Kinetic first order

The most crucial observation concerning the effects of added species is that nitrate ion anticatalyses nitration without changing the kinetic form of the reaction. This shows that nitrate does not exert its effect by consuming a proportion of the nitronium ion, for, as outlined above, this would tend to bring about a kinetically first-order reaction. Nitrate ions must be affecting the concentration of a precursor of the nitronium... 

Diels-Alder reactions with butadiene are generally thermally reversible and can proceed in both gas and Hquid phases. The reactions are exothermic and foUow second-order kinetics first-order with respect to each reactant. 

The concerted displacement mechanism implies both kinetic and stereochemical consequences. The reaction will exhibit second-order kinetics, first-order in both reactant... 

TWo types of rate expressions have been found to describe the kinetics of most aromatic nitration reactions. With relatively unreactive substrates, second-order kinetics, first-order in the nitrating reagent and first-order in the aromatic, are observed. This second-order relationship corresponds to rate-limiting attack of the electrophile on the aromatic reactant. With more reactive aromatics, this step can be faster than formation of the active electrq)hile. When formation of the active electrophile is the rate-determining step, the concentration of the aromatic reactant no longer appears in the observed rate expression. Under these conditions, different aromatic substrates undergo nitration at the same rate, corresponding to the rate of formation of the active electrophile. 

Het = heteroaryl residue] follow second-order kinetics, first order with respect to each reactant. Regular kinetics of this kind are also observed in the reaction of sodium arylsulfide in methanol provided that no free thiol is present (see Section II,D, l,c). As to other heterocyclic systems, A -oxides and bromofuran derivatives show similar kinetic behavior. 

The S il reaction occurs when the substrate spontaneously dissociates to a carbocation in a slow rate-limiting step, followed by a rapid reaction with the nucleophile. As a result, SN1 reactions are kinetically first-order and take place with racemization of configuration at the carbon atom. They are most favored for tertiary substrates. Both S l and S 2 reactions occur in biological pathways, although the leaving group is typically a diphosphate ion rather than a halide. 

KBS—See Nuclear Fuel Safety Project Kinetics, first-order Pu(IV)... 

The Cr(VI) oxidation of di- and triarylcarbinols in acetic acid-sulphuric acid mixtures shows normal kinetics (first-order each in alcohol and Cr(VI) and an... 

Kinetics First-order First-order after initial enzyme induction phase First-order First-order First-order... 

Both complexes (867) and (868) promote the hydrolysis of urea in a two-step process.2080 Heating of (867) or (868) in acetonitrile solution produced ammonia with kinetic first-order dependence on complex concentration and an observed rate constant of (7.7 0.5) x 10-4 h-1 to yield a cyanate complex as the reaction product. When the reaction was carried out in 50% aqueous acetonitrile solution, ammonia was produced at the same rate but without buildup of the cyanate-containing product, suggesting that the latter is hydrolyzed in the presence of water. The hydrolysis rate was also first order in water, indicating that it occurred by attack of an external water on the coordinated cyanate.2080... 

Note that if a multiple-step reaction is occurring, then this equation relates only to the case where the slowest (i.e. rate-limiting) step is kinetically first order. We will return to this idea when we consider pseudo reactions in Section 8.4. 

To show that this reaction is kinetically first order, we take the logarithm of the concentration, and plot ln[A]r (as y ) against time t (as V) see Figure 8.11. That the graph in Figure 8.11 is linear with this set of axes demonstrates its first-order character. 

Fig. 5 Plausible mechanistic path for the oxidative addition of bromine to diphenylselenide, dicyanomethylidene telluropyran 20, and 2,6-diphenyltelluropyran-4-one (22) based on stopped-flow kinetics. An initial fast reaction followed second-order kinetics (first order in both bromine and substrate) while a second, slow reaction followed first-order kinetics. For diphenylselenide, a third very-slow reaction was observed.

The cis-trans isomerization of cyclopropanes is not restricted to the deuterium-substituted molecules, cis- and traws-l,2-Dimethylcyclo-propane have been shown to imdergo reversible geometrical isomerization as well as slower structural isomerization. All the processes are homogeneous and kinetically first order, and almost certainly unimolecular. The reaction scheme is shown below. 

