Third-order kinetic equation

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 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)... 

The general kinetic equation of the uncatalysed polyesterification is a third-order kinetic equation ... 

The third-order kinetic equation of the acid catalysed polyesterification is presented in equation 8.15. 

Flory (loc. dt.) analysed only the last 20% of reaction and showed that over this range the results can be fitted to a third-order kinetic equation. 

Although Hammett convincingly explained the nitrosation of aliphatic amines and the diazotization of aniline under the conditions employed by Schmid and others, one unsatisfactory point remained namely the second-order kinetic equation obtained by Hantzsch and the workers who followed him for diazotization in a more weakly acidic medium. Comparison of experimental details shows that at concentrations of free mineral acid below 0.05 m the reaction is apparently second-order, but it becomes third-order at higher concentrations of acid. 

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). 

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... 

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... 

There remains one objection—of a less precise kind but felt by many chemists. It is that third-order kinetics as embodied in the representation of step (1) are intrinsically objectionable. If the equations had to be interpreted as representing elementary steps, this would be a weightier consideration, but it has also been asserted that the oscillatory properties of certain other model schemes collapse completely (King, 1983 Gray and Morley-Buchanan, 1985) if the third-order steps therein are replaced. Accordingly it is most desirable to establish whether oscillations and other exotic behaviour arising from a cubic rate-law of the form k ab2 can also arise from a series of successive second-order or bimolecular steps. Similar interests have been expressed previously by Tyson (1973) and Tyson and Light (1973). 

An example of equation (101) with X = I and E = HI was found for methanol-DMF solutions both second- and third-order terms were retained . Dvorko s group also found that when X = Cl, a weak nucleophile, the formation of V in equation (100) was slow and subsequent protonation was fast, leading to second-order kinetics (Atj 0) - - when X = I or SCN, the formation of V was often fast and the protonation slow, leading to third-order kinetics (Atj = 0) . Examples of solvent effects superimposed on the basic rate laws are found in Figure 9 , and even more complex effects are found when chlorobenzene, toluene, chlorobenzene-THF mixtures, etc. were used -... 

Kinetics. In aqueous solution, second-order kinetics (Equation 39) are found for condensation of simple carboxylic acids and amines (10). Studies of polyamidation when a 90% conversion level is reached indicate second-order kinetics for this reaction (11). At conversions above 90%, evidence suggests that a carboxyl-catalyzed third-order reaction assumes increasing importance and becomes predominant. 

There was a solvent kinetic isotope effect on the tribromide reaction in CHCla/CDCla, with ku/kx) = 1.175, but there was no solvent isotope effect for the addition of Bra. Reaction with Bra (the third-order reaction, equation 9.7) gave a AH value of -8.4 kcal/mol, while the reaction with tribromide (equation 9.8) gave a AH value of -t- 6.0 kcal/mol. For reactions exhibiting third-order kinetics, the rate-limiting step appears to involve formation of a bromonium ion-tribromide ion pair from a complex of one alkene and two bromine molecules. With tetra-n-butylammonium tribromide as the source of bromine, the rate-limiting step is thought to be a backside nucleophilic attack at an olefin-Bra charge transfer complex (in equilibrium with Brs" and the olefin) by the ammonium bromide ion pair that has become detached from Bra at the moment of formation of the CT complex or that is present as added salt. ... 

Markovic and co-workers [13] investigated the effects of the phenol to formaldehyde ratio used for the preparation of novolac and the nature of methylene linkages on the curing behaviour of the novolac/HMTA system using rheological studies. Cure kinetics were described by a third-order phenomenological equation, which took into account the self-acceleration effect that arises from the chemical reaction and phase separation. The reaction rate was found to increase with an increase in phenol to formaldehyde ratio. For the same phenol to formaldehyde ratio, the reaction rate increased with an increase in o, o methylene linkages (Table 2.2). 

Using DMA the curing reactions of phenol-formaldehyde resins have been followed [1]. The evolution of various rheological parameters was recorded for samples of the resins on cloth. A third-order phenomenological equation described the curing reaction. The influences of the structure, composition, and physical treatment on the curing kinetics were evaluated. 

On the other hand, with less reactive aromatics of the order of benzene, or less, the reaction obeys third order kinetics rate = [ArH] [AICI3] [PhS02Cl]. With reactive substrates, the rate-decisive step is the ionization of the addition complex (Equation 22). However, for less reactive aromatics, the rate-determining step is the subsequent reaction of the ionized complex with the aromatic compoimd (Equation 23). ° The kinetic isotope effect ( h d) was 1.0 for benzenesulfony-lation in nitrobenzene, nitromethane and trichlorofluoromethane while for /7-toluenesulfonylation in nitromethane and in dichloromethane the values were determined to be 1.5 and 3.3 respectively. ... 

The kinetics of PA 66 post-SSP has been studied by a number of researchers who developed proper kinetic equations in order to describe the process. More specifically, Vouyiouka et used the Flory equations for second- and third-order kinetics and integrated them based on the polymerization conversion (pt) (eqns [6] and [7]) ... 

The autooxidation of [Cu(phen)2] follows third-order kinetics as in equation (14), with an inverse dependence of kobs on [Cu(phen)2f. ... 

X has been adjusted to a single value within this small range in fitting both theoretical equations for n and E. The (y )-scale is based on scaling the time measurements to independent measurements by the steam pressure technique of the kinetic rate curve (i.e. third order kinetics), using the observed gel time as the fixed point for the scaling. The error in the (y 0-scale factor is unlikely to exceed 3%, (The observed gel times of the runs v ere... 

With these kinetic data and a knowledge of the reactor configuration, the development of a computer simulation model of the esterification reaction is iavaluable for optimising esterification reaction operation (25—28). However, all esterification reactions do not necessarily permit straightforward mathematical treatment. In a study of the esterification of 2,3-butanediol and acetic acid usiag sulfuric acid catalyst, it was found that the reaction occurs through two pairs of consecutive reversible reactions of approximately equal speeds. These reactions do not conform to any simple first-, second-, or third-order equation, even ia the early stages (29). 

Schmid (1936 a) was the first to observe a third-order reaction in the diazotization of aromatic amines in the presence of sulfuric acid, and he proposed the kinetic equation of Scheme 3-3. In subsequent work (1936b, 1937 Schmid and Muhr, 1937), he investigated the course of the reaction in dilute hydrochloric or hydrobromic acid, which could be described by incorporating an extra term for the halide ion with only a first-order dependence on (HNO2), as in Scheme 3-4. 

With gallium chloride, ferric chloride and antimony pentachloride the rate coefficients were dependent upon the concentration of chlorobenzene and the square of the concentration of the catalyst, but the third-order coefficients varied with the initial concentration of the catalyst (Table 103)394. The overall kinetic equation was, therefore,... 

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