Pseudo-first order mechanisms

The first studies on esterifications were carried out by Berthelot233,234). Goldschmidt235-239 studied many proton-catalyzed esterifications in alcohol at relatively low temperatures (below 80 °C) without removal of water. He suggested a pseudo first-order mechanism ... 

Decomposition of diphenoylperoxide [6109-04-2] (40) in the presence of a fluorescer such as perylene in methylene chloride at 24°C produces chemiluminescence matching the fluorescence spectmm of the fluorescer with perylene was reported to be 10 5% (135). The reaction follows pseudo-first-order kinetics with the observed rate constant increasing with fluorescer concentration according to = k [flr]. Thus the fluorescer acts as a catalyst for peroxide decomposition, with catalytic decomposition competing with spontaneous thermal decomposition. An electron-transfer mechanism has been proposed (135). 

The two main termination steps for neutral solutions are HO + HO — H2O2 + 2 O3 and HO + HO3 — H2O2 + O3 + O2. An alternative mechanism has been proposed that does not involve HO and HO but has a different initiation step (26). Three ozone molecules are destroyed for each primary event. In the presence of excess HO radical scavengers, ie, bicarbonate, the pseudo-first-order rate constant at 20°C for the initiation step is 175 X. This yields an ozone half-hfe of 66 min at pH 8. In distilled water = 50 mmol/L), the half-hfe is significantly lower, ie, 7 min. 

The kinetics of hydrolysis reactions maybe first-order or second-order, depending on the reaction mechanism. However, second-order reactions may appear to be first-order, ie, pseudo-first-order, if one of the reactants is not consumed in the reaction, eg, OH , or if the concentration of active catalyst, eg, reduced transition metal, is a small fraction of the total catalyst concentration. 

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. 

Quantitative structure-reactivity analysis is one of the most powerful tools for elucidating the mechanisms of organic reactions. In the earliest study, Van Etten et al. 71) analyzed the pseudo-first-order rate constants for the alkaline hydrolysis of a variety of substituted phenyl acetates in the absence and in the presence of cyclodextrin. The... 

The data of Fig 26 can be converted into the extent of reaction plot of Fig 27. Fig 27 is a typical first-order plot and this and other data were interpreted to mean that the reaction is pseudo first-order in glycol and nitration proceeded via a N02+ mechanism... 

The anticipated rate for mechanism (i) is rate = E[C 2H220,], while the expected rate for mechanism (ii) is rate = EfC HvjOnllHjOJ. The rate for mechanism (ii) will be pseudo-first-order in dilute solutions of sucrose because the concentration of water will not change. Therefore, in dilute solutions kinetic data can not be used ro distinguish between... 

The fact that the rate of silanization is influenced by the moisture content of the sUica supports the mechanism wherein a hydrolysis step is involved. The reaction follows pseudo first-order kinetics. Figure 29.1 shows the mechanism of the primary reaction. 

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. 

Absorption rates of carbon dioxide were measured in organic solutions of glycidyl methacrylate at 101.3 kPa to obtain the reaction kinetics between carbon dioxide and glycidyl methacrylate using tricaprylylmethylammonium chloride(Aliquat 336) as catalysts. The reaction rate constants were estimated by the mass transfer mechanism accompanied by the pseudo-first-order fast reaction. An empirical correlation between the reaction rate constants and the solubility parameters of solvents, such as toluene, A-methyl-2-pirrolidinone, and dimethyl sulfoxide was presented. 

The successive equilibria are characterized by K12 and K23, respectively, and when Kl2 (often denoted K0) cannot be directly determined, it may be estimated from the Fuoss equation (3), where R is the distance of closest approach of M2+ and 1/ (considered as spherical species) in M OH2 Um x) +, e is the solvent dielectric constant, and zM and zL are the charges of Mm+ and Lx, respectively (20). Frequently, it is only possible to characterize kinetically the second equilibrium of Eq. (2), and the overall equilibrium is then expressed as in Eq. (4) (which is a general expression irrespective of mechanism). Here, the pseudo first-order rate constant for the approach to equilibrium, koba, is given by Eq. (5), in which the first and second terms equate to k( and kh, respectively, when [Lx ] is in great excess over [Mm+]. When K0[LX ] <11, koba - k,K0[Lx ] + k.it and when K0[LX ] > 1, fc0bs + k l. Analogous expressions apply when [Mm+] is in excess. 

