Kinetics of reversible reactions

Kinetics of Reversible Reactions with Dual Substrate Reaction... 

A1.5 APPROACH TO EQUILIBRIUM AN EXAMPLE OF THE KINETICS OF REVERSIBLE REACTIONS... 

In this chapter, we examine in depth the kinetics of reversible reactions, chain reactions, parallel reactions, and other reactions. 

Oshanin G S, Ovchinnikov A A and Burlatsky S F 1989 Fluctuation-induced kinetics of reversible reactions J. Phys. A Math. Gen. 22 L977-L982... 

Silberberg, A., and Simha, R., Kinetics of reversible reactions on linear lattices with neighbor effects, Biopolymers, 6(4), 479 90 (1968). 

The kinetics of reversible reactions demands a more laborious mathematical treatment. The reader can find a detailed description in the recommended reading. It should be stressed that enzymes can favor a reaction in one direction rather than its reverse. This is not contradictory with the fact that enzymes can never alter the equilibrium constant of a catalyzed reaction because they can favor one direction by binding strongly, as enzyme-reactants complexes, the... 

Arising from his interest in esterification, Berthelot studied the kinetics of reversible reactions. Working with Saint Gilles, he produced an equation for the reaction velocity depending on reactants concentrations. This was incorrect because they did not considered in the expression the inverse reaction. Other interesting considerations was the hypothesis of an exponential dependence on temperature and the fact that equilibrium position is independent from the kind of alcohols and acids used. 

Since A can be obtained from thermodynamic data, and a a can be determined if V and V are known, a a plays a very important role in verifying reaction mechanism. If there is no rate determining step in a catalytic reaction, the concept of average chemical stoichiometric number can be introduced. The kinetics of reverse reaction can be determined from that of forward-reaction kinetics by crj or... 

Study of reversible reactions close to equilibrium. This possibility was discussed in eonnection with Scheme II and is further treated in Chapter 4. It turns out that if the displacement from equilibrium is small, the kinetics approach first-order behavior. 

The ratio of products 15 and 16 is dependent on the structures, base, and the solvent. The kinetics of the reaction is likewise dependant on the structures and conditions of the reaction. Thus addition or cyclization can be the rate-determining step. In a particularly noteworthy study by Zimmerman and Ahramjian, it was reported that when both diastereomers of 20 were treated individually with potassium r-butoxide only as-epoxy propionate 21 was isolated. It is postulated that the cyclization is the rate-limiting step. Thus, for these substrates, the retro-aldolization/aldolization step reversible. ... 

Sodium dodecyl sulfate and hydrogen dodecyl sulfate have been used as catalysts in the denitrosation iV-nitroso-iV-methyl-p-toluenesulfonamide [138]. The kinetics of condensation of benzidine and p-anisidine with p-dimethylamino-benzaldehyde was studied by spectrophotometry in the presence of micelles of sodium dodecyl sulfate, with the result that the surfactant increases the rate of reaction [188]. The kinetics of reversible complexation of Ni(II) and Fe(III) with oxalatopentaaminecobalt(III) has been investigated in aqueous micellar medium of sodium dodecyl sulfate. The reaction occurs exclusively on the micellar surface [189]. Vitamin E reacts rapidly with the peroxidized linoleic acid present in linoleic acid in micellar sodium dodecyl sulfate solutions, whereas no significant reaction occurs in ethanol solution [190]. 

Miller RJ, Smith CR, DeMaster DJ, Pomes WL (2000) Feeding selectivity and rapid particle processing by deep-sea megafaunal deposit feeders A " Th tracer approach. J Mar Res 58 653-573 Moore RM, Hunter KA (1985) Thorium adsorption in the ocean - reversibility and distribution amongst particle sizes. Geochim Cosmochim Acta 49 2253-2257 Moore RM, Millward GE (1988) The kinetics of reversible Th reactions with marine particles. Geochim Cosmochim Acta 52 113-118... 

In this chapter we have seen that enzymatic catalysis is initiated by the reversible interactions of a substrate molecule with the active site of the enzyme to form a non-covalent binary complex. The chemical transformation of the substrate to the product molecule occurs within the context of the enzyme active site subsequent to initial complex formation. We saw that the enormous rate enhancements for enzyme-catalyzed reactions are the result of specific mechanisms that enzymes use to achieve large reductions in the energy of activation associated with attainment of the reaction transition state structure. Stabilization of the reaction transition state in the context of the enzymatic reaction is the key contributor to both enzymatic rate enhancement and substrate specificity. We described several chemical strategies by which enzymes achieve this transition state stabilization. We also saw in this chapter that enzyme reactions are most commonly studied by following the kinetics of these reactions under steady state conditions. We defined three kinetic constants—kai KM, and kcJKM—that can be used to define the efficiency of enzymatic catalysis, and each reports on different portions of the enzymatic reaction pathway. Perturbations... 

Commercially useful materials require that the rate of the combined reaction is rapid. If the darkening takes place too slowly, or if the subsequent fading of the color is too slow, the materials will not be useful. The presence of the copper halide is essential in ensuring that the kinetics of the reaction are appropriate and that the process is reversible. 

