Computation in kinetics, II. Simultaneous regression estimation of rate constants and initial concentrations

The general regression program KILET was used for simultaneous estimation of rate constants and initial concentrations. The method can be used either to improve the quality of fit calculating the possible analytical errors of some initial concentrations of a kinetic experiment or for analytical purposes, i.e. for the determination of analytes, while any side reactions can be taken into account.

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Application of chemometrics methods with kinetic constraints for estimation of rate constants of second order consecutive reactions.

To determine the rate constants for the second order consecutive reactions of the form U + V -(k1)--> W -(k2)--> P, a number of chemometrics and hard modeling-based methods are described. The absorption spectroscopic data from the reaction were utilized for performing the analysis. Concentrations and extinctions of components were comparable, and all of them were absorbing species. The number of steps in the reaction was less than the number of absorbing species, which resulted in a rank-deficient response matrix. This can cause difficulties for some of the methods described in the literature. The standard MATLAB functions were used for determining the solutions of the differential equations as well as for finding the optimal rate constants to describe the kinetic profiles. The available knowledge about the system determines the approaches described in this paper. The knowledge includes the spectra of reactants and products, the initial concentrations, and the exact kinetics. Some of this information is sometimes not available or is hard to estimate. Multiple linear regression for fitting the kinetic parameters to the obtained concentration profiles, rank augmentation using multiple batch runs, a mixed spectral approach which treats the reaction using a pseudo species concept, and principal components regression are the four groups of methods discussed in this study. In one of the simulated datasets the spectra are quite different, and in the other one the spectra of one reactant and of the product share a high degree of overlap. Instrumental noise, sampling error are the sources of error considered. Our aim was the investigation of the relative merits of each method.     

Computation in kinetics V. A new KINDC computational method. Comparative study with other computer programs for kinetic treatment

A new KINDC kinetic computational method is proposed that offers a greatly improved version of the KILET program. A comparative study is made of its performance and those of the most recent computational methods reported in the literature.

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Computation in kinetics, IV. Regression estimation of Arrhenius equation parameters from non-isothermal kinetic data

Computer method for evaluation of Arrhenius equation parameters from non-isothermal kinetic data is offered in KILET program. Changes of temperature can be linear, hyperbolic or of any smooth function which could be expressed by a polynomial of up to 4th degree. The method is demonstrated on examples of linear and hyperbolic changes for simulated and experimental data. The advantage of non-isothermal experiment over isothermal one for evaluation of kinetic solution data is stressed.

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A new kinetic photometric method for the simultaneous determination of metals based on catalytic and activating effects

Summary The potential use of the activating effect of Pb(II) on the Mn(II)-catalysed oxidation of Tiron by hydrogen peroxide in the presence of 1,10-phenanthroline for the simultaneous determination of the two metals was investigated. The results obtained allowed the development of a new kinetic photometric method for the simultaneous determination of Pb(II) and Mn(II). The catalysed reaction was monitored by the initial rate method, which was applied to absorbance-time curves. Different Mn(II) concentrations were used to construct calibration graphs by plotting the slopes of the photometric curves obtained against the Mn(II) concentration at each Pb(II) concentration assayed. A new calibration graph was obtained in terms of the Pb(II) concentration from the slopes of such graphs. By applying the standard-addition method to the sample to be assayed a third graph was obtained, the slope and intercept of which provided the analytical concentration of Pb(II) and Mn(II), respectively. The optimized values of the different variables involved were used to determine Mn(II) and Pb(II) over the concentration ranges 1–5 and 200–800 ng/ml, respectively.     

The heating rate as a variable in non-isothermal kinetics. A new method to evaluate the nonisothermal kinetic parameters

The heat exchange calorimetry, hitherto developed for ordinary size samples, was modified for diminishing the sample size to one tenth or less of that commonly used in previous reports. Improvements were made with respect to the vessels for sample and reference, the stirrer of the sample solution, the thermistor and the calibration heater. The value of α, a constant relating to the heat transfer and critically affecting the sensitivity to smaller heat effects, was given an appropriately small value. The improved version of the calorimeter employed a sample vessel of a capacity of 6 cm³ and was suited to accomodate about 3 cm³ of a solution. The calorimeter proved to give sufficiently precise results when total heats ranging from 0.05 to 0.4 J were evolved.     

