Radicals activation energies

Fig. 20 AGactivation versus temperature for unimolecular pathways for 2-picolinylperoxy radical. Activation energy for 2 3 denoted by open diamond activation energy for 2 4a denoted by solid square activation energy for 2 4b denoted by open triangle activation energy for 2 6 denoted by symbol x. All energies calculated at the B3LYP/ 6-311+G(d,p)//B3LYP/6-31G(d) level of theory.

However this type of expression can never account for the reversal in orientation observed for the less electrophilic radicals. Even if the constant B changes sign, the proposed expression will still not give a good correlation with experimental methyl radical activation energies. 

Table 6.3 lists the activation energies for termination (these are overall values, not identified as to mode) of several different radicals. The rate constants for termination at 60°C are also given. We shall see in Sec. 6.6 how these constants are determined. 

Decomposition. Acetaldehyde decomposes at temperatures above 400°C, forming principally methane and carbon monoxide [630-08-0]. The activation energy of the pyrolysis reaction is 97.7 kj/mol (408.8 kcal/mol) (27). There have been many investigations of the photolytic and radical-induced decomposition of acetaldehyde and deuterated acetaldehyde (28—30). 

The two possible initiations for the free-radical reaction are step lb or the combination of steps la and 2a from Table 1. The role of the initiation step lb in the reaction scheme is an important consideration in minimising the concentration of atomic fluorine (27). As indicated in Table 1, this process is spontaneous at room temperature [AG25 = —24.4 kJ/mol (—5.84 kcal/mol) ] although the enthalpy is slightly positive. The validity of this step has not yet been conclusively estabUshed by spectroscopic methods which makes it an unsolved problem of prime importance. Furthermore, the fact that fluorine reacts at a significant rate with some hydrocarbons in the dark at temperatures below —78° C indicates that step lb is important and may have Httie or no activation energy at RT. At extremely low temperatures (ca 10 K) there is no reaction between gaseous fluorine and CH or 2 6... 

The overall requirement is 1.0—2.0 s for low energy waste compared to typical design standards of 2.0 s for RCRA ha2ardous waste units. The most important, ie, rate limiting steps are droplet evaporation and chemical reaction. The calculated time requirements for these steps are only approximations and subject to error. For example, formation of a skin on the evaporating droplet may inhibit evaporation compared to the theory, whereas secondary atomization may accelerate it. Errors in estimates of the activation energy can significantly alter the chemical reaction rate constant, and the pre-exponential factor from equation 36 is only approximate. Also, interactions with free-radical species may accelerate the rate of chemical reaction over that estimated solely as a result of thermal excitation therefore, measurements of the time requirements are desirable. 

Activation Parameters. Thermal processes are commonly used to break labile initiator bonds in order to form radicals. The amount of thermal energy necessary varies with the environment, but absolute temperature, T, is usually the dominant factor. The energy barrier, the minimum amount of energy that must be suppHed, is called the activation energy, E. A third important factor, known as the frequency factor, is a measure of bond motion freedom (translational, rotational, and vibrational) in the activated complex or transition state. The relationships of yi, E and T to the initiator decomposition rate (kJ) are expressed by the Arrhenius first-order rate equation (eq. 16) where R is the gas constant, and and E are known as the activation parameters. 

Because the chemiluminescence intensity can be used to monitor the concentration of peroxyl radicals, factors that influence the rate of autooxidation can easily be measured. Included are the rate and activation energy of initiation, rates of chain transfer in cooxidations, the activities of catalysts such as cobalt salts, and the activities of inhibitors (128). 

Chlorination of Methane. Methane can be chlorinated thermally, photochemicaHy, or catalyticaHy. Thermal chlorination, the most difficult method, may be carried out in the absence of light or catalysts. It is a free-radical chain reaction limited by the presence of oxygen and other free-radical inhibitors. The first step in the reaction is the thermal dissociation of the chlorine molecules for which the activation energy is about 84 kj/mol (20 kcal/mol), which is 33 kJ (8 kcal) higher than for catalytic chlorination. This dissociation occurs sufficiendy rapidly in the 400 to 500°C temperature range. The chlorine atoms react with methane to form hydrogen chloride and a methyl radical. The methyl radical in turn reacts with a chlorine molecule to form methyl chloride and another chlorine atom that can continue the reaction. The methane raw material may be natural gas, coke oven gas, or gas from petroleum refining. 

The ESR spectrum of the pyridazine radical anion, generated by the action of sodium or potassium, has been reported, and oxidation of 6-hydroxypyridazin-3(2//)-one with cerium(IV) sulfate in sulfuric acid results in an intense ESR spectrum (79TL2821). The self-diffusion coefficient and activation energy, the half-wave potential (-2.16 eV) magnetic susceptibility and room temperature fluorescence in-solution (Amax = 23 800cm life time 2.6 X 10 s) are reported. 

The individual steps in chain reactions involving radicals are characteristically of small activation energy, between about 10 and 50kJmol and so these reactions should occur at an immeasurably high rate at temperatures above 500 K (see Table 2.1), which is a low temperature for a useful combustion process. The overall rate of the process will tlrerefore depend mainly on the concentrations of tire radicals. 

The relatively low rate and high activation energy noted for entry 32 also reflect a stereoelectronic effect. The preference for delocalization at the radical center requires... 

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 ... 

It has been possible to measure absolute rates and activation energies for rearrangement of the substituents in a series of 2-substituted 2,2-dimethylethyl radicals. The rates at 25°C and the E for several substituents are indicated below. 

A distinction between these four possibilities can be made on the basis of the kinetic isotope effect. There is no isotope effect in the arylation of deuterated or tritiated benzenoid compounds with dibenzoyl peroxide, thereby ruling out mechanisms in which a C5— bond is broken in the rate-determining step of the substitution. Paths (ii) and (iii,b) are therefore eliminated. In path (i) the first reaction, Eq. (6), is almost certain to be rate-determining, for the union of tw o radicals, Eq. (7), is a process of very low activation energy, while the abstraction in which a C—H bond is broken would require activation. More significant evidence against this path is that dimers, Arz, should result from it, yet they are never isolated. For instance, no 4,4 -dinitrobiphenyl is formed during the phenylation of... 

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