The Limit of Detection of a Weak Acid,in the Presence of Another,by Potentiometric Acid-Base Titrimetry and Deviation-Pattern Recognition

Abstract

When a solution containing a single monobasic weak acid is titrated potentiometrically with a strong base, non-linear regression analysis of the data yields a random scatter of the residuals around the best fit to the appropriate equation. If the same equation is used when a second weak acid is also present, systematic errors arise and yield a deviation plot having a characteristic shape. If the amplitude of that plot is substantially larger than the random error of measurement, the presence of the second acid can be detected, and its concentration can then be evaluated by non-linear regression onto the equation that takes its presence into account. The amplitude increases as the relative concentration of the second acid increases, and as the difference between the values of pK_a for the two acids increases. Examination of these dependences shows, for example, that it should be possible to detect 1 per cent of an impurity for which pK_a differs by 0.57 unit from that of the major component.     

对“氧化石墨烯对水中内分泌干扰物双酚A的吸附性能”评论

Xu and Zhu published the paper entitled“Elimination of Bisphenol A from Water via Graphene Oxide Adsorption”. In section of 3.2 BPA adsorption kinetics, authors stated that “The pseudo-first- order model”and cited Blanchard et al. to be a reference. There is nothing about the pseudo- first- order model in the reference. It is a quotation error. The Lagergren rate equation presented in 1898, is a first order model. Basically, the rate of a reaction is defined as the change in concentration of a reactant or product per unit time. Concentrations of products do not appear in the rate law because the reaction rate is studied under conditions where the reverse reactions do not contribute to the overall rate. The reaction order and rate constant must be determined by experiments. In order to distinguish the kinetic equation based on the concentration of a solution from the adsorption capacity of solids, this Lagergren first order rate equation has been called a pseudo-first-order one. In addition, regression of pseudo-first-order kinetic model in Fig.1 would not be possible.     

Method of kinetic analysis of photodegradation: nifedipine in solutions

A rate equation for photodegradation was derived from Lambert-Beer's law and Grotthus-Draper's law: -dc/dt=k1(1-exp(-(k2c+k3(c0-c))))k2c/(k2c+k3(c0-c)) where c is the concentration of reactant, c0 is the initial concentration of reactant, t is time, k1 is the rate constant, and k2 and k3 are the absorption coefficient of reactant and its photodegradation product, respectively. In a case where the photodegradation products have no photoabsorption, k3 assumes the value of zero in the above general equation. In a case where the photodegradation products have the same spectrum and molar absorptivity as that of the reactant, k3 assumes the value of k2, and hence the photodegradation is not a first-order reaction; however, the equation itself gives the pseudo-first-order reaction rate equation. In a case where the concentration of reactant is high enough, the equation approaches a zero-order reaction rate equation. The photodegradation rate of nifedipine in solutions under a germicidal lamp, near an ultraviolet fluorescent lamp and a fluorescent lamp was analyzed using the above equation. The photodegradation rate was directly proportional to the amount of light absorbed, and fitted well with the equation. The above theoretical equation was substantiated by the photodegradation of nifedipine, and hence is expected to apply to other photosensitive drugs.     

Reaction pathway and rate-determining step of the Schmidt rearrangement/fragmentation: a kinetic study

The Schmidt rearrangement of substituted 3-phenyl-2-butanone with trimethylsilyl azide in 90% (v/v) aqueous TFA gave two types of product, fragmentation and rearrangement, the ratio of which depends on the substituent: more fragmentation for a more electron-donating substituent. Rate measurements by azotometry indicated the presence of an induction period, and the pseudo-first-order rate constants showed saturation kinetics with respect to the azide concentration. It was indicated that the reaction proceeds through pre-equilibrium in the formation of iminodiazonium (ID) ion and that the N(2) liberation from the ID ion is rate-determining. Under high azide concentration conditions, where the effective reactant is the ID ion, the reaction gave a linear Hammett plot with a ρ value of -0.50. The observed substituent effects on the rate and the product selectivity imply that path bifurcation on the way from the rate-determining TS to the product states occurs, as suggested by previous molecular dynamics simulations, in a similar manner to the analogous Beckmann rearrangement/fragmentation reactions.     

Esterification of sorbitol and lauric acid with catalystp-TSA

Kinetics of the esterification of sorbitol with lauric acid in the presence ofp-TSA as a catalyst has been studied. A kinetic model of reversible second order reaction was proposed for the esterification. Parameters in the model (kinetic constants) were estimated by non-linear regression. The temperature dependence of the rate was calculated from the experimental constants estimated at various temperatures, using the Arrhenius equation. Experimental results are in good accordance with the proposed theoretical model.     