In general, the structure of sol gel materials evolves sequentially as the product of successive and/or simultaneous hydrolysis and condensation and their reverse reactions (esterification and depolymerization). Thus, in principle, by chemical control of the mechanisms and kinetics of these reactions, namely the catalytic conditions, it is possible to tailor the structure (and properties) of the gels over a wide range. For example, stable silica xerogels of tailored particle dimensions, pore morphology, density and porosity, from relatively... 

The phenomena of surface precipitation and isomorphic substitutions described above and in Chapters 3.5, 6.5 and 6.6 are hampered because equilibrium is seldom established. The initial surface reaction, e.g., the surface complex formation on the surface of an oxide or carbonate fulfills many criteria of a reversible equilibrium. If we form on the outer layer of the solid phase a coprecipitate (isomorphic substitutions) we may still ideally have a metastable equilibrium. The extent of incipient adsorption, e.g., of HPOjj on FeOOH(s) or of Cd2+ on caicite is certainly dependent on the surface charge of the sorbing solid, and thus on pH of the solution etc. even the kinetics of the reaction will be influenced by the surface charge but the final solid solution, if it were in equilibrium, would not depend on the surface charge and the solution variables which influence the adsorption process i.e., the extent of isomorphic substitution for the ideal solid solution is given by the equilibrium that describes the formation of the solid solution (and not by the rates by which these compositions are formed). Many surface phenomena that are encountered in laboratory studies and in field observations are characterized by partial, or metastable equilibrium or by non-equilibrium relations. Reversibility of the apparent equilibrium or congruence in dissolution or precipitation can often not be assumed. 

There is ample evidence that the reductive elimination of alkanes (and the reverse) is a not single-step process, but involves a o-alkane complex as the intermediate. Thus, looking at the kinetics, reductive elimination and oxidative addition do not correspond to the elementary steps. These terms were introduced at a point in time when o-alkane complexes were unknown, and therefore new terms have been introduced by Jones to describe the mechanism and the kinetics of the reaction [5], The reaction of the o-alkane complex to the hydride-alkyl metal complex is called reductive cleavage and its reverse is called oxidative coupling. The second part of the scheme involves the association of alkane and metal and the dissociation of the o-alkane complex to unsaturated metal and free alkane. The intermediacy of o-alkane complexes can be seen for instance from the intramolecular exchange of isotopes in D-M-CH3 to the more stable H-M-CH2D prior to loss of CH3D. 

The kinetics of the reaction of bis(iym-collidine)bromonium triflate (17) with adamantylideneadamantane (12), pent-4-en-l-ol (20), and cyclohexene (22) have been investigated in 1,2-dichlorethane at 25 °C under a variety of conditions (Scheme 2). The rates of all the reactions proved to be depressed by added collidine, indicating that the first step for all is a reversible dissociation of (17) into free collidine and a reactive intermediate (18), which is then captured by the alkene. The product of the reaction of (12) with (18) is complex (19), while that of reaction of (20) is... 

Although reversible or equilibrium polymerizations would almost always be carried out in an irreversible manner, it is interesting to consider the kinetics of polymerization for the case in which the reaction was allowed to proceed in a reversible manner. (The kinetics of reversible ring-opening polymerizations are discussed in Sec. 7-2b-5). 

We discussed thermodynamic equilibrium previously in relating kinetics to reversible reactions. One should always estimate these quantities and keep them in mind before performing more detailed design of reactors and separation units. We also note that one must consider aU chemical reactions that may occur for a given feed, not just the one desired. 

Geologists often must deal with chemical reactions during cooling. The quantitative aspects for a simple case of reaction kinetics during cooling, and the qualitative aspects for more complicated reactions during cooling, were presented in Chapter 1. In this section, the quantitative aspects of reversible reactions are presented. A simple first-order reversible reaction is used as an example to de-... 

The cathodic pinacolisation of 2- and 4-acetylpyridine, which had been investigated by one of the present authors (231-233), offered the chance for a complete kinetic analysis as the respective current voltage curves are of reversible character. They allow for evaluation of the kinetics of consecutive reactions, and one can show that at low pH reaction, Eq. (45c) is only possible if strong surfactants are absent. Such surfactants, by occupying the electrode surface, displace ketyl radicals, RiR2(OH)C , from the electrode surface because the latter are relatively weakly adsorbed and cannot compete with strong surfactants in adsorption. Ketyl radicals dissolved in aqueous or organic solvents of low pH are protonated in a fast almost diffusion-controlled reaction. After protonation they are further immediately reduced to form the monomeric carbinol instead of the hydrodimer—the pinacol ... 

In hydrochloric acid solution arsenious acid is oxidised by iodine, but the reaction is reversible owing to the reducing action of hydriodic acid. The kinetics of the reaction were first investigated by Roebuck,2 who concluded that the balanced reaction could be represented thus—... 

We first consider the case of reversible reactions before going on to discuss the general case of mixed kinetic and transport control. 

The presentation of the rate of reversible reaction, r, as a difference of two values, r+ and r, helps in the derivation of kinetic equations instead of deriving the equation for r, one may derive the equation for r+ by means of (71), which is simpler, and then obtain at once the equation for r, applying (73). 

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