Two-rate method for simultaneous kinetic determination based on detecting the reagent in successive reactions

A simultaneous kinetic method based on the measurement of two rates at two points during the course of the successive reactions is proposed. The successive kinetics of the reaction of tris(1,10-phenanthroline)iron(III) with epinephrine (EP) and norepinephrine (NE) (10⁻⁵ to 10⁻⁴ M) is investigated and exploited for the determination of binary mixtures of the two catecholamines using the two-rate method. The method is compared with classical and extension proportional equation methods and a smaller error is obtained for the two-rate method. The reason why the two-rate method based on successive reactions works well is explained by studies on a series of simulated kinetic curves.     

Continuous flow method for the simultaneous determination of phosphate/arsenate based on their different kinetic characteristics

This paper proposes a new automated spectrophotometric method for the simultaneous determination of phosphate and arsenate without pre-treatment, which is faster, simpler, less expensive and hazardous than other well-known methods used with water samples. Such method is based on the different kinetic characteristics of complex formation of phosphate and arsenate with ammonium molybdate. A flow system was used in order to achieve good mixing and to provide precise time control. All the measurements were performed at the isosbestic point wavelength (885 nm). Chemical variables were optimized by factorial design (ammonium molybdate 0.015 mol L⁻¹, potassium antimony tartrate 1 × 10⁻⁴ mol L⁻¹, and sulphuric acid 0.7 mol L⁻¹). An appropriate linear range for both analytes (0.50-8.00 μmol L⁻¹), good inter-day reproducibility (4.9% [P] and 3.3% [P + As]) and a sample throughput of 6 h⁻¹ were obtained. The detection limits are 0.4 μmol L⁻¹ P and 0.19 μmol L⁻¹ [P + As] (3.3 Sy/x). The method was validated.     

A new kinetic model for bulk polymerization of vinyl chloride based on two-phase hypothesis

A kinetic model has been developed for the bulk polymerization of vinyl chloride using Talamini's hypothesis of two-phase polymerization and a new concept of kinetic solubility which assumes that rapidly growing polymer chains have considerably greater solubility than the thermodynamic solubility of preformed polymer molecules of the same size and so can remain in solution even under thermodynamically unfavourable conditions. It is further assumed that this kinetic solubility is a function of chain length. The model yields a rate expression consistent with the experimental data for vinyl chloride bulk polymerization and moreover is able to explain several characteristic kinetic features of this system. Application of the model rate expression to the available rate data has yielded 2.36 × 10⁸l mol^?1 sec^?1 for the termination rate constant in the polymer-rich phase; as expected, this value is smaller than that reported for homogenous polymerization by a factor of 10–30.     

A new kinetic approach to the evaluation of rate constants for the spin trapping of superoxide/hydroperoxyl radical by nitrones in aqueous media

A new kinetic approach to the evaluation of rate constants for the spin trapping of superoxide/hydroperoxyl radical by nitrones in buffered media is described. This method is based on a competition between the superoxide trapping by the nitrone and the spontaneous dismutation of this radical in aqueous media. EPR spectra are recorded as a function of time at various nitrone concentrations, and kinetic curves are obtained after treatment of these spectra using both singular value decomposition and pseudo-inverse deconvolution methods. Modelling these curves permits the determination of the rate constants k(T) and k(D) for the superoxide trapping and the adduct decay reactions, respectively. Kinetics parameters thus obtained with six nitrones, namely the 2-ethoxycarbonyl-2-methyl-3,4-dihydro-2H-pyrrole N-oxide (EMPO), the 5-diethoxyphosphoryl-5-methyl-3,4-dihydro-5H-pyrrole N-oxide (DEPMPO), the 5,5-dimethyl-3,4-dihydro-5H-pyrrole N-oxide (DMPO), the 1,3,5-tri[(N-(1-diethylphosphono)-1-methylethyl)-N-oxy-aldimine]benzene (TN), the N-benzylidene-1-ethoxycarbonyl-1-methylethylamine N-oxide (EPPN), and the N-[(1-oxidopyridin-1-ium-4-yl)methylidene]-1-ethoxycarbonyl-1-methylethylamine N-oxide (EPPyON), indicate that cyclic nitrones trapped superoxide faster than the linear ones. However, the low k(T) values obtained for compounds show that there is still a need for new molecules with better spin trapping capacities.     

