Liquid-phase chain oxidation, equations

A set of equations has been developed to estimate the effect of a magnetic field on radical recombination during the liquid-phase chain oxidation of Pb(C2H5)4 [81]. 

The effect of the medium on the rates and routes of liquid-phase oxidation reactions was investigated. The rate constants for chain propagation and termination upon dilution of methyl ethyl ketone with a nonpolar solvent—benzene— were shown to be consistent with the Kirkwood equation relating the constants for bimolecular reactions with the dielectric constant of the medium. The effect of solvents capable of forming hydrogen bonds with peroxy radicals appears to be more complicated. The rate constants for chain propagation and termination in aqueous methyl ethyl ketone solutions appear to be lower because of the lower reactivity of solvated R02. .. HOH radicals than of free RO radicals. The routes of oxidation reactions are a function of the competition between two R02 reaction routes. In the presence of water the reaction selectivity markedly increases, and acetic acid becomes the only oxidation product. 

Reaction 1 has been postulated both in oxidations of alkanes in the vapor phase (29) and in the anti-Markovnikov addition of hydrogen bromide to olefins in the liquid phase (14). Reaction 2 involves the established mechanism for free-radical bromination of aromatic side chains (2). Reaction 4 as part of the propagation step, established in earlier work without bromine radicals (26), was not invoked by Ravens, because of the absence of [RCH3] in the rate equation. Equations 4 to 6, in which Reaction 6 was rate-determining, were replaced by Ravens by the reaction of peroxy radical with Co2+ ... 

In order to avoid overtiring the reader we will skip the kinetic equations that are derived from the detailed reaction mechanism of the liquid-phase oxidation of ethylbenzene. This is if, for example, referring to [2,57] one can make certain of the equivalence between the equations derived by the empirical and non-empirical ways. Similar equations might be obtained if one supposed from the outset that the quadratic termination of the chain carriers is peculiar to the reaction considered. Consequently, this would result in a square root dependence for the accmnulation rates of reaction species on the concentration of hydroperoxide, which is responsible for the autoinitiation of reactions. 

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