Kinetics, third-order

The form of this third-order kinetic expression is identical to that in the case where the second step was rate-determining. 

Propose a mechanism that could account for the overall four-thirds-order kinetics and the appearance of the dialkylaluminum hydride concentration to the one-third power. 

The first-order and second-order kinetics of desorption are by far the most common and practically considered cases. Less than first-order desorption kinetics indicates multilayer adsorption or transport limited desorption (101). An actual significance of the third-order kinetics in desorption has been found recently by Goymour and King (102, 103). 

The reaction of p-toluenesulphonyl chloride with toluene at 25 °C gave ditolyl sulphone and third-order kinetics, viz. 

Carr and England211 investigated the kinetics of the hydrochloric acid-catalysed chlorination of phenol by N-chloro-succinimide, -acetamide, and -morpholine, and found that the latter compound gave third-order kinetics, viz. 

The kinetics of bromination with the complex formed between bromine and dioxan have been examined using benzene (which is unattacked) as solvent311, and it is probably appropriate to regard this as a catalysed bromination in view of the effect of dioxan upon the polarity of the bromine-bromine bond. With anisole, phenetole, and isopropoxybenzene, third-order kinetics are obtained, viz. 

Third-order kinetics, equation (166), have also been obtained330 for the iodination of mesitylene and pentamethylbenzene by iodine monochloride in carbon tetrachloride, the negative activation energies of —4.6 and —1.6 (from measurements at 25.2 and 45.7 °C) obtained being attributed to a mildly exothermic preformation of ArHICl complexes (c/. molecular bromination, p. 123) which subsequently react with two further molecules of iodine monochloride to give the products, viz. equilibria (167) and (168)... 

The most valuable and comprehensive kinetic studies of alkylation have been carried out by Brown et al. The first of these studies concerned benzylation of aromatics with 3,4-dichloro- and 4-nitro-benzyl chlorides (these being chosen to give convenient reaction rates) with catalysis by aluminium chloride in nitrobenzene solvent340. Reactions were complicated by dialkylation which was especially troublesome at low aromatic concentrations, but it proved possible to obtain approximately third-order kinetics, the process being first-order in halide and catalyst and roughly first-order in aromatic this is shown by the data relating to alkylation of benzene given in Table 77, where the first-order rate coefficients k1 are calculated with respect to the concentration of alkyl chloride and the second-order coefficients k2 are calculated with respect to the products of the... 

The kinetics of alkylation by triphenylmethyl compounds have been studied. Hart and Cassis353 found that the alkylation of phenol and o-cresol by triphenylmethyl chloride in o-dichlorobenzene gave non-linear kinetic plots which were, however, rendered linear by presaturation of the reaction mixture with hydrogen chloride, precise third-order kinetics, equation (182)... 

With a non-polar medium, carbon tetrachloride, third-order kinetics were obtained (in the initial reagent concentration range of 4-50 x 10"4 M)749, whereas with a polar medium, methanol, the order with respect to iodine was reduced to one750. 

Ionic strength effect. If three ions (A, B, and C) react following third-order kinetics, can Eq. (9-45) be extended to give a coefficient of Fp equal to 2Az z%zcl... 

The evaluation of the 220 C reaction data show (fig. 2) that the reaction does not follow third order kinetics, sra g. 

A homogeneous gas-phase reaction that follows a third-order kinetic scheme is... 

The herbicide glyphosate was nitrosated in aqueous solution by third order kinetics to N-nitrosoglyphosate. 

N02 did not accumulate in lake sediments under conditions where nitrate rapidly disappeared. The low levels of both nitrite and nitrosatable amines in natural waters, along with expected third order kinetics fc make extensive nitrosamine formation unlikely. The prospect has been discussed by Dressel. ... 

Numerical solutions to equation 11.2.9 have been obtained for reaction orders other than unity. Figure 11.11 summarizes the results obtained by Levenspiel and Bischoff (18) for second-order kinetics. Like the chart for first-order kinetics, it is most appropriate for use when the dimensionless dispersion group is small. Fan and Bailie (19) have solved the equations for quarter-order, half-order, second-order, and third-order kinetics. Others have used perturbation methods to arrive at analogous results for the dispersion model (e.g. 20,21). 