Determination of Bromide Production in Radiolysis of Nucleobases,Nucleosides, and Nucleotides Using HPLC

Abstract

Determination of the formation of bromide ions in intermolecular electron transfer in 5-bromouracil (BrUr) and its nucleoside and nucleotide derivatives with nucleobases, nucleosides, and nucleotides was carried out with high performance liquid chromatography (HPLC). Initial electron attachment, at high concentration of nucleobases, nucleosides, or nucleotides, is mainly on these molecules; intermolecular electron transfer then occurs between theses molecules and BrUr and the derivatives. The elimination of bromide ions from BrUr and the derivatives then follows. It is concluded that in neutral and basic solution (pH 6 to 10) there is a significant electron transfer from thymine (T), uracil (Ur), thymidine (dT), 2′-deoxyuridine (dU), or 2′-deoxyuridine-5′-monophosphate (dUMP) to BrUr and the derivatives. For example, at a concentration ratio of BrUr and T of 1 : 100, the yield of bromide ions is about 1.6, amounting to 59% of hydrated electron (e^{aq .}) yield in the radiolysis, in which the pseudo-first-order rate constants predict a bromide yield of less than 0.03.     

Kinetic models of sorption: a theoretical analysis

The kinetics of sorption from a solution onto an adsorbent has been explored theoretically. The general analytical solution was obtained for two cases. It has been shown that at high initial concentration of solute (sorbate) the general equation converts to a pseudo-first-order model and at lower initial concentration of solute it converts to a pseudo-second-order model. In other words, the sorption process obeys pseudo-first-order kinetics at high initial concentration of solute, while it obeys pseudo-second-order kinetics model at lower initial concentration of solute. The theoretical results (derived equations) show that the observed rate constants of pseudo-first-order and pseudo-second-order models are combinations of adsorption and desorption rate constants and also initial concentration of solute. The obtained theoretical equations are used to correlate experimental data for sorption kinetics of some solutes on various sorbents. The predictions of the theory are in excellent agreement with the experimental data.     

Kinetic modeling of liquid-phase adsorption of reactive dyes on activated carbon

In this paper, adsorption equilibrium and kinetics of three reactive dyes from their single-component aqueous solutions onto activated carbon were studied in a batch reactor. Effects of the initial concentration and adsorbent particle size on adsorption rate were investigated Adsorption equilibrium data were then correlated with several well-known equilibrium isotherm models. The kinetic data were fitted using the pseudo-first-order equation, the pseudo-second-order equation, and the intraparticle diffusion model. The respective characteristic rate constants were presented. A new adsorption rate model based on the pseudo-first-order equation has been proposed to describe the experimental data over the whole adsorption process. The results show that the modified pseudo-first-order kinetic model generates the best agreement with the experimental data for the three single-component adsorption systems.     

The effects of errors in measurements of absorbance and time on the calculated value of a pseudo-first-order rate constant

When data on the variation with time of the absorbance of a reactant or product are used to evaluate the rate constant of a first- or pseudo-first-order reaction, the precision of the result depends on the precisions with which both the time and the absorbance are measured. The natures of the dependences, and the ways in which they are affected by both constant and linearly varying background absorbances, are examined. If the standard error σ_t of a measurement of time is below about 0.005 t_{$\text{1}\text{2}$}, the standard error of the rate constant is virtually identical for an experiment in which the concentration of the reactant is followed as for one in which the concentration of the product is followed, but for larger values of σ_t it is better to follow the concentration of the reactant. In any event, errors in the measurements of time are much more likely to be significant than they are usually assumed to be. Other sources of error in such experiments, including constant and time-dependent background absorbances, are examined more briefly, with emphasis on the requirements that should be satisfied in work of the highest quality.     

Calculation of the rate constants of diffusion-controlled chemical reactions for reagents of arbitrary shape

A method of describing small-size reactant diffusion in the presence of any amount of arbitrary located sinks is developed. The propagation function of mobile reagent (MR) in such a system is found. The developed method was used to calculate rate constants of bimolecular reactions of MRs with absorbents (traps) having arbitrary shape. The procedure of calculation of the rate constant has been reduced to integral equation for flux density towards a trap which is MRs' absorber. If small parameters exist, the expansion in powers of these parameters is possible. The bimolecular rates were calculated for traps of different shape. The equation was obtained which permits to determine the asymptotic time dependence of rate constants.     

