First-order termination reaction

Howard and Ingold (7) proposed participation of a first-order termination reaction in the autoxidation of styrene. If such contributions from first-order terminations are real and widespread in autoxidation, more knowledge about them becomes essential. 

First order termination reaction, likely to be reaction with Oj. ) CI2 vapor pressure measurement in gas phase above solution. 

Equation (XIV.G.3) represents, of course, one special case among many possible examples of chain-branching reactions. Variations of this equation may be obtained by adding terms that represent homogeneous first-order termination ka C) to Eq. (XIV.6.3) or wall-initiation terms to the auxiliary boundary equation (XIV.6.4). The addition of terms which are second-order in radicals, such as second-order recombination in the gas phase, or second-order branching leads to equations which are nonlinear and which may only be solved cither numerically or by approximation. 

Chemical reactions that proceed through free radical intermediates can explode if there is a branching step in the reaction sequence. Consider the overall reaction of A = B with initiator / and first-order termination of free radical R ... 

The kinetics of the photolysis is much more complex at lower temperatures than at around 300 °C. The role of rate-determining step, i.e. the hydrogen atom transfer reaction (20) at high temperatures, is taken over by the decomposition of the acetyl radical as the temperature decreases. At the highest temperatures, the chains are terminated almost exclusively by the recombination of the methyl radicals, while at medium and low temperatures the disproportionation step (26) as well as self combination of the formyl and acetyl radicals are dominant. The first-order wall reaction of the radicals, such as reactions (22) and (31), may also play an important role, especially at low light intensities and pressures. On account of the aforesaid, it seems almost impossible to attempt a general discussion of the kinetics of the reaction. Instead, only selected questions will be dealt with in detail. 

Kinetics of the overall reaction proceeding in ethanol was investigated239 . A pseudo-first order termination was assumed to take place in this solvent, namely,... 

Example First-order termination steps are often associated with extraneous factors, for example, the adsorption of chain carriers on the walls of a reaction vessel. 

Quinn [36] has performed further experiments indicating that the first-order initiation is prol ly more correct. To obtain the propa overall first-order behavior, he had to assume that the radical decomposition step (d) has a rate intermediate between first- and second-order kinetics, approximately proportional to [C2H5][C2Hs]. This makes the ethyl radical have behavior between fi and fi, say (,pn)> the table then indicates approximate first-order overall reaction, tending toward termination—and j order—for lower pressures. More recent data indicate that a wide range of observations is best represented by Quinn s mechanism. 

Olefin polymerization with metallocene catalysts involves initiation, chain propagation, formation of a dead chain with a saturated chain end through the chain transfer agent, p-hydride elimination to form a dead chain with a vinyl terminal double bond, insertion of a macromer with a vinyl end group, and catalyst deactivation. Assuming that all the reactions associated with each step are first order, the reaction processes can be expressed as... 

With triethyloxonium tetrafluoroborate, the initiation reaction is fast compared with propagation, so that f a- 1. The type of termination reaction defines the functional form of mg, m and Cq, i.e. eqn. [4] or [s]. Consequently the (grafical) solution cf these equations permits to distinguish between first order and second order termination reaction and to determine the values of p t ... 

The kinetics of the reactions were complicated, but three broad categories were distinguished in some cases the rate of reaction followed an exponential course corresponding to a first-order form in others the rate of reaction seemed to be constant until it terminated abruptly when the aromatic had been consumed yet others were susceptible to autocatalysis of varying intensities. It was realised that the second category of reactions, which apparently accorded to a zeroth-order rate, arose from the superimposition of the two limiting kinetic forms, for all degrees of transition between these forms could be observed. 

Although primary and secondary alkyl hydroperoxides are attacked by free radicals, as in equations 8 and 9, such reactions are not chain scission reactions since the alkylperoxy radicals terminate by disproportionation without forming the new radicals needed to continue the chain (53). Overall decomposition rates are faster than the tme first-order rates if radical-induced decompositions are not suppressed. 

The concentration of monomers in the aqueous phase is usually very low. This means that there is a greater chance that the initiator-derived radicals (I ) will undergo side reactions. Processes such as radical-radical reaction involving the initiator-derived and oligomeric species, primary radical termination, and transfer to initiator can be much more significant than in bulk, solution, or suspension polymerization and initiator efficiencies in emulsion polymerization are often very low. Initiation kinetics in emulsion polymerization are defined in terms of the entry coefficient (p) - a pseudo-first order rate coefficient for particle entry. 

This expression suggests a rate-controlling step in which RM reacts with an intermediate. If so, [Int] °c [RM] /2. To be consistent with this, the initiation step should be first-order in [RM] and the termination step second-order in [Int]. Since O2 is not involved in the one propagation step deduced, it must appear in the other, because it is consumed in the overall stoichiometry. On the other hand, given that one RM is consumed by reaction with the intermediate, another cannot be introduced in the second propagation step, since the stoichiometry [Eq. (8-3)] would disallow that. Further, we know that the initiation and propagation steps are not the reverse of one another, since the system is not well-behaved. From this logic we write this skeleton ... 

A first-order rate expression results when the termination process involves the dissimilar radicals, Rl and R2. That is, reaction (4b) is the chain breaking step. 

In order for the overall rate expression to be 3/2 order in reactant for a first-order initiation process, the chain terminating step must involve a second-order reaction between two of the radicals responsible for the second-order propagation reactions. In terms of our generalized Rice-Herzfeld mechanistic equations, this means that reaction (4a) is the dominant chain breaking process. One may proceed as above to show that the mechanism leads to a 3/2 order rate expression. 

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