Elimination reaction, first-order

The fact that the rate law of hydrogen bromide elimination is first order with respect to the base may be interpreted by an E2 mechanism. The antiperiplanar position of the hydrogen and the bromine atoms in Ih also makes this mechanism very likely. Earlier the same mechanism was proposed for the elimination reaction of some tertiary a-halo ketones (ref. 19). Other mechanism, such as ElcB or El, seems to be very improbable considering the lack of any deuteration at C-2 or the lack of any rearrangement and the fact that the generation of a-keto cations requires acidic conditions (ref. 20). 

The mechanisms of the reductive eliminations in Scheme 5 were studied [49,83], and potential pathways for these reactions are shown in Scheme 6. The reductive eliminations from the monomeric diarylamido aryl complex 20 illustrate two important points in the elimination reactions. First, these reactions were first order, demonstrating that the actual C-N bond formation occurred from a monomeric complex. Second, the observed rate constant for the elimination reaction contained two terms (Eq. (49)). One of these terms was inverse first order in PPh3 concentration, and the other was zero order in PPh3. These results were consistent with two competing mechanisms, Path B and Path C in Scheme 6, occurring simultaneously. One of these mechanisms involves initial, reversible phosphine dissociation followed by C-N bond formation in the resulting 14-electron, three-coordinate intermediate. The second mechanism involves reductive elimination from a 16-electron four-coordinate intermediate, presumably after trans-to-cis isomerization. 

Chapter 3 is an overview of chemical and biological nonlinear dynamics. The kinetics of several types of reactions -first order, binary, catalytic, oscillatory, etc - and of ecological interactions -predation, competition, birth and death, etc - is described, nearly always within the framework of differential equations. The aim of this Chapter is to show that, despite the great variety of mechanisms and processes occurring, a few mathematical structures appear recurrently, and archetypical simplified models can be analyzed to understand whole classes of chemical or biological phenomena. The presence of very different timescales and the associated methodology of adiabatic elimination is instrumental in recognizing that. 

In the less basic medium of aqueous acetone or aqueous dioxan containing hydroxide ion, a carbene mechanism has been suggested to explain the quantitative conversion of 4-nitrobenzyl chloride and 4-nitrobenzyl dimethyl-sulphonium ion into cis- and /ra/is-4,4 -dinitrostilbenes . In both cases, the rate of elimination follows first-order kinetics in both the substrate and hydroxide ion, and deuterium exchange of labelled substrates occurs more rapidly than stilbene formation. In this aqueous medium, a rate-determining ion-pair dissociation is unlikely. However, again the selectivity of the carbene is astonishing and it is difficult to explain the lack of insertion products with the reaction medium or the failure to isolate cyclopropane adducts when the elimination reactions are performed in the presence of added olefins. 

Hughes, E. D. Wilby, J. /. CItem. Soc. 1960,4094. The product distributions reflect second-order elimination. Some first-order elimination accompanied the reaction. 

The mechanism of reductive elimination with C—C bond formation has been studied for [Ni(CN)PhPa], where P=PEta or PCys (tricyclohexylphosphine). The thermal decomposition of [Ni(CN)Ph(PCy3>2] gives very little PhCN, but with an excess of P(OEt)3 this is formed quantitatively by a reaction, first-order in both complex and triethyl phosphite. An associative reaction with reductive elimination from the five-co-ordinate intermediate is most likely since there is no rate retardation by added PCys, and the rate characteristics are very like those of bimolecular substitution, which, of course, requires the formation of a very similar intermediate. For the reaction of P(OEt)a with [Ni(CN)Ph(PEt3)2] competitive substitution of phosphine by phosphite and reductive elimination need to be considered to account for the kinetics in this case added PEts does lead to rate retardation. Nonetheless, reductive elimination from a five-coordinate species still seems to operate. 

Elimination of Ci and C3 from these equations will result in the desired relation between inlet Cj and outlet Co concentrations, although not in an exphcit form except for zero or first-order reactions. Alternatively, the Laplace transform could be found, inverted and used to evaluate segregated or max mixed conversions that are defined later. Inversion of a transform hke that of Fig. 23-8 is facilitated after replacing the exponential by some ratio of polynomials, a Pade approximation, as explained in books on hnear control theory. Numerical inversion is always possible. 

For a first-order reaction, m = I, the catalyst effectiveness T] is independent of A so that after elimination of A and A, the exphcit solution for the rate is... 

The reverse reaction (formation of metal alkyls by addition of alkenes to M-H) is the basis of several important catalytic reactions such as alkene hydrogenation, hydroformylation, hydroboration, and isomerization. A good example of decomposition by y3-elimination is the first-order intramolecular reaction ... 

Some reactions of PtMe4L2 systems do not involve reductive elimination thus reaction of PtMe4(NN) (NN = phen, bipy) with organic acids yielding PtMe3A(NN) (A = formate, acetate, benzoate, salicylate) is first order in both reactants [201]. 

Pyruvic acid is an intermediate in the fermentation of grains. During fermentation the enzyme pyruvate carboxylase causes the pyruvate ion to release carbon dioxide. In one experiment a 200.-mL aqueous solution of the pyruvate in a sealed, rigid 500.-mL flask at 293 K had an initial concentration of 3.23 mmol-L -l. Because the concentration of the enzyme was kept constant, the reaction was pseudo-first order in pyruvate ion. The elimination of CU2 by the reaction was monitored by measuring the partial pressure of the C02 gas. The pressure of the gas was found to rise from zero to 100. Pa in 522 s. What is the rate constant of the pseudo-first order reaction ... 

The chemical meaning of these mathematical equations is that the rate law is first order with respect to the amine base for each reaction (i.e. interconversion of la and Ih and hydrogen bromide elimination). 

The values of the apparent rate constants kj for each temperature and the activation enthalpies calculated using the Eyring equation (ref. 21) are summarized in Table 10. However, these values of activation enthalpies are only approximative ones because of the applied simplification and the great range of experimental errors. Activation entropies were not calculated in the lack of absolute rate constants. Presuming the likely first order with respect to 3-bromoflavanones, as well, approximative activation entropies would be between -24 and -30 e.u. for la -> Ih reaction, between -40 and - 45 e.u. for the Ih la reaction and between -33 and -38 e.u. for the elimination step. These activation parameters are in accordance with the mechanisms proposed above. 

The permanganate oxidation of oxalic acid has been studied exhaustively and has been reviewed by Ladbury and Cullis . It is characterised by an induction period and a sigmoid dependence of rate upon time. Addition of manganous ions eliminates the induction period and produces first-order decay kinetics . Addition of fluoride ions, however, practically eliminates reaction . ... 

Pectins were incubated in buffered medium in mild alkaline conditions (pH 8.5 to 11.2) at room temperature, leading to both demethylation and P-elimination. At higher pHs p-elimination had increased initial speed but soon plateaued. Demethylation was slower but proceeded until completion. It followed a (pseudo)-first order kinetics with respect to concentration of methylesterified carboxyl groups. A rate constant of 27.2 9.0 moT 1 min was calculated after correction for the pH variation during the course of the reaction. 

Let us now consider how the external surface concentrations can be eliminated when our reaction follows simple irreversible first-order kinetics. In this instance equation 12.4.20 becomes... 

---