that the partition functions of the system will be given correctly. This will be very important in applications to chemical reactions, because the partition function plays an important role in determining Arrhenius activation parameters. The dependence of P on the reaction coordinate simply accounts for this effect. For example, the reactant and transition state configurations are defined by the minima and maxima of P at qi and gj, and the Boltzmann factor for activation is... 

TEMPERATURE EFFECTS. The Arrhenius activation parameters viz., Ep and Ep for the processes of diffusion and permeation have been... 

Table 5. Arrhenius and Activation Parameters for [1,5] Sigmatropic Hydrogen Shifts in Methyl-1,3-cyclohexadienes (1 -3)12 5...

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