Some Third-order Reactions

There are relatively few systems in either category of termolecular reactions which have been studied in any great detail, and the data for these are presented in Table XII.9. Only three wholly chemical processes are included, and all involve the reaction of NO. The data for the reaction of NO with H2 which has been studied above lOOO K, appear to be third-order, but the mechanism is probably not simple. 

Of the three wholly chemical termolecular reactions listed in Table XII.9, only the reaction of NO with O2 has been studied over an extended range of conditions. All three reactions, however, have preexponential factors of about the same order of magnitude, corresponding to a steric 

Such a formulation also can account for the small, negative activation energy which has been observed for the reaction of NO with O2. Since fcobs is now a combination of an equilibrium constant K with a rate constant frs, i cxrj == + Ez. Since the association equilibrium will be exo- 

Reaction Preexponential factor log A, liters /mole -sec Activation energy, Kcal/mole 

Rabinowitch and W. C. Wood, Trans. Faraday Soc., 32,907 (1936), from direct photometric measurements of Br2 concentrations during the photostationarj - state of Br2 + hv 2Br. Other measurements by M. Ritchie, Proc. Roy. Soc. (London), A146, 828 (1934), and by K. Hil-ferding and W. Steiner, Z. physik. Chem., 30, 399 (1935), are based on the inhibition of the photolysis of H2 + Br by foreign gases and are about three- to fourfold lower. Values reported for I and Br recombinations are based on dX /di = k(M) XY. 

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Reactions of higher orders than two are less common, though some third-order reactions are encountered. Proceeding in a similar way for reaction of nh order,... 

An explanation which is advanced for these reactions is that some molecules collide, but do not immediately separate, and form dimers of the reactant species which have a long lifetime when compared with the period of vibration of molecules, which is about 10 11 seconds. In the first-order reaction, the rate of the reaction is therefore determined by the rate of break-up of these dimers. In the third-order reaction, the highly improbable event of a three-body collision which leads to the formation of the products, is replaced by collisions between dimers of relatively long lifetime with single reactant molecules which lead to the formation of product molecules. 

A third order reaction can be the result of the reaction of a single reactant, two reactants or three reactants. If the two or three reactants are involved in the reaction they may have same or different initial concentrations. Depending upon the conditions the differential rate equation may be formulated and integrated to give the rate equation. In some cases, the rate expressions have been given as follows. 

It is worth noting that the dimer and trimer generated in reactions (8) and (9) can react with polymeric radicals as a chain transfer agent, and therefore their effect on the polymer molecular weight should not be neglected the quantitative estimation of the concentration of these byproducts depends on the fact that whether the rate of thermal initiation is a second- or third-order reaction of monomer concentration. More kinetic information for such transfer reactions can be found in a number of publications [14-19]. Nevertheless, detailed kinetic studies on such Diels-Alder byproducts remain scarce. Katzenmayer [20], Olaj et al. [21,22], and Kirchner and Riederle [23] have published some quantitative results on this matter. 

In the early work on these reactions, some inconsistencies appear which have been accounted for chiefly by the recent work of Ashmore et al. However, the homogeneous third-order reaction (I) seems to be very well established and an important part of the mechanism. 

The rate constant will always have these units for an overall third-order reaction with the time unit in seconds. Table 16.3 shows the units of k for some common overall reaction orders, but you can always determine the units mathematically. 

Some early studies suggested that only the k2 process should occur in polar solvents at low [Br2], that the process alone should be seen in nonpolar solvents, and that both the 2 and fcs processes can occur in polar solvents at higher [Br2]. Fukuzumi and Kochi demonstrated that both second-order and third-order reactions could occur in Schmid and Toyonaga deter-... 

Some important hydride complexes are available by a reaction that appears to be the hydrogenolysis of a metal-metal single bond (Equation 3.103). However, this reaction occurs only when the metal-metal bond is weak, and probably proceeds via the third-order reaction with of the two metalloradicals [i.e., CofCO) ] formed when the metal-metal bond dissociates. - More recent observations of the reaction of monomeric metalloradicals with Hj are shown in Equations 3.104 and 3.105. - ... 

Previously, from the point of the intensive studying of nonlinear behavior (see Chapter 7), by default it was considered fliat the properties of simple kinetic models, in particular linear kinetic models of many reactions and models of single nonlinear first- second-, and third-order reactions, are completely known from the literature and therefore there is nothing interesting in studying these models. This was otxr opinion as well, until recent results regarding simple linear models and some nonlinear models of single reactions were revealed (Yablonsky et al., 2010, 201 la,b).Three classes of models have been discovered ... 

Give some examples of Third Order Reactions and one example of a Fourth Order Reaction. 

It is clear from figure A3.4.3 that the second-order law is well followed. Flowever, in particular for recombination reactions at low pressures, a transition to a third-order rate law (second order in the recombining species and first order in some collision partner) must be considered. If the non-reactive collision partner M is present in excess and its concentration [M] is time-independent, the rate law still is pseudo-second order with an effective second-order rate coefficient proportional to [Mj. 

Bimolecular rate constants determined at temperatures giving conveniently measurable rates and calculated for the temperature given in parentheses, except for some of the catalyzed reactions (lines 1-4 and 14—19) which are third-order. 

Third-order rate coefficients were determined for reaction of some aromatics with 3,4-dichlorobenzyl chloride at 25 °C as follows chlorobenzene, 0.745 x 10 3 benzene, 1.58 x 10-3 toluene 2.60 x 10—3 m-xylene, 3.30 x 10-3 and these show the unselective nature of the reaction. With 4-nitrobenzyl chloride, benzene gives a third-order rate coefficient of 4.78 x 10 6, which diminishes to 2.4 and 1.9 x 10-6 as the benzene composition of the solvent was increased to 50 and 83 vol. %, respectively. 

