Pre-equilibrium constant

The first indication that A-acyloxy-A-alkoxyamidcs reacted by an acid-catalysed process came from preliminary H NMR investigations in a homogeneous D20/ CD3CN mixture, which indicated that A-acetoxy-A-butoxybenzamide 25c reacted slowly in aqueous acetonitrile by an autocatalytic process according to Scheme 4 (.k is the unimolecular or pseudo unimolecular rate constant, K the dissociation constant of acetic acid and K the pre-equilibrium constant for protonation of 25c).38... 

Upon addition of a solution of sulfuric acid in D20 the reaction of A-acetoxy-A-alkoxyamides obeys pseudo-unimolecular kinetics consistent with a rapid reversible protonation of the substrate followed by a slow decomposition to acetic acid and products according to Scheme 5. Here k is the unimolecular or pseudo unimolecular rate constant and K the pre-equilibrium constant for protonation of 25c. Since under these conditions water (D20) was in a relatively small excess compared with dilute aqueous solutions, the rate expression could be represented by the following equation ... 

Pohl and Osterholtz determined the equilibrium (pre-equilibrium) constants for the reaction in aqueous solution ... 

For the acid-catalysed reaction, substituent effects have been examined principally in water and acetic acid-water mixtures. The main feature is that the effects are usually small. In Table 3 are also listed the Hammett p-values obtained for acetophenones and arylmethyl phenyl ketones. The slightly negative p-values account for the cationic character of the transition state and for opposite effects on the pre-equilibrium constant and on the elementary rate constant for proton abstraction. 

The effective pre-equilibrium constant for the formation of the precursor state, expressed in nm or A, describes the statistical probability of the formation of an electrode-reactant configuration appropriate for the electrode reaction [131, 134] ... 

In Eq. (6.35) electrical charges are omitted, k represents the intrinsic forward rate constant. The pre-equilibrium constant is given by... 

The nitrito-nitro linkage isomerization of [Co(NH3)5(ONO)] in liquid ammonia has been shown to proceed entirely by an intramolecular conjugate-base mechanism. The use of liquid ammonia as solvent allowed the separate determination of the pre-equilibrium constant Kqb (AH = 27 kJ moP A5 = -14 J moP ) and the rate constant fccB for the ratedetermining step = 78 kJ moP = 29 J moP ). 

As the pre-equilibria in Schemes 5-10 and 5-11 are not identical and their equilibrium constants are therefore likely to be different from one another, the rate constants k - and are not intrinsic rate constants of the corresponding slow dissociation steps, but are dependent in addition on the constants of these pre-equilibria. 

The curve for the conversion of the unsubstituted ( -benzenediazoate in Figure 5-3 is consistent with the (ii)-diazoate-diazohydroxide pre-equilibrium followed by the slow and pH-independent elimination of the hydroxide ion from the ( )-diazohydroxide (rate constant 6 in Scheme 5-14) as found by Lewis and Suhr. Below pH 3 the acid-catalyzed dissociation of ( >diazohydroxide (k 6) is observable. Electron-withdrawing substituents such as N02 in the 2- or 4-position reduce the rate of dissociation of diazohydroxides and increase the rate of (E) (Z)... 

The first step was found to be a fast pre-equilibrium (Scheme 12-8). The dependence of the measured azo coupling rate constants on the acidity function and the effect of electron-withdrawing substituents in the benzenediazo methyl ether resulting in reduced rate constants are consistent with a mechanism in which the slow step is a first-order dissociation of the protonated diazo ether to give the diazonium ion (Scheme 12-9). The azo coupling proper (Scheme 12-10) is faster than the dissociation, since the overall rate constant is found to be independent of the naphthol con-... 

They argued that pre-equilibria to form Cl+ or S02C1+ may be ruled out, since these equilibria would be reversed by an increase in the chloride ion concentration of the system whereas rates remained constant to at least 70 % conversion during which time a considerable increase in the chloride ion concentration (the byproduct of reaction) would have occurred. Likewise, a pre-equilibrium to form Cl2 may be ruled out since no change in rate resulted from addition of S02 (which would reverse the equilibrium if it is reversible). If this equilibrium is not reversible, then since chlorine reacts very rapidly with anisole under the reaction condition, kinetics zeroth-order in aromatic and first-order in sulphur chloride should result contrary to observation. The electrophile must, therefore, be Cli+. .. S02CI4- and the polar and non-homolytic character of the transition state is indicated by the data in Table 68 a cyclic structure (VII) for the transition state was considered as fairly probable. 

Another problem which can appear in the search for the minimum is intercorrelation of some model parameters. For example, such a correlation usually exists between the frequency factor (pre-exponential factor) and the activation energy (argument in the exponent) in the Arrhenius equation or between rate constant (appears in the numerator) and adsorption equilibrium constants (appear in the denominator) in Langmuir-Hinshelwood kinetic expressions. 

The observed hyperbolic dependences suggest a mechanism that involves a pre-equilibrium binding of two pyridine carboxylates to the Fem of lm, followed by the intramolecular proton transfer from the coordinated acid (Scheme 3). This option has been supported by measurements of the binding constants for py and related ligands. The data in Fig. 8 agree with the mechanism in Scheme 3. The reactive intermediate for robust lm is the diaxially coordinated species, one of the two ligands being picolinic acid (L). 

The final rate expressions, which were used in the present work, were given by Hou and Hughes (2001). In these rate expressions all reaction rate and equilibrium constants were defined to be temperature-dependent through the Arrhenius and van t Hoff equations. The particular values for the activation energies, heats of adsorption, and pre-exponential constants are available in the original reference and were used in our work without alteration. 

The non-linear dependence of the relaxation process on the DNA concentration was also observed in stopped-flow experiments and the same mechanism, i.e. fast pre-equilibrium followed by a slow intercalation step, was proposed." This latter study did not report values for the individual rate constants. The mechanism proposed in Scheme 4 was employed in subsequent studies despite the criticism on the accuracy for the data related to the fast kinetic component (see below). The original temperature jump study also showed that the relaxation kinetics depend on the structure of the DNA.117 The slower intercalation rate for 5 with T2 Bacteriophage DNA when compared to ct-DNA was ascribed to the glucosylation of the former DNA (Table 3). 

The generally accepted process for metal ion-catalyzed reactions of the sort we consider here involves pre-equilibrium binding with the substrate, followed by a reaction of the complex as schematized in Equation (1). Whether the metal ion is free or complexed by ligands, or bears an associated lyate, or whether the substrate is neutral or anionic, these appear to be just the sort of processes one might expect to experience large rate accelerations in passing from water to a medium of reduced dielectric constant such as alcohols or other lower polarity solvents. 

The kinetics of the ionic hydrogenation of isobutyraldehyde were studied using [CpMo(CO)3H] as the hydride and CF3C02H as the acid [41]. The apparent rate decreases as the reaction proceeds, since the acid is consumed. However, when the acidity is held constant by a buffered solution in the presence of excess metal hydride, the reaction is first-order in acid. The reaction is also first-order in metal hydride concentration. A mechanism consistent with these kinetics results is shown in Scheme 7.8. Pre-equilibrium protonation of the aldehyde is followed by rate-determining hydride transfer. 

The equilibrium constant Kf for reaction i is computed from thermodynamic considerations using Gibbs free energies. The Arrhenius form for the rate constants is written in terms of the pre-exponential factor A,, the temperature exponent /( , the activation energy Ei, and the universal gas constant R in the same units as the activation energy. 

Since this step is fast in comparison to the subsequent ones, this reaction can be considered as a pre-equilibrium, is the surface complex formation (equivalent to the Langmuir) constant. 

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