Thus, according to this three-step mechanism, a bimolecular recombination reaction is second-order at relatively high concentration (cM), and third-order at low concentration. There is a transition from second- to third-order kinetics as cM decreases, resulting in a fall-off regime for kbi. 

The explanation lies in the rate law for the autoxidation of NO in aqueous solution, which follows third-order kinetics (Eq. (46) where... 

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... 

However, experimental results show that in batch operation third-order kinetics are not observed until the conversion has reached about 80%. In most practical cases, Ca Cb. It was pointed out by Amass [50] that the carboxyl groups in the reaction species are weak acids which are only partly dissociated... 

Aa > 0.8, the dissociation of acid groups (which are diluted by the reaction) increases and Ch+ becomes almost proportional to C. Third-order kinetics are then observed. 

An apparent order in nitrite of 3 or more would also be consistent with a-amino nitrite fragmentation mechanisms if one assumes that nitrite is preferentially consumed in redox or nitrosation reactions elsewhere in the molecule which compete with nitrosation of the dimethylamino group. One such possibility was suggested by Dr. R.N. Loeppky (private communication), as shown in Fig. 6. This mechanism, which postulates the intermediacy of two different o-amino nitrites, le and If, should obey third order kinetics, since dimethylnitrosamine is produced only after aminopyrine reacts with the third mole of nitrite. Moreover, this pathway offers a mechanistic explanation for the direct production of nitrosohydrazide V, which has also been reported to be a product of aminopyrine nitrosation (12.17). 

Thus, the predicted time for 100 nM nitric oxide at physiological oxygen tensions to decrease to 50 nM by Reaction 4 would take 1 hr, then 2 hr to decrease to 25 nM, and an additional 4 hr to reach 12.5 nM. The overall time for 100 nM nitric oxide to decompose to 10 nM purely by Reaction 4 is thus about 7 hr. Clearly, the third-order kinetics for the formation of nitrogen dioxide is far too slow to account for the biological inactivation of nitric oxide (Fig. 6). 

The electrode mechanisms treated, along with the rate laws and the appropriate digital simulation parameters, are shown in Table 16. The symbols for mechanisms 5 and 6, RS-2 and RS-3, indicate that these reactions represent cases of radical (primary intermediate B) reacting with substrate (A). Mechanism 5 foDows second-order kinetics while third-order kinetics characterize mechanism 6. The theoretical data for the mechanisms are summarized in Tables 17—23. The calculations are for EX — f revI equal to 300 mV. Data are also available for EX — Eiev — 100 mV. In the following paragraph, the data are explained with reference to the eC mechanism, i.e. Table 17. 

If the above meohanwm in operative, third-order kinetics should be observed. This has indeed been done by Bailee ter and Bartlett, who found for the condensation of phenaoyl chloride and bemzaldehydo in the presence of OH- ion that the reaction is first-order with respect to each of these, or third-order overall. 

Platinum(IV) is kinetically inert, but substitution reactions are observed. Deceptively simple substitution reactions such as that in equation (554) do not proceed by a simple SN1 or 5 2 process. In almost all cases the reaction mechanism involves redox steps. The platinum(II)-catalyzed substitution of platinum(IV) is the common kind of redox reaction which leads to formal nucleophilic substitution of platinum(IV) complexes. In such cases substitution results from an atom-transfer redox reaction between the platinum(IV) complex and a five-coordinate adduct of the platinum(II) compound (Scheme 22). The platinum(II) complex can be added to the solution, or it may be present as an impurity, possibly being formed by a reductive elimination step. These reactions show characteristic third-order kinetics, first order each in the platinum(IV) complex, the entering ligand Y, and the platinum(II) complex. The pathway is catalytic in PtnL4, but a consequence of such a mechanism is the transfer of platinum between the catalyst and the substrate. 10 This premise has been verified using a 195Pt tracer.2011... 

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