Activation energy difference

It may be unsafe to carry this discussion further until more data are available. Knowledge of the activation parameters would be especially desirable in several respects. Reactivity orders involving different reagents or substrates may be markedly dependent on temperature. Thus, in Table IV both 2- and 4-chloroquinolines appear to be about equally reactive toward sodium methoxide at 86,5°. However, the activation energies differ by 3 kcal/mole (see Section VII), and the relative rates are reversed below and above that temperature. Clearly, such relative rates affect the rs-/ ro- ratios. 

The activation energy differences of My as well as of and M, and k /kp and kt/kp. were calculated from Arrhenius and Mayo plots, respectively, by linear regression analysis using a computer. Hie AEjjw values given in kcal/mole can be converted to kJ/mole by multiplying with 4.18. 

The activation energy differences and frequency factor ratios have been calculated from measurements of Cs at several temperatures and in most cases not merely from the 60° and 100°C results shown here. 

Fig. 29.—Semilog plot of molecular weight against the reciprocal of the polymerization temperature for isobutylene polymerized in the presence of BF3. Results have been recalculated from the data of Thomas et al. The slope of the line corresponds to an activation energy difference of 4.6 kcal./mole.

A very incisive set of experiments on Pd(lll) (16a) and Pt(lll) (16b) done in Gerhard Ertl s lab, show that the Eley-Rideal pathway makes no measurable contribution to the C0 production rate for many low pressure conditions. In these experiments, a steady-state CO pressure was established, the 0 pressure was modulated and the phase-lag of the modulated CO2 product signal was measured. The slope of In (tamj)), where 4> is the phase lag, as a function of T- can be interpreted in terms of an activation energy difference (Er - E ) between reaction and desorption. The result for Pt(lll) is -10.8 kcal mole- as shown in Figure 12 (16b). For an Eley-Rideal pathway in which a gas phase CO molecule makes a direct or impact attack on an oxygen adatom, E[Pg.51]

The temperature dependence of the large isotope effect for the 2,4,6-collidine is just as striking (see Chart 1 and Fig. 2). In place of the expected unit value of Ah/Aq, a value around 0.15 was found accompanied by an enormous isotopic difference in enthalpies of activation, equivalent to an isotope effect of 165. Both of these results had earlier been shown by Bell (as summarized by Caldin ) to be predicted by a onedimensional model for tunneling through a parabolic barrier. The outlines of Bell s treatment of tunneling are given in Chart 2, while Fig. 3 shows that the departure of the isotopic ratios of pre-exponential factors from unity and isotopic activation energy differences from the expected values are both predicted by the Bell approach. 

Ah/At = 7.4 and A /Ax = 1.8 and isotopic activation energy differences that are within the experimental error of zero. The values of the two A-ratios correspond to a Swain-Schaad exponent of 3.4, not much different from the semiclassical expectation of 3.3. The a-secondary isotope effects are 1.19 (H/T), 1.13 (H/D), and 1.05 (D/T), which are exactly at the limiting semiclassical value of the equilibrium isotope effect. The secondary isotope effects generate a Swain-Schaad exponent of 3.5, again close to the semiclassical expectation. At the same time that the isotope effects are temperature-independent, the kinetic parameter shows... 

In the two different steps, Eqns. 9-24a and 9-24b, for the formation of intermediate radicals, the initial state differs in energy by an amount equivalent to the band gap as shown in Fig. 9-8. Consequently, the activation energy differs in the two steps as shown in Eqn. 9-26 ... 

Thermal rearrangement of propadienylcyclopropanes to methylenecyclopentenes has been examined in several cases however, selective transformation to the product has not necessarily been easy due to the harsh reaction conditions required for the rearrangement. The first example of this type of reaction was reported by Dewar, Fonken, and co-workers in a paper on the kinetics of the thermal reaction of 3-cyclopropyl-l,2-butadiene (44), and the reaction was found to proceed much faster (activation energy difference 8.2 kcal) than that of the corresponding vinylcyclopropane [25]. Several examples have appeared since this initial work, most of which have dealt with the mechanistic aspect of the reaction, but none of them has reached a synthetically useful level [26]. For example, thermal reaction of 3-(2-methylcyclopropyl)-1,2-butadiene (45) gives a mixture of five products, as shown in Scheme 20 [27]. 