Some results which are consistent with this mechanism have been obtained by Ishii and Yamashita385, who found that the kinetics of the reaction of m-xylene with formaldehyde and hydrogen chloride (to give the 4-substituted product) were third-order overall. However, this was followed by a slow di-chloromethylation which was of zeroth-order, but no interpretation or further mechanistic details are available. 

Exps. 3 and 4 represented positive controls, in which morpholine and sodium nitrite (NaN02) were administered in the diet. This system is known to induce tumors attributed to iji vivo NMOR production (3,. The rats were fasted overnight, presented with 2 g diet containing freshly added morpholine and NaNO , and killed 2 h later. At the higher doses, the large NMOR yield was clearly produced for the most part Jji vivo. The DMNM yield in this group indicated that some NMOR was also produced during the workup. The NMOR yield in exp. 4 was 1/1,270 of that in exp. 3, approximately in accord with the 1/1,000 ratio derived from the third-order nitrosation kinetics (3). (Both the morpholine and the NaNO doses in exp. 4 were 1/10 for those in exp. 3. Reaction rate is proportional to amine concentration and to nitrite concentration squared, and hence should be reduced 1/10 because of the drop in morpholine concentration and a further 1/100 because of the drop in nitrite concentration.)... 

In initial studies with /3-CD it was noted that values of ka vary in inverse proportion to the inhibition constant, Kt, suggesting that PI is bound in the CD cavity in the transition state (Tee and Hoeven, 1989). Therefore, the Pi-mediated reaction is more reasonably viewed as being between the ester and the PI-CD complex. The third-order processes in (21) and (24) are kinetically equivalent (k2 = k.JKs = kJKy), and so kb values are easily found from k.t. Such values of kb show some variation with structure but they are quite similar for different Pis and not very different from k2 for the reaction of the CD with pNPA For example, for pNPA reacting with 15 different alcohol /3-CD complexes values of kb span the range 10-95 m 1 s l (Table A5.14), close to k2 = 83m-1s-1 for the reaction of pNPA with /3-CD alone. Similar behaviour was observed for other Pis (Table A5.14) and for aCD (Table A5.13), for which k2 = 26 m-1 s 1. 

Data of Alves el al. (1978), in 20% ethanol. The intermolecular reference reaction is the general acid catalysed addition of phenylhydrazine to the methyl ether, calculated from feH,o using a = 0.35 and determined for the reaction with o-methoxybenzaldehyde (Bastos and do Amaral, 1979). The EM, which is in some doubt because of possible mechanistic complications, is determined by comparison of the rate constant given (dm3 mol-1 s 1) with the third order rate constant for the reference reaction... 

The classical two-step base-catalysed S Ar reaction with amines, B, follows the third-order kinetic law given by equation 2. As noted in Section II, this equation predicts a straight line in the plot of a vs [B] or a downward curvature. But several SjvAr reactions with amines in aprotic solvents studied in the last decade exhibit an upward curvature, as is shown in Figure 10 for the reactions of 2,4-dinitroanisole with w-butylamine and the SvAr reaction of 2,6-dinitroanisole with n-butylamine in benzene143. In these systems, if a/[B] is plotted vs [B], straight lines are obtained and a downward curvature may be observed in some cases (as shown in Figure 11 for the reaction of 2,4-dinitroanisole with butylamine in benzene at 60 °C), which demonstrates that a new kinetic law is obeyed... 

Although these peculiar kinetics had never been observed before, a careful search in the literature revealed that some anomalous results ambiguously ascribed by the authors to unspecific solvent effects 103,147, were indeed due to the fact that these S/y Ar reactions exhibit a fourth-order kinetic law144. Some of them are shown in Table 20. Shortly afterwards, some other authors reported third-order dependence in amine in S/v Ar reactions in aprotic solvents148-152. Several alternative mechanisms have been suggested to rationalize this kinetic finding and many studies in the last years have attempted to... 

In some of Forlani s works, such as the reactions of l-halogeno-2,4,6-trinitrobenzene with 2-hydroxypyridine123,125, a substrate-catalyst molecular complex was assumed, but the kinetic law showed the regular second order in amine. Rather interestingly in this scheme, the authors assume that the molecular complex can lead to the formation of products following a second order in nucleophile kinetics, while in the reactions with amines it was presumed that the complex was not on the reaction coordinate, and that an additional molecule of amine was required (the authors needed to include this additional molecule to account for the third order in amine rate law). 

In the mechanisms involving molecular complexes discussed in Section II.E, several authors were able to calculate the equilibrium association constants, in reactions showing classical kinetics. On the other hand, Forlani and coworkers, in the reactions discussed in Section III.I, assume that the complexes intervene in determining the third order in amine kinetic law, and make calculations of some K some results were presented in Table 13. Several features arise from this Table ... 

If a single reaction order must be selected, an examination of the 95 % confidence intervals (not shown) indicates that the two-thirds order is a reasonable choice. For this order, however, estimates of the forward rate constants deviate somewhat from an Arrhenius relationship. Finally, some trend of the residuals (Section IV) of the transformed dependent variable with time exists for this reaction order. 

If the rate constants for parallel reactions are to be resolved, then analysis of the products is essential (Sec. 1.4.2). This is vital for understanding, for example, the various modes of deactivation of the excited state (Sec. 1.4.2), Only careful analysis of the products of the reactions of Co(NH3)jH20 + with SCN, at various times after initiation, has allowed the full characterization of the reaction (1.95) and the detection of linkage isomers. Kinetic analysis by a number of groups failed to show other than a single second-order reaction.As a third instance, the oxidation of 8-Fe ferredoxin with Fe(CN)g produces a 3Fe-cluster, thus casting some doubt on the reaction being a simple electron transfer. 

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