A quantitative study of alkyl radical reactions by kinetic spectroscopy III. Absorption spectrum and rate constants of mutual interaction for the ethyl radical

Intrinsic spectral and kinetic parameters have been measured for the ethyl radical, which was formed in the gas phase by the flash photolysis of azoethane. Absolute values of the extinction coefficient ?(λ) were derived from complementary measurements of the yield of nitrogen and the absorbance of an equivalent concentration of the ethyl radical. The absorption spectrum is broad, structureless, and comparatively weak; ?(247) = 4.8 × 10² l/mol·cm at the maximum, and the oscillator strength is (9.1 ± 0.5) × 10^?3. This is in good qualitative agreement with a spectrum obtained independently using the technique of molecular modulation spectrometry. The biomolecular reactions of mutual interaction were the only significant reactions of the ethyl radical in this system; kinetic analysis of the second-order decline of the absorbance during the dark period yielded a value of k/?(λ) for each experiment. The rate constant for mutual interaction was evaluated from the product of corresponding measurements of k/?(λ) and ?(λ) individual values are independent of the wavelength of measurement, and the mean value is k = (1.40 ± 0.27) × 10¹⁰ l/mol·sec. The rate constant for mutual combination was derived with the aid of product analysis as k₂ = (1.24 ± 0.23) × 10¹⁰ l/mol·sec; it stands in close agreement with the set of “high” values obtained by direct measurement using a variety of methods.     

Computation in kinetics I. A general program KILET for simulation and evaluation of kinetic experimental data in multicomponent systems

A general regression program KILET written in FORTRAN IV for an IBM PC and other computers (MV 4000 Eclipse and EC 1033) enables (i) to model multicomponent kinetic data (ii) to load the smooth curves with random noise of required level (iii) to evaluate rate constants and/or simultaneously concentrations. Complete statistical analysis of residuals is performed. The program can be used for the discrimination of chemical kinetic models and for analytical purposes.

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A new method for the determination of the rate constants for the disproportionation of semiquinone radicals from nonstationary kinetics of Chain reactions between quinoneimines and hydroquinones

A new method is suggested for the determination of the rate constants for the disproportionation of semiquinone radicals k ₆ from the kinetics of chain reactions between quinoneimines and hydroquinones under nonstationary conditions. The k ₆ values were determined in solvents of various natures, including comparatively low-polarity solvents in which hydroquinones are poorly soluble. The k ₆ values were found from the dependence of the degree of quinoneimine concentration lowering during a certain time (∼20 s) after reaction beginning (when the reaction occurred under nonstationary conditions) on the rate of initiation. Techniques for overcoming difficulties caused by the absence of the limiting chain propagation stage in reactions between quinoneimines and hydroquinones were suggested. The developed method of the nonstationary kinetics of chain reactions was applied to selectively determine the rate constant for the disproportionation of 2,5-dichloroseniquinone radicals, which is one of parallel chain termination stages in the chain reaction between N,N’-diphenyl-1,4-benzoquinonediimine and 2,5-dichlorohydroquinone, k ₆ = (5.8−7.1) × 10⁶ l/(mol s) in chlorobenzene at 298 K.     

