Dominant termination steps

The rate constants of the propagation steps determine the relative concentrations of the chain carriers. If these only appear in propagation or termination, then, and only then, will the rates of the two propagation steps be equal. 

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A reaction rate expression that is proportional to the square root of the reactant concentration results when the dominant termination step is reaction (4c), that is, the termination reaction occurs between two of the radicals that are involved in the unimolecular propagation step. The generalized Rice-Herzfeld mechanism contained in equations 4.2.41 to 4.2.46 may be employed to derive an overall rate expression for this case. 

The DP can also be described when internal dissociation is the dominant termination step as follows ... 

But if chain transfer is the dominant termination step then... 

Using this mechanism and considering step 4 to be the dominant termination step, show that this will lead to 3/2 order kinetics. 

Under certain conditions the reaction appears to have 3/2 order kinetics. Use the Rice-Herzfeld rules to identify the dominant termination step. 

Is it likely that a third body would be required for this dominant termination step Explain your reasoning. 

El and Es are known (see above) and must be very small, so 12 = 23.5 kcal. mole- (the value 28.6 kcal given by Kalb and Allen appears to be incorrect). Hence reaction (84) is quite slow, and the steady-state concentration of sulphate radical-ions relatively high. This would account for reaction (66) being favoured as the chain-termination step, rather than reaction (77), the dominant termination step in the silver ion-catalysed reaction. 

Figure 1.7 shows a [product]-time plot for the mixture C3H6 = 12, O2 = 30 and N2 = 18 Torr at 713 K. The single most vital feature is the very high yield of HDE which, on the basis of the mechanism, implies that about 70% of the allyl radicals recombine in reaction (19), which must therefore be the dominant termination step. As a result could be determined with only minor (ca 20%) correction by use of the principle that at the steady state the rate of initiation equals the rate of termination. 

Providing R has a facile reaction, usually with O2, such as (27) for butenyl radicals, then [allyl] [R], and the recombination of allyl radicals (19) remains by far the dominant termination step. With (19) the only termination, and low [O2] so that radical branching reactions are negligible, then the ratio ki/kip can be obtained from the initial rates of formation of HDE in the presence (Rhde) and absence (Rhde)o of RH and the use of equation (1.7)... 

In this copolymerization, the reactivity ratios are such that there is a tendency for S and the acrylic monomers to alternate in the chain. This, in combination with the above-mentioned specificity in the initiation and termination steps, causes chains with an odd number of units to dominate over those with an even number of units. 

The chemical mechanisms of transition metal catalyses are complex. The dominant kinetic steps are propagation and chain transfer. There is no termination step for the polymer chains, but the catalytic sites can be activated and deactivated. The expected form for the propagation rate is... 

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. 

Free radical addition of HBr to buta-1,2-diene (lb) affords dibromides exo-6b, (E)-6b and (Z)-6b, which consistently originate from Br addition to the central allene carbon atom [37]. The fact that the internal olefins (E)-6b and (Z)-6b dominate among the reaction products points to a thermodynamic control of the termination step (see below). The geometry of the major product (Z)-(6b) has been correlated with that of the preferred structure of intermediate 7b. The latter, in turn, has been deduced from an investigation of the configurational stability of the (Z)-methylallyl radical (Z)-8, which isomerizes with a rate constant of kiso=102s 1 (-130 °C) to the less strained E-stereoisomer (fc)-8 (Scheme 11.4) [38]. 

Thus for a temperature and pressure condition where areact > crit, the system becomes explosive for the reverse situation, the termination steps dominate and the products form by slow reaction. 

A steady state treatment shows the overall order to depend on the type of step in which the radical is formed, and also on which termination step is dominant. 

Using the Rice-Herzfeld rules, predict the overall kinetics, if each of the other termination steps were dominant in turn. 

The Rice-Herzfeld rules indicate that 3/2 order occurs for termination via like radicals produced in initiation, which then undergo reaction of the type R + reactant —> . Hence step 4 is the dominant termination. 

The steady state equations for step 5 being the dominant termination are... 

The dominant termination being recombination of unlike radicals and production of CH3CH2COCOCH2CH3 suggests that the dominant first propagation step is... 

