Reaction kinetics third order

This reaction shows third-order kinetics as the rate expression is rate = [ketone][HO-]2. Suggest a mechanism that explains these observations. 

Equation 20.17 puts the kinetic expression entirely in terms of the initial concentration of monomer, Cq, and is in the form useful for following the rates of linear (only bifunctional monomers) self-catalyzed polycondensations. If 1/p is plotted against t one gets a straight line. Under self-catalyzed conditions, the reaction is third order, and the degree of polymerization (DP, or Xn) is approximately proportional to t. This third-order dependency of the rate of self-catalyzed polycondensations also means that the rate of increase in the molecular weight (degree of polymerization) slows down quite rapidly as the reaction proceeds. 

This reaction shows third-order kinetics as the rate expression is... 

The reaction is third order overall with firei-o icier dependenca on oxygen and second-order dependence on ferrous ion. These authors and others14 have noted the catalytic effect of cupric ions on die kinetics of (ferrous km oxidation, explained by the reaction... 

Despite earlier claims of a carbene mechanism , more recent kinetic studies indicate that the conversion of diphenylmethyl chloride into tetraphenylethyl-ene by r-butoxide in dimethyl sulphoxide follows the displacement mechanism. The reaction is third-order, second in substrate and first in the medium basicity and a-hydrogen exchange in the substrate is a rapid process ". 

Quantum theory of an elementary electron transfer act confirms this suggestion. In the early 1970s, using Marcus idea on the fluctuations of solvent energy as a driving force for electron transfer [1], Vorotyntsev and Kuznetsov [2] showed theoretically that, for non-adiabatic reactions, the elementary two-electron step is highly improbable, while Dogonadze and Kuznetsov proved that the steps with more than two transferred electrons are practically impossible [3]. It is consistent with the rules of chemical kinetics mentioned above two-electron elementary step can formally be presented as almost improbable reaction of third order, and three or more electron steps as the impossible reactions of more than third order. 

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. ... 

More recently ion cyclotron resonance (ICR) mass spectrometric techniques have been applied to proton transfer equilibria measurements [8, 9]. One advantage of this method is the in situ determination of the ion concentrations. The reaction chamber is the resonance cavity in which the microwave absorption by the ions is measured. The method works only at low pressures / <10 torr and has been used only at room temperature. Clustering reactions like (3) are kinetically third order at low pressures since they require a third body collision for stabilization of the exothermic association product of the reaction. Therefore they are too slow for equilibrium determinations by ICR. The flowing afterglow technique which uses a flow rather than a stationary reaction system, and external ion sampling (as in the Alberta apparatus) has been also used with very good success for ion equilibria measurements [10,11]. 

Theoretical studies of the gas-phase hydrolysis or methanolysis of methylsul-fonyl chloride indicated a concerted Sn2 process involving a four-membered cyclic transition state. The tertiary amine-catalysed hydrolysis of benzenesul-fonyl chloride was shown to be inhibited by chloride ion and a nucleophilic mechanism of catalysis was favoured. Kinetic studies" of the solvolysis of p-substituted benzenesulfonyl chlorides in aqueous binary mixtures with acetone, methanol, ethanol, acetonitrile and dioxime showed that the reactions were third order processes, with first order rate constants determined mainly by the molar concentrations of the protic solvent, so that the reaction rates appear to be dominated by solvent stoichiometry. The solvolyses in methanol and ethanol yield both an alcoholysis (ap) and a hydrolysis product (hp). Solvolyses of electron-rich arylsulfonyl chlorides, under neutral or acidic conditions, exhibited surprising maxima in solvent-dependent S values as defined by Equation 15. 

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. ... 

Holt and co-workers ° demonstrated that aluminium chloride readily dissolved in dichloromethane and they successfully sulfonylated several aromatic compounds by treatment with this homogeneous reagent. Studies of the />-toluene-sulfonylation of benzene and bromobenzene using /7-toluenesulfonyl chloride and aluminium chloride in dichloromethane showed that the reaction followed third order kinetics with substantial kinetic isotope effects ( h 2.0-2.8). The IR... 

A C-C f7-bond activation and hydrogenation of [2.2]paracyclophane with water in a neutral reaction medium is catalysed by [Rh(III)(ttp)Me] (Up = tetratolylporphyrinato dianion). Carrying out the reaction in deuterium oxide indicated that the hydrogen from water is transferred to the hydrocarbon to furnish hydrogen enrichment in good yields. The reaction showed third-order kinetics, second order with respect to the catalyst and first order in the substrate. The reaction has been studied at different temperatures between 140 and 170 C and the activation parameters have been calculated. A large and positive entropy of activation indicated the dissociative nature of the transition state." ... 

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). 

The reactivity of NO towards atoms, free radicals, and other paramagnetic species has been much studied, and the chemiluminescent reactions with atomic N and O are important in assaying atomic N (p. 414). NO reacts rapidly with molecular O2 to give brown NO2, and this gas is the normal product of reactions which produce NO if these are carried out in air. The oxidation is unusual in following third-order reaction kinetics and, indeed, is the classic... 

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. 

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. 

There have been comparatively few kinetic studies of the decompositions of solid malonates [1103]. The sodium and potassium salts apparently melt and non-isothermal measurements indicate second-order rate processes with high values of E (962 125 and 385 84 kJ mole-1, respectively). The reaction of barium malonate apparently did not involve melting and, from the third-order behaviour, E = 481 125 kJ mole-1. 

The vast majority of the kinetic detail is presented in tabular form. Amassing of data in this way has revealed a number of errors, to which attention is drawn, and also demonstrated the need for the expression of the rate data in common units. Accordingly, all units of rate coefficients in this section have been converted to mole.l-1.sec-1 for zeroth-order coefficients (k0), sec-1 for first-order coefficients (kt), l.mole-1.sec-1 for second-order coefficients (k2), l2.mole-2.sec-1 for third-order coefficients (fc3), etc., and consequently no further reference to units is made. Likewise, energies and enthalpies of activation are all in kcal. mole-1, and entropies of activation are in cal.deg-1mole-1. Where these latter parameters have been obtained over a temperature range which precludes the accuracy favoured by the authors, attention has been drawn to this and also to a few papers, mainly early ones, in which the units of the rate coefficients (and even the reaction orders) cannot be ascertained. In cases where a number of measurements have been made under the same conditions by the same workers, the average values of the observed rate coefficients are quoted. In many reactions much of the kinetic data has been obtained under competitive conditions such that rate coefficients are not available in these cases the relative reactivities (usually relative to benzene) are quoted. 

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

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