A new semiempirical kinetic method for the determination of ion exchange constants for counterions of cationic micelles: Study of the rate of pH‐independent hydrolysis of phthalimide as the kinetic probe

Pseudo‐first‐order rate constants (k_obs) for pH‐independent hydrolysis of phthalimide ( 1 ), obtained at a constant total concentration of cetyltrimethylammonium bromide and hydroxide ([CTABr]_T), 2.0 × 10^?4 M 1 , 0.02 M MOH (M⁺ = Li⁺, Na⁺ and K⁺) and various concentrations of inert salt MX (= LiCl, LiBr, NaCl, NaBr, KCl and KBr), follow a relationship derived from the pseudophase micellar (PM) model coupled with an empirical equation. This relationship gives empirical constants, F_X/S and K_{X /S}, with S representing anionic 1 . The magnitude of F_X/S is the measure of the fraction of micellized anionic 1 (S^?_M) transferred to the aqueous phase by the limiting concentration of X^?. The value of K_X/S is the measure of the ability of the counterions (X^?) to expel the reactive counterions (S^?) from the cationic micellar surface to the aqueous phase. The values of F_{X/ S} are ～ 1 for MBr (M⁺ = Li⁺, Na⁺ and K⁺) and in the range ? 0.7 to ? 0.5 for MCl (M⁺ = Na⁺ and K⁺) at 0.006, 0.010 and 0.016 M CTABr. For LiCl, the values of F_X/S become ～1 at 0.006 and 0.010 M CTABr and 0.8 at 0.016 M CTABr. The values of the empirical constants, F_X/S and K_X/S, have been used to determine the usual ion exchange constant (K^Cl_Br). The mean values of K^Cl_Br are 3.9 ± 0.5, 2.7 ± 0.1, and 2.6 ± 0.3 for LiX, NaX, and KX, respectively. These values of K^Cl_Br are comparable with those obtained directly by other physicochemical techniques. Thus, this new method for the determination of ion exchange constants for various counterions of cationic micelles may be considered as a reliable one. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 43: 9–20, 2011     

A new method for the calculation of vibrational force constants. Application to H2

A new method for the quantum mechanical calculation of vibrational force constants is presented. This method is applied to the calculation of the vibrational force constant of H₂, using a completely optimized wavefunction constructed from a single gaussian orbital. The value of the force constant obtained using this method is k₀ = 0.422341088751 au (= 6.5754 × 10⁵ dyne/cm), compared to the value of k₀ = 0.42234079S380 au (= 6.5754 × 10⁵ dyne/cm) obtained using an analytic method, and the experimental value of k_e = 0.3692 au (= 5.748 × 10⁵ dyne/cm).     

A new intraparticle mass transfer rate model for cyclic adsorption and desorption in a slab, cylinder or sphere

A new intraparticle mass transfer rate model for cyclic adsorption and desorption in a slab, cylinder or sphere is proposed on the basis of the asymptotic behaviors of the adsorption rate for short and long cycle periods. Through comparison with the exact solution and the linear driving force (LDF) model, the new model is shown to provide a very good approximation for the instantaneous amount adsorbed as well as the adsorption rate for dimensionless half-cycle period τ _c =0.001～1 and is much better than the LDF model.     

A new spectrofluorometric method for the determination of ascorbic acid based on its activating effect on a hemoglobin-catalyzed reaction.

A spectrofluorometric method for the determination of ascorbic acid (AA) based on its activation on the hemoglobin-catalyzed reaction was proposed. The fluorescence intensity of the product was measured under the optimal experimental conditions, i.e. 4.0 x 10(-6) M H2O2, 6.0 x 10(-5) M p-cresol, 1.2 M NH3-NH4Cl (pH 10.4) and 2.0 x 10(-7) M hemoglobin. The order of additions of the reagents was also studied. The activation of AA was found to be associated with a high ammonia concentration. The linear range of the method was 9.0 x 10(-10)-3.6 x 10(-8) M of AA. The detection limit was calculated to be 3.0 x 10(-10) M. The relative standard deviation of this method is 1.6% at 7.0 x 10(-9) M for 11 determinations.