Each time an a-olefin readsorbs, there is a chance that it will desorb as a larger paraffin. Desorption as a paraffin is an irreversible termination step. At high carbon numbers, pore diffusion effects dominate and a-olefins do not exit the catalyst particles unreacted because of enhanced readsorption only unreactive paraffins are observed. As a result, the olefin/paraffin ratio decreases asymptotically to zero as carbon number increases. 

This complexity is involved in almost any kinetic study on radical processes. The consumption of radicals ooour now, in effect, in the competing reactions (1), (8) and (9). Measurable quantities are often the yields of R—H and R—R products of reactions (4) and (1), respectively, (e.g., Majer et al., 1969) and the reactivity of H—Y toward R is often expressed by the ratio, k/kj12. It is extremely important, however, that reactions (4) and (1) are of different orders with respect to R and simple neglect of reaction (8) (which is often the dominating termination process in retarded chain reactions, Semenov, 1958) implies that the concentration of R will not vary throughout the whole reaction (Giles and Whittle, 1966). If all possible steps are considered, the evaluation of k/k lz from the yields requires knowledge of two additional parameters, as shown by Bazilevskii and Trosman (1968), and the calculation becomes tedious. 

The possible types of chain mechanisms for peroxodisulphate oxidation have been classified by Wilmarth and Haim according to the dominant initiation and termination steps, and the relative importance of sulphate radical-ions and hydroxyl radicals in the propagation steps. Some of the rate equations corresponding to the different types of mechanisms are the same, so the observation of a particular rate equation does not always permit a unique mechanism to be inferred. In certain cases the nature of the chain initiation step can be deduced from the effect of a free-radical scavenger on the reaction rate. Thus in the oxidation of 2-propanol, the addition of allyl acetate reduces the rate to that observed for the spontaneous decomposition of peroxodisulphate, indicating that the chain initiation step is the same as the rate-determining step of the spontaneous decomposition, viz. the fission of peroxodisulphate into sulphate radical-ions. 

Several factors determine the nature of the termination step. What radicals are involved in termination depends on the relative concentrations of the radicals. If P radicals are predominant, fifi or PPM combination will be most important if g radicals are present in much larger concentrations than p then gg or ggM combination will be most important. Radical combinations occur with little or no activation energy so that their rate coefficients are determined largely by the frequency factors these do not vary greatly, so that concentrations appear to play the dominant role in determining the nature of the termination process. The matter is often complicated by the simultaneous occurrence of two or more important termination processes. 

According to our present knowledge, the recombination of methyl radicals is the dominant chain termination step in the thermal decomposition of acetaldehyde, though ethane is only a minor product of the reaction ... 

From these results the conclusion may be drawn that termination steps (5)-(7) all participate to some extent. Each one may become dominant depending on the experimental conditions. 

The ignition limit lies in the region of the p-T plane, corresponding to the second limit in classical closed vessels, and so we may surmise that the dominant features of the mechanism will be the competition between the branching cycle (1-3) and the gas-phase termination step producing HO2, step (5). A full steady-state analysis on the intermediates OH and O would introduce (out)flow terms for each species and a fairly complex polynomial in terms of fres- The full analysis appears in Chapter 4 of this volume. For now, we can note that the typical residence times of interest, 1 to 10 s,... 

Many of the basic kinetic techniques of physical organic chemistry lose their usefulness when applied to radical reactions. Because of quantum-mechanical restrictions on spin multiplicity, reaction of a radical with a closed-shell molecule or ion generates another radical, with the radical species themselves being present in low concentration. For this reason, radical reactions are often chain reactions, whose kinetics are dominated by initiation or termination steps, with the rates of reactions generating most product frequently having little influence on the overall rate law. 

There is also a natural ceiling temperature for chain studies at about 1000°K. Above 1000°K, A has become so small that the rates and product distributions are dominated by the initiation and termination steps above. 

K [197]. This rate constant is nearly independent of temperature and is in good agreement with the result of Zellner [198]. These experimental and theoretical results suggest that cycles V and VII are unfeasible, because rather than facilitating the conversion of FC(0)0 to FCO by means of oxidizing NO, the FC(0)0 + NO reaction provides a terminal step in the photooxidation process. Moreover, a comparison of the rates for removal of FC(0)0 radicals with NO, O3, and CH4 suggest that the dominant removal process for FC(0)0 radicals is the FC(0)0 + NO reaction (131), and hence that this terminates CX3 photooxidation. 

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