For 20, the isotope effect k /kP can be traced to a difference E - E of 4 Kcal/mole in the activation energies which is countered by a preexponential factors ratio of A°/A = 87 (Table 23). A similar situation is observed for 44. Here the Arrhenius activation energy difference amounts to E - E = 4.4 Kcal/mole and the preexponential factors ratio is A /A = 53 (Table 24). 

There is ample preparative evidence that we have to assume dual reaction pathways which differ with respect to the symmetry behavior of the process. Here we are not faced with large differentiation energies leading to a concept of forbidden to allowed but with reactions separated by smaller activation energy differences more appropriate represented by the terms preferred and/or restricted . 

Kinetic product ratios show dependence with activation energy differences which are identical to thermodynamic product ratios with difference in reactant and product energies (see box on page 9). 

In order to understand why the activation energies differ between the two pathways, Mui et al. examined the transition state geometries [279]. They found that as electron density is donated from the amine lone pair to the down silicon atom upon adsorption into the precursor state, the up Si atom in the dimer becomes electron rich. At this stage, the dative bonded precursor can be described as a quaternary ammonium ion. The N—H dissociation pathway can thus be interpreted as the transfer of a proton from the ammonium ion to the electron-rich up Si atom through a Lewis acid-base reaction. In the transition state for this proton transfer, the N—H and Si—H... 

Above 300°C. the effective reaction of an alkyl radical with oxygen may be Reaction 3 rather than 2 because of the reversibility of Reaction 2. If it is assumed that Reaction 3 is important at about 450°C., its rate can be estimated from the competition between pyrolysis and oxidation of alkyl radicals. Falconer and Knox (21) observed that the ratio of (pro-pene)/(ethylene) from the oxidation of propane between 435° and 475°C. increased with oxygen concentration and decreased with temperature—the apparent activation energy difference for the two reactions forming the olefins being 27 =t 5 kcal. per mole. They interpreted this result in terms of a competition between Reactions 1 and 3. The observed ratio (propene)/(ethylene) was 3.5 at 435°C. and 10 mm. of Hg pressure. If log ki(propyl) = 13.2 — 30,000/2.30RT, the value for the n-propyl radical (34), then log k3 = 8.0. If the A factor is 109-3, we derive the Arrhenius equation... 

The activation energy difference Ei — E3 = 25 kcal per mole then agrees with the experimental value. 

The two rates are thus equal at about 400°C., and Reaction 3, if it occurred, would slowly take over from 2 + 8 at above this temperature. The rate of Reaction 3 relative to 7 would show an activation energy difference of about 24 kcal. per mole, so that it gives no help in explaining the apparent lack of dependence of (conjugate olefin)/(other products) on temperature. 

The decrease in the activation energy difference in the series EtAlCl2 to PF5 might be due to differences in the nucleophilicity of the counterions formed by the various coinitiators. The less nucleophilic counterion forms a looser ion pair with the cationic chain end, which in turn reduces the steric barrier to propagation without affecting isomerization. This is reflected in a decrease in the activation energy difference between the two processes and results in a decrease in the change of I with temperature. 

If the activation energy difference, (E34 — E32), is known, rate constant ratios may be evaluated. Conversely, if the latter are known, (E34 - E32) may be evaluated. If second explosion limits for a series of undiluted mixtures of hydrogen and oxygen are compared, Equation 42 becomes... 

The remarkable regularity observed in the asymmetric induction for a large number of substrates and for widely different reaction conditions is surprising in view of the relatively small overall activation energy difference involved for the formation of the two antipodes... 

There appear to be two C5-dehydrocyclizations over platinum-on-carbon catalyst. Activation energy differences suggest that the reaction involving an sp2 and an sp3 carbon atom (a cyclization in which the new bond is formed between an aliphatic and an aromatic carbon atom) is different from cyclizations involving two sp3 carbon atoms (in which the new bond is formed between aliphatic carbon atoms of two side-chains). 

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