Overberger and Borchert (1960) were the first to report that the P3u olysis of vinylcyclopropane yielded cyclopentene as the major product. Independently Flowers and Frey (1961b) studied this isomerization and found that it was homogeneous and kinetically first order and almost certainly unimolecular. The Arrhenius equation for the isomerization was found to be... 

The thermal isomerization of this compound was first studied in detail by Halberstadt and Chesick (1962) in the temperature range 288-310° C and in the pressure range 67 to 0-04 mm, and was found to be homogeneous and kinetically first order. Cyclopentene was the major product (> 99 %) and the high-pressure Arrhenius equation obtained was... 

The thermal decomposition of cyclobutane to yield ethylene has been very extensively investigated (Genaux and Walters, 1951 Kem and Walters, 1952, 1953). The reaction is homogeneous and kinetically first order. Addition of inhibitors to the reactant does not affect the rate, and... 

In order to predict the effect of a mixture of chemicals with the same target receptor, but with different nonlinear dose-effect relationships, either physiological or mathematical modeling can be applied. For interactions between chemicals and a target receptor or enzyme, the Michaelis-Menten kinetics (first order kinetics but with saturation) are often applicable. This kind of action can then be considered a special case of similar combined action (dose addition). 

CHEMICAL KINETICS First-order rate behavior, AUTOPHOSPHORYLATION FIRST-ORDER REACTION KINETICS ORDER OF REACTION HALF-LIFE... 

ORDER OF REACTION MOLECULARITY CHEMICAL KINETICS FIRST-ORDER REACTIONS RATE CONSTANTS... 

Tetralin hydroperoxide (1,2,3,4-tetrahydro-l-naphthyl hydroperoxide) and 9,10-dihydroanthracyl-9-hydroperoxide were prepared by oxidizing the two hydrocarbons and purified by recrystallization. Commercial cumene hydroperoxide was purified by successive conversions to its sodium salt until it no longer increased the rate of oxidation of cumene at 56°C. All three hydroperoxides were 100% pure by iodometric titration. They all initiated oxidations both thermally (possibly by the bi-molecular reaction, R OOH + RH — R O + H20 + R (33)) and photochemically. The experimental conditions were chosen so that the rate of the thermally initiated reaction was less than 10% of the rate of the photoreaction. The rates of chain initiation were measured with the inhibitors 2,6-di-ter -butyl-4-methylphenol and 2,6-di-fer -butyl-4-meth-oxyphenol. None of the hydroperoxides introduced any kinetically first-order chain termination process into the over-all reaction. 

Bunting and Kauffman (84CJC729) studied both the kinetics and mechanism of disproportionation and ferricyanide oxidation of 154 in aqueous base. Ferricyanide ion oxidation is kinetically first-order in each of ferricyanide ion... 

With Os(CO)4H2 and other complexes to be discussed later, dinuclear elimination is kinetically first order. The detailed mechanism for Os(CO)4H2 appears (19) to be ... 

Phenomenological Description of Reaction Kinetics First-Order Kinetics... 

Direct evidence that hydrolysis reactions going by the Aac1 mechanism are kinetically first-order can be obtained, at least in principle, for reactions in strongly acidic solution, because the activity of water varies significantly with the acid concentration. Graham and Hughes 7 showed that the hydrolysis of methyl benzoate in sulphuric acid at 20°C is first-order with respect to ester concentration, but zeroth-order with respect to water in concentrations up to 1 M. Leisten6 showed further that the first-order rate coefficient for this reaction is almost independent of the initial concentration of the ester, and thus ruled out the possibility that a bimolecular attack by bisulphate ion is involved, since the ester is completely protonated in 100% sulphuric acid and tfe concentration of bisulphate ion depends on the concentration of the ester, viz. 

The procedure used for the kinetic analysis is that described by Wei and. Prater (f), and it has been applied in the following manner. The isomerization of xylenes is assumed to be kinetically first order and can be described by the following apparent reaction scheme ... 

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... 

We cannot compare the rate constants for these two reactions directly because they are expressed in different units. The intramolecular reaction [equation (1)] is kinetically first order, whereas the intermolecular reaction [equation (2)] is second order. But suppose the two molecules of acetic acid that enter into reaction (2) are labeled isotopically to make them distinguishable and that one type of molecule is present in great excess over the other. The process is then kinetically first order in the concentration of the limiting reactant. To make the rate constant the same as for reaction (1), the more abundant species has to be present at a concentration of 3 x 105 m This is far above any concentration that can actually be obtained. 

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