Endothermic bimolecular reactions

The activation energies o/endothermic bimolecular reactions of free radicals are only marginally higher than the respective reaction enthalpies, AH° the difference is found smallest for the most strongly endothermic reactions. 

Bateman and Hughes [43, 45] found that, in the case of the oxidation of polyolefines, the decomposition of hydroperoxides is initially a reaction of the first order (24), but subsequently, with increasing concentration of hydroperoxide as the oxidation progresses, the less endothermic bimolecular reaction (25) assumes greater importance ... 

The standard entropy change for the atom-molecule reactions is in the range 5-20 JK-1 mole-1, and the halogen molecule dissociation has an entropy change of about 105 e.u. The halogen molecule dissociation energy decreases from chlorine to iodine, but the atom-molecule reactions become more endothermic from chlorine to iodine, and this latter effect probably influences the relative contributions to the mechanism from chain reaction and bimolecular reaction. 

The above discussion shows that several possible pathways for the interconversion of sulfur rinp exist. However, none of these alone can explain all the experimental observations. It therefore seems likely that several of them are effective simultaneously. Unimolecular dissociation reactions as discussed under (a) and (d) will dominate at high temperatures due to the increase in entropy. At lower temperatures, however, bimolecular reactions like the dimerization (c) may be most important, at least in case of the small rings (Sg, S, Sg) whose unimolecular dissociation is strongly endothermic. Larger rings will probably decompose according to mechanism (d), which in a way is the reversal of the dimerization (c). 

E.E.Nikitin, On the statistical theory of endothermic reactions. I. Bimolecular reactions, Teor. Eksp. Khim. 1, 135 (1965)... 

It is valid for both endothermic and exothermic bimolecular reactions between simple radicals and molecules (mostly organic) in gaseous phase. Semenov realized that the coefficients of the correlation formula may differ somewhat for individual classes of the reaction partners. Ref. [15] reviews the empirical models of radical abstraction. A rationale for the above correlation was provided by Morse or Lennard-Jones who considered the potentials of overlap in the reacting partners [16]. 

Some reactions occur thermally at temperatures too low for homolysis of any of the covalent bonds present to provide enough radicals to start the reaction. For example, mixtures of fluorine and methane explode at room temperature, and many hydrocarbons are oxidized slowly by molecular oxygen (see below). It has been postulated that the bimolecular reactions (6.10) and (6.11) are responsible. In (6.10), the formation of the very strong H-F bond makes this reaction much less endothermic than the simple homolysis of the fluorine molecule. In (6.11), a strong O-H bond is formed in the hydroperoxyl radical 18, whereas two relatively weak bonds are broken, the 0=0 n bond and the C-H bond in 16 which is weakened by the stabilization of the product benzylic radical 17. The occurrence of these molecule-induced homolysis reactions is difficult to prove because the compounds formed tend to be swamped by those from the subsequent radical reactions. 

Recent extensions to bimolecular reactions include a study by Marcus (1970) on the relation between state-selected cross sections of endothermic reactions and rate constants of exothermic reactions. This study was prompted by the investigation of Anlauf et al. (1969), and applied a micro-canonical activated-complex theory to bimolecular reactions. 

Using a guided ion beam instrument the translational energy dependent reaction cross sections of endothermic fragmentation processes can be determined [32]. Modelling these cross sections ultimately yields their energy thresholds and a great deal of valuable thermochemical information has been derived with this technique. Precision of 0.2 eV can be obtained for reaction thresholds. Bimolecular reactions can also be studied and reaction enthalpies derived from the analysis of the cross section data. 

E. E. Nikitin, Statistical theory of endothermic reactions. Part 1. Bimolecular reactions, Theor. Exp, Chem. 1, 83-89 (1965). 

As can be seen from the data presented, the high energies of complex formation decrease sharply the endothermicity of the retro-Wittig type decomposition and, moreover, fundamentally change the reaction mechanism. As has been shown for betaines (")X-E14Me2-CH2-E15( + )Me3 (X = S, Se E14 = Si, Ge E14 = P, As), the reaction occurs as bimolecular nucleophilic substitution at the E14 atom. For silicon betaines, the transition states TS-b-pyr with pentacoordinate silicon and nearby them no deep local minima corresponding to the C-b complexes can be localized in the reaction coordinate. 

While reaction (69) is strongly exothermic, it requires a three-body collision. Reaction (70) is slightly endothermic but is bimolecular. Also, if excess energy available at 1849 A. is equipartitioned between two O atoms, each O atom can have 18 kcal./g. atom excess translational energy. These considerations make reaction (70) appear to be more probable. This argument is additionally supported by the observation that OH is formed in the reaction between 0(1Z>) and H2. 

Addition reactions of carbon radicals to C—O and C—N multiple bonds are much less-favored than additions to C—C bonds because of the higher ir-bond strengths of the carbon-heteroatom multiple bonds. This reduction in exothermicity (additions to carbonyls can even be endothermic) often reduces the rate below the useful level for bimolecular additions. Thus, acetonitrile and acetone are useful solvents because they are not subject to rapid radical additions. However, entropically favored cyclizations to C—N and C—O bonds are very useful, as are fragmentations (see Chapter 4.2, this volume). 

The energetics of the H abstraction reaction [reaction (27)], AG= -11.4 kcal moH, and the /3-scission [reaction (28)], AG = -1-8.1 kcal mol are from DFT calculations. The two-step mechanism was excluded because of the endothermic step in reaction (28). However, a concerted reaction [combining reactions (27) and (28)] would be spontaneous, but with only a small exothermicity, AG ncerted = -3.3 kcal mol Therefore, the source of these radicals appears to be a bimolecular homolytic substitution (Sjj2) of the acetamide, by hydrogen atoms [reaction (29)] ... 

The first bimolecular step is rate-limiting. Its activation energy is close to the endothermicity of the reaction, and the pre-exponential factor is close to the collision frequency (Table 21). A linear dependence is observed between log k and a with p = —5.0 at 180°C. 

Where RH - the monomer units of polymer. Reaction can be triggered by physical factors such as ultraviolet and ionizing radiation, heat, ultrasound, or mechanical treatment chemical factors, such as catalysis, a direct reaction with molecular, singlet or atomic oxygen and ozone. However, initiation by direct interaction of molecular oxygen with the polymer, leads to detachment of a hydrogen atom, was unlikely, because it is endothermic reaction, enthalpy is 126-189 kj/mol (Chan J.H., Balke S.T., 1997). Often, the birth of the chain portrayed as the bimolecular interaction of oxygen with the monomer units of polymer... 

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