Kinetic theory indicates that equation (32) should apply to this mechanism. Since the extent of protonation as well as the rate constant will vary with the acidity, the sum of protonated and unprotonated substrate concentrations, (Cs + Csh+), must be used. The observed reaction rate will be pseudo-first-order, rate constant k, since the acid medium is in vast excess compared to the substrate. The medium-independent rate constant is k(), and the activity coefficient of the transition state, /, has to be included to allow equation of concentrations and activities.145 We can use the antilogarithmic definition of h0 in equation (33) and the definition of Ksh+ in equation (34) ... 

Net addition of CO to 3Fe(CO)3(H2) to form Fe(CO)4(H)2 was observed upon photolysis of Fe(CO)s in sc Ar in the presence of H2 (24). The intermediate species 3Fe(CO)3(H2) is involved as a minor product of the photolysis, and was proposed to arise from addition of H2 to Fe(CO)3 or Fe(C0)3Ar (24). Experimentally, this species was shown to decay in the presence of excess CO with a pseudo-first-order rate constant 0bs — 4.1( + 0.3) x 107s-1. The mechanism for this spin-forbidden process was however unclear from experiment alone, and computation was used to explore the various possibilities (24). 

A mechanism for a pseudo-first-order reaction involving the hydrolysis of substrate S catalyzed by acid HA that is consistent with the observed rate law rs = kohscs, is as follows ... 

By lifting the simplifying restrictions, the kinetic observations can be examined in more detail over much wider concentration ranges of the reactants than those relevant to pseudo-first-order conditions. It should be added that sometimes a composite kinetic trace is more revealing with respect to the mechanism than the conventional concentration and pH dependencies of the pseudo-first-order rate constants. Simultaneous evaluation of the kinetic curves obtained with different experimental methods, and recorded under different conditions, is based on fitting the proposed kinetic models directly to the primary data. This method yields more accurate estimates for the rate constants than conventional procedures. Such an approach has been used sporadically in previous studies, but it is expected to be applied more widely and gain significance in the near future. 

The reactant R2 can also be considered to be a solvent molecule. The global kinetics become pseudo first order in Rl. For a SNl mechanism, the bond breaking in R1 can be solvent assisted in the sense that the ionic fluctuation state is stabilized by solvent polarization effects and the probability of having an interconversion via heterolytic decomposition is facilitated by the solvent. This is actually found when external and/or reaction field effects are introduced in the quantum chemical calculation of the energy of such species [2]. The kinetics, however, may depend on the process moving the system from the contact ionic-pair to a solvent-separated ionic pair, but the interconversion step takes place inside the contact ion-pair following the quantum mechanical mechanism described in section 4.1. Solvation then should ensure quantum resonance conditions. 

The EC mechanism (Scheme 2.1) associates an electrode electron transfer with a first-order (or pseudo-first-order) follow-up homogeneous reaction. It is one of the simplest reaction schemes where a heterogeneous electron transfer is coupled with a reaction that takes place in the adjacent solution. This is the reason that it is worth discussing in some detail as a prelude to more complicated mechanisms involving more steps and/or reactions with higher reaction orders. As before, the cyclic voltammetric response to this reaction scheme will be taken as an example of the way it can be characterized qualitatively and quantitatively. 

In the CE mechanism (Scheme 2.2), a first-order (or pseudo-first-order) homogeneous reaction precedes the electron transfer step. In the case where the initial electron transfer is fast enough not to interfere kinetically, the electrochemical response is a function of two parameters the first-order (or pseudo-first-order) equilibrium constant, K, and a dimensionless kinetic... 

The preceding approach applies to all linear systems that is, those involving mechanisms in which only first-order or pseudo-first-order homogeneous reactions are coupled with the heterogeneous electron transfer steps. As seen, for example, in Section 2.2.5, it also applies to higher-order systems, involving second-order reactions, when they obey pure kinetic conditions (i.e., when the kinetic dimensionless parameters are large). If this is not the case, nonlinear partial derivative equations of the type... 

These prodrugs underwent spontaneous hydrolysis in aqueous solution. The mechanism of reaction (Fig. 11.10) was postulated to involve nucleophilic hydration of the C=N bond to yield an intermediate carbinolamine. The latter breaks down with loss of the dialkylamine to form an Af4-formyl intermediate, which, in turn, hydrolyzes to the active agent (11.68, Fig. 11.10). The hydrolysis of these prodrugs followed pseudo-first-order kinetics with tm values at pH 7.4 and 37° that were mostly influenced by the steric properties of the dialkylamino group. Thus, tm values were ca. 4, 9 - 10, 14 -15, and 48 - 52 h for R = Me, Et, Pr, and i-Pr, respectively. Interestingly, the rates of hydrolysis were decreased in human serum, indicating protective... 

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