Activation energy, stability

They also studied decomposition rates at several different temperatures. These data were fitted into the Arrhenius equation with an excellent correlation (half-life in minutes was plotted against 1000/T in °K.). The slope of the lines is E/2.303R, where E is the activation energy. Stabilizers were shown to raise this activation energy. This is not surprising in that a stabilizer actually physically separates the toxicant from the catalytic site. 

Activation energy, stability in trickle-bed reactors, 76 Activation overpotential, cross-flow monolith fuel cell reactor, 182 Activity balance, deactivation of non-adiabatic packed-bed reactors, 394 Adiabatic reactors stability, 337-58 trickle-bed, safe operation, 61-81 Adsorption equilibrium, countercurrent moving-bed catalytic reactor, 273 Adsorption isotherms, countercurrent moving-bed catalytic reactor, 278,279f... 

Hawkins J M, Nambu M and Meyer A 1994 Resolution and configurational stability of the chiral fullerenes C-g, C g, and Cg. A limit for the activation energy of the Stone-Wales transformation J. Am. Chem. Soc. 116 7642-5... 

For many practically relevant material/environment combinations, thennodynamic stability is not provided, since E > E. Hence, a key consideration is how fast the corrosion reaction proceeds. As for other electrochemical reactions, a variety of factors can influence the rate detennining step. In the most straightforward case the reaction is activation energy controlled i.e. the ion transfer tlrrough the surface Helmholtz double layer involving migration and the adjustment of the hydration sphere to electron uptake or donation is rate detennining. The transition state is... 

This involves a more uniform distribution of charge because of the identical substituents and thus lacks the stabilizing effect of the polar resonance form. The activation energy for this mode of addition is greater than that for alternation, at least when X and Y are sufficiently different. 

The polycyclic aromatic hydrocarbons such as naphthalene, anthracene, and phenan-threne undergo electrophilic aromatic substitution and are generally more reactive than benzene. One reason is that the activation energy for formation of the c-complex is lower than for benzene because more of the initial resonance stabilization is retained in intermediates that have a fused benzene ring. 

There is another usefiil viewpoint of concerted reactions that is based on the idea that transition states can be classified as aromatic or antiaromatic, just as is the case for ground-state molecules. A stabilized aromatic transition state will lead to a low activation energy, i.e., an allowed reaction. An antiaromatic transition state will result in a high energy barrier and correspond to a forbidden process. The analysis of concerted reactions by this process consists of examining the array of orbitals that would be present in the transition state and classifying the system as aromatic or antiaromatic. 

Calculations at several levels of theory (AMI, 6-31G, and MP2/6-31G ) find lower activation energies for the transition state leading to the observed product. The transition-state calculations presumably reflect the same structural features as the frontier orbital approach. The greatest transition-state stabilization should arise from the most favorable orbital interactions. As discussed earlier for Diels-Alder reactions, the-HSAB theory can also be applied to interpretation of the regiochemistry of 1,3-dipolar cycloaddi-... 

Important differences are seen when the reactions of the other halogens are compared to bromination. In the case of chlorination, although the same chain mechanism is operative as for bromination, there is a key difference in the greatly diminished selectivity of the chlorination. For example, the pri sec selectivity in 2,3-dimethylbutane for chlorination is 1 3.6 in typical solvents. Because of the greater reactivity of the chlorine atom, abstractions of primary, secondary, and tertiary hydrogens are all exothermic. As a result of this exothermicity, the stability of the product radical has less influence on the activation energy. In terms of Hammond s postulate (Section 4.4.2), the transition state would be expected to be more reactant-like. As an example of the low selectivity, ethylbenzene is chlorinated at both the methyl and the methylene positions, despite the much greater stability of the benzyl radical ... 

For the 2-1-2 pathway the FMO sum becomes (ab — ac) = a b — c) while for the 4 -I- 2 reaction it is (ab-I-ab) — a (2b). As (2b) > (b — c), it is clear that the 4 + 2 reaction has the largest stabilization, and therefore increases least in energy in the initial stages of the reaction (eq. (15.1), remembering that the steric repulsion will cause a net increase in energy). Consequently the 4 - - 2 reaction should have the lowest activation energy, and therefore occur easier than the 2-1-2. This is indeed what is observed, the Diels-Alder reaction occurs readily, but cyclobutane formation is not observed between non-polar dienes and dieneophiles. 

The activation energies were computed to 3.0 (toward 183), 0.3 (toward 182), and 21.8 kcal/mol (toward 184) at the B3-LYP/6-31G level, and thus the mechanism leading to 182 is the preferred one. The transition states of all three reactions belong to concerted but asynchronous reaction paths. The transacetalization of 177 with acylium cations results in the formation of the thermodynamically stabilized 187 (Scheme 121) [97JCS(P2)2105]. 186 is less stable than 187, and 185 is destabilized by 32.5 kcal/mol. Moreover, transacetalization of 177 with sulfinyl cations is not a general reaction. Further computational studies on dioxanes cover electrophilic additions to methylenedioxanes [98JCS(P2)1129] and the influence... 

What we have not yet seen is how these two points are related. Why does the stability of the carbocation intermediate affect the rate at which it s formed and thereby determine the structure of the final product After all, carbocation stability is determined by the free-energy change AG°, but reaction rate is determined by the activation energy AG. The twro quantities aren t directly related. 

However, the relative stabilities of azepine conformers are highly dependent on the nature of the ring substituents, and some substantial inversion energy barriers have been noted, e.g. dimethyl 2,7-dimethyl-3//-azepine-4,6-dicarboxylate [57.3 kJ - mol-coalescence temperature (Tc) 25 5°C],76 isochalciporone (26)(49.4kJ mol-1 Tc 2 + 1 C),40 and 2,4,6,7-tetraphenyl-3/7-azepine (68.1 kJ mol-1 Tt 80°C).37 Ring-inversion activation energies of similar magnitudes have been determined for 4//-azepines.83 85... 

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