Pseudo-first order kinetics, substitution

Apeloig and Nakash have reported recently a Hammett-type study for the addition reactions of seven para- and meto-substituted phenols to tetramesityldisilene 39 (equation 10)54. They used a large excess of the phenol to enforce pseudo-first-order kinetics. The addition reactions are indeed firstorder in both the disilene and the phenol. 

The unit of the velocity constant k is sec-1. Many reactions follow first order kinetics or pseudo-first order kinetics over certain ranges of experimental conditions. Examples are the cracking of butane, many pyrolysis reactions, the decomposition of nitrogen pentoxide (N205), and the radioactive disintegration of unstable nuclei. Instead of the velocity constant, a quantity referred to as the half-life t1/2 is often used. The half-life is the time required for the concentration of the reactant to drop to one-half of its initial value. Substitution of the appropriate numerical values into Equation 3-33 gives... 

Examination of these data clearly shows that none of the three compounds Is as effective as terbufos In the jar test. Perhaps the most Interesting aspect of this data Is the relative soil efficacy of the second compound compared to the first. The substitution of a methyl group for a hydrogen between the two sulfur atoms greatly enhances the soil activity of this molecule. Quantitation of the relative soil stability of these three molecules as measured by the bioassay data are collected in Table 5 using a pseudo first order kinetic analysis of the data. 

Numerous evidence clearly indicates that the reaction occurs in the organic phase. In particular, the irreversible nucleophilic substitution (Scheme 2) in the presence of an excess of anionic nucleophile in the aqueous phase follows pseudo first-order kinetics ... 

When the omega phase is formed, the overall reaction rate can be described by pseudo-first-order kinetics with respect to the organic reactant. While the reaction follows pseudo-zero-order kinetics as the substitution reaction is conducted in the presence of crown ether and in the absence of water, it is independent of the benzyl halide concentration. Crown ether directly dissociates the cation of the reacting salt. A reaction mechanism was proposed for the esterification reaction of solid potassium 4-nitrobenzoate and benzyl bromide by using crown ether [197], The overall reaction is... 

The hydrolysis of 25 borazine derivatives in dilute 90% THF-10%H2O solutions follow pseudo-first-order kinetics. The hydrolysis rates were determined using a new analytical procedure, KBrOa-KBr solutions being used to brominate the arylamine liberated. In A-phenylborazines, ortho-substitution in the phenyl ring decreases the rate of hydrolysis markedly. 

In Equation (19.8), a similar mechanism occurs for the 18-electron [(> 6 6H6) Mo(CO)3] molecule, with the coordinated benzene ring slipping to an i/ -linkage to allow room for the initial PR3, where the intermediate [(>/4-C6H6)Mo(CO)3(PR3)] has been isolated and characterized in the solid state. Sometimes an associative mechanism will also involve a second term in its kinetics rate law involving a competition between addition of Y and addition of solvent, as was observed in Chapter 17 for square planar substitution reactions. In this case, the solvent term will follow pseudo-first-order kinetics. 

A series of tests indicates that the reaction takes place in the organic phase and thus governs the process as a whole. In particular, in the simplest case of an irreversible nucleophilic substitution (Eqs. (2) and (13)) and in the presence of an excess of the anionic reagent in the aqueous phase, the reaction follows pseudo-first-order kinetics (Eq. (14)). The observed rate constants depend linearly on the concentration of the catalyst in the organic phase (Eq. (15))... 

The points that we have emphasized in this brief overview of the S l and 8 2 mechanisms are kinetics and stereochemistry. These features of a reaction provide important evidence for ascertaining whether a particular nucleophilic substitution follows an ionization or a direct displacement pathway. There are limitations to the generalization that reactions exhibiting first-order kinetics react by the Sj l mechanism and those exhibiting second-order kinetics react by the 8 2 mechanism. Many nucleophilic substitutions are carried out under conditions in which the nucleophile is present in large excess. When this is the case, the concentration of the nucleophile is essentially constant during die reaction and the observed kinetics become pseudo-first-order. This is true, for example, when the solvent is the nucleophile (solvolysis). In this case, the kinetics of the reaction provide no evidence as to whether the 8 1 or 8 2 mechanism operates. 

Kinetic studies of the hydride cluster [W3S4H3(dmpe)3] with acids in a non-coordinating solvent, i.e., dichloromethane, under the pseudo-first-order condition of acid excess, show a completely different mechanism with three kineti-cally distinguishable steps associated to the successive formal substitution of the coordinated hydrides by the anion of the acid, i.e., Ch in HCl [37]. The first two kinetic steps show a second-order dependence with the acid concentration. 

The usual kinetic law for S/v Ar reactions is the second-order kinetic law, as required for a bimolecular process. This is generally the case where anionic or neutral nucleophiles react in usual polar solvents (methanol, DMSO, formamide and so on). When nucleophilic aromatic substitutions between nitrohalogenobenzenes (mainly 2,4-dinitrohalogenobenzenes) and neutral nucleophiles (amines) are carried out in poorly polar solvents (benzene, hexane, carbon tetrachloride etc.) anomalous kinetic behaviour may be observed263. Under pseudo-monomolecular experimental conditions (in the presence of large excess of nucleophile with respect to the substrate) each run follows a first-order kinetic law, but the rate constants (kQbs in s 1 ruol 1 dm3) were not independent of the initial concentration value of the used amine. In apolar solvents the most usual kinetic feature is the increase of the kabs value on increasing the [amine]o values [amine]o indicates the initial concentration value of the amine. 

Bacchetti et have investigated the kinetics of the nucleophilic substitution of 2-aryl-5-chloro-l,3,4-thiadiazoles with piperidine in ethanol and benzene. In ethanol, the reaction was first order in both components, whereas in benzene it was pseudo-first order in thiadia-zole, but intermediate between first and second order in piperidine, indicating intervention of associated amine molecules in the substitution. The logarithms of the rate constants from ethanol gave an excellent Hammett plot against the a values for the para substituents in the phenyl ring. 

The sequential equilibria in Equation (4) are characterized by 12 = 12/ 21 (often denoted as K0) and K23 = k23/k32, respectively. When Kn cannot be directly determined it is often estimated using the electrostatic Fuoss equation.215 Usually, it is only possible to characterize the kinetics of the second equilibrium of Equation (4) so that the overall equilibrium is expressed as in Equation (5) irrespective of the intimate mechanism of ligand substitution. The pseudo-first-order rate constant for the approach to equilibrium, kabs, is given by Equation (6)... 

Because transition states may have lifetimes of only several nanoseconds, in most cases, it is impossible to observe them directly. However, there are numerous lines of evidence for the existence of a tetrahedral-like transition state for non-enzymatic ester hydrolysis a) substitution at a carbonyl group (as is the case of the hydrolysis of esters) most often proceeds by a tetrahedral mechanism, a second-order addition-elimination (for a review of this mechanism, see (23)) b) the kinetics are pseudo-first order either in the substrate or in the nucleophile, as predicted by the mechanism c) for the 180 labeled esters, the 180 isotope is detectable in both products (in a "normal" Sjj2 reaction all the 180 isotopes should remain in the acid functionality)(24) d) in a few cases tetrahedral intermediates have been isolated or detected spectrally (25). 

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