Transesterification of phenyl salicylate II. Kinetics and mechanism of intramolecular general base-catalyzed cleavage of phenyl salicylate under the presence of 1,2-ethanediol and 2-ethoxyethanol

The first-order rate constants, k₁, for 1,2-ethanediolysis (within the content of 1,2-ethanediol of 5% to 90%, v/v) and 2-ethoxyethanolysis (within the 2-ethoxyethanol content of 5% to 60%, v/v) of phenyl salicylate, PSH, in alkaline aqueous mixed solvents, fit to a relationship: k₁ = k[ROH]_T/(1 + K[ROH]_T) where k and K represent the secondorder rate constant for the reaction of alkanol, ROH, with ionized phenyl salicylate, PS^?, and association constant for the dimerization of ROH, respectively, and [ROH]_T is the total concentration of ROH. Similar relationship between k₁ and [ROH]_T has been found for 1,2-ethanediolysis of PS^? studied in mixed solvents containing 1,2-ethanediol and MeCN. In the alkaline aqueous mixed solvents containing 2-ethoxyethanol, the k₁-[ROH]_T profile reveals the change in the solvent structure of the reaction medium at >60% (v/v) of ROH content. It is proposed that alkanols exist in polymeric form, (ROH)_n, and the alkanolysis of PS^? involves the pre-equilibrium formation of monomeric ROH from (ROH)_n, followed by an intramolecular general base-catalyzed nucleophilic attack at carbonyl carbon of ester. A slight negative KCl salt- and slight positive n-Bu₄NI salt-effect are obtained for 1,2-ethanediolysis while a significant positive n-Bu₄NI salt-effect is obtained for 2-ethoxyethanolysis of PS^?.     

Kinetic evidence for the occurrence of trianionic tetrahedral intermediate in the hydroxide ion-catalyzed cleavage of 1, 2-benzisothiazolin-3-one-1, 1-dioxide (saccharin)

The kinetics of hydrolytic cleavage of saccharin has been studied at 60°C within the [ōH] range of 0.1 to 3.0 M. The observed pseudo first-order rate constants, k_obs, follow an empirical relationship: k_obs = B[ōH] + [C[ōH]]². The B and C terms are attributed to the formation of dianionic and trianionic tetrahedral intermediates on the reaction path. It is concluded that the ionized form of saccharin is the major reacting species under the present experimental conditions. The positive ionic strength effect and the negative effect of 1,4-dioxan on the rate of hydrolysis favor the proposed reaction mechanism. The analysis of the observed activation parameters indicates that the increase in the contribution of C term to k_obs causes the slight increase in both ΔH* and ΔS*. A significantly large negative value of ΔS* favors the proposed mechanism.     

Kinetic studies on the reaction of phthalimide with ethane-1,2-diamine

General base-catalyzed and uncatalyzed nucleophilic cleavage of both unionized (SH) and ionized (S^–) phthalimide have been observed in ethane-1,2-diamine buffer solutions of pH 7.46–8.60. General base catalysis appears to be insignificant in the pH range of 9.17–10.10.     

Effects of Organic Salts on the Rate of Alkaline Hydrolysis of Phthalimide in the Presence Ofcationic Micelles

Pseudo-first order rate constants (k_obs) for alkaline hydrolysis of phthalimide (PTH), obtained at constant concentration of cetyltrimethylammonium bromide (CTABr) and 35°C, vary with the concentration of organic salts ([MX]) according to the relationship: k_obs = (k₀ + K [MX])/(1 + K [MX]) where and K are empirical parameters. The values of K at 0.01 M CTABr are nearly 2 times larger than the corresponding K values at 0.02 M CTABr for sodium benzoate, disodium phthalate and disodium isophthalate.     

Kinetic evidence for the occurrence of kinetically detectable intermediates in the cleavage of N‐ethoxycarbonylphthalimide under N‐methylhydroxylamine buffers

The kinetics of the aqueous cleavage of N‐ethoxycarbonylphthalimide (NCPH) in CH₃NHOH buffers of different pH reveals that the cleavage follows the general irreversible consecutive reaction path NCPH ENMBC A B , where ENMBC, A , and B represent ethyl N‐[o‐(N‐methyl‐N‐hydroxycarbamoyl)benzoyl]carbamate, N‐hydroxyl group cyclized product of ENMBC, and o ‐(N‐methyl‐N‐hydroxycarbamoyl)benzoic acid, respectively. The rate constant k_{1 obs} at a constant pH, obeys the relationship k_{1 obs} = k_w + k_n^app [Am]_T + k_b[Am]_T², where [Am]_T is the total concentration of CH₃NHOH buffer and k_w is first‐order rate constant for pH‐independent hydrolysis of NCPH. Buffer‐dependent rate constant k_b shows the presence of both general base and general acid catalysis. Both the rate constants k_{2 obs} and k_{3 obs} are independent of [Am]_T (within the [Am]_T range of present study) at a constant pH and increase linearly with the increase in a_OH with definite intercepts. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 34: 95–103, 2002     

Expanding the Applicability of High-Order Traub-Type Iterative Procedures

We propose a collection of hybrid methods combining Newton’s method with frozen derivatives and a family of high-order iterative schemes. We present semilocal convergence results for this collection on a Banach space setting. Using a more precise majorizing sequence and under the same or weaker convergence conditions than the ones in earlier studies, we expand the applicability of these iterative procedures.     

Chaotic dynamics of a third-order Newton-type method

The dynamics of a classical third-order Newton-type iterative method is studied when it is applied to degrees two and three polynomials. The method is free of second derivatives which is the main limitation of the classical third-order iterative schemes for systems. Moreover, each iteration consists only in two steps of Newton's method having the same derivative. With these two properties the scheme becomes a real alternative to the classical Newton method. Affine conjugacy class of the method when is applied to a differentiable function is given. Chaotic dynamics have been investigated in several examples. Applying the root-finding method to a family of degree three polynomials, we have find a bifurcation diagram as those that appear in the bifurcation of the logistic map in the interval.     

ON NEW STRATEGIES TO CONTROL THE ACCURACY OF WENO ALGORITHM CLOSE TO DISCONTINUITIES Ⅱ:CELL AVERAGES AND MULTIRESOLUTION

This paper is the second part of the article and is devoted to the construction and analysis of new non-linear optimal weights for WENO interpolation capable of rising the order of accuracy close to discontinuities for data discretized in the cell averages. Thus, now we are interested in analyzing the capabilities of the new algorithm when working with functions belonging to the subspace $L^1\cap L^2$ and that, consequently, are piecewise smooth and can present jump discontinuities. The new non-linear optimal weights are redesigned in a way that leads to optimal theoretical accuracy close to the discontinuities and at smooth zones. We will present the new algorithm for the approximation case and we will analyze its accuracy. Then we will explain how to use the new algorithm in multiresolution applications for univariate and bivariate functions. The numerical results confirm the theoretical proofs presented.