Kinetic and isotherm studies of Cu(II) adsorption onto H3PO4-activated rubber wood sawdust

Adsorption of Cu(II) from aqueous solution onto H(3)PO(4)-activated carbon using rubber wood sawdust (RSAC) was investigated in a batch system. Kinetic and isotherm studies were carried out by considering the effects of various parameters, such as initial concentration, contact time, pH, and temperature. The optimal pH value for Cu(II) adsorption onto RSAC was found to be 6.0. Thermodynamic parameters such as standard Gibbs free energy (DeltaG(0)), standard enthalpy (DeltaH(0)), and standard entropy (DeltaS(0)) were evaluated by applying the Van't Hoff equation. The thermodynamics of Cu(II) adsorption onto RSAC indicates its spontaneous and exothermic nature. Langmuir, Freundlich, and Temkin isotherms were used to analyze the equilibrium data at different temperatures. The Langmuir isotherm fits the experimental data significantly better than the other isotherms. Adsorption kinetics data were tested using pseudo-first-order, pseudo-second-order, and intraparticle diffusion models. Kinetic studies showed that the adsorption followed a pseudo-second-order reaction. The initial sorption rate, pseudo-first-order, pseudo-second-order, and intraparticle diffusion rate constants for different initial concentrations were evaluated and discussed. Adsorption mechanism studies revealed that the process was complex and followed both surface adsorption and particle diffusion. The rate-controlling parameter and effective diffusion coefficient were determined using the Reichenberg plot. It was found that the adsorption occurs through film diffusion at low concentrations and at higher concentration the particle diffusion becomes the rate-determining step.     

On the Use of a Modified Mayo Plot

Abstract

The most usual procedure to estimate the chain transfer ratio in vinyl polymerization is to use a Mayo plot. This plot can only be applied directly when the polymerization rate is not modified by the chain transfer agent. In spite of this, the equation has been applied to several systems where this condition is not fulfilled. In the present work we present a slightly modified equation that can be employed irrespective of the changes in rate. This equation is applied to several systems reported in the literature. The improvement in the interpretation of the results in these systems is discussed.     

Equilibrium, kinetics, mechanism, and process design for the sorption of methylene blue onto rice husk

Batch experiments were carried out for the sorption of methylene blue onto rice husk particles. The operating variables studied were initial solution pH, initial dye concentration, adsorbent concentration, and contact time. Equilibrium data were fitted to the Freundlich and Langmuir isotherm equations and the equilibrium data were found to be well represented by the Langmuir isotherm equation. The monolayer sorption capacity of rice husks for methylene blue sorption was found to be 40.5833 mg/g at room temperature (32 degrees C). The sorption was analyzed using pseudo-first-order and pseudo-second-order kinetic models and the sorption kinetics was found to follow a pseudo-second-order kinetic model. Also the applicability of pseudo second order in modeling the kinetic data was also discussed. The sorption process was found to be controlled by both surface and pore diffusion with surface diffusion at the earlier stages followed by pore diffusion at the later stages. The average external mass transfer coefficient and intraparticle diffusion coefficient was found to be 0.01133 min(-1) and 0.695358 mg/g min0.5. Analysis of sorption data using a Boyd plot confirms that external mass transfer is the rate limiting step in the sorption process. The effective diffusion coefficient, Di was calculated using the Boyd constant and was found to be 5.05 x 10(-04) cm2/s for an initial dye concentration of 50 mg/L. A single-stage batch-adsorber design of the adsorption of methylene blue onto rice husk has been studied based on the Langmuir isotherm equation.     

Reactions in a non-uniform flow tube temperature profile: effect on the rate coefficient for the reaction C2H5OH+OH

The influence of non-linear temperature profiles in a flow reactor on the determination of rate constants is discussed for the case of pseudo-first-order reactions. The effects are investigated for the reaction C₂H₅OH+OH and taken into account in the evaluation of experimental data.     

Kinetics and Mechanism of Oxidation of Hydroquinone by Tetrabutylammonium Tribromide Ion in Aqueous Acetic Acid

The oxidation of hydroquinone by environmentally benign tetrabutyl ammonium tribromide (TBATB) was carried out in 50% V/V aqueous acetic acid medium under pseudo-first-order conditions, keeping a large excess of hydroquinone over the oxidant. The main reactive species of oxidant and substrate were found to be the Br₃^-\mathrm{Br}_{3}^{-} ion and hydroquinone, respectively. The reaction proceeds with prior complex formation between the reactants followed by its slow decomposition to generate semiquinone and bromine radicals. The complex formation was kinetically verified by its Michaelis–Menten plot. The solvent effect was verified by using Grunwald–Winstein equation which is consistent with an S_N2 mechanism. The formation constants for the complex and rate constant for the slow decomposition step were determined by studying the reaction at five different temperatures. The values of formation constant of the complex and the rate constant for its decomposition were determined at these temperatures. The activation parameters with respect to the slow step of the reaction have also been determined.     

Errors associated with nonuniform concentrations upon rate constants using absorption techniques

Kinetic absorption spectroscopy is a commonly used technique in the experimental determination of rate constants. Here we consider the effect of nonuniform reactant concentrations upon the measured results and the errors associated with the final determination of second-order rate constants in particular. We conclude that the errors associated with nonuniformity of reactant, while significant, are comparable or less than other common systematic or random errors. © 1993 John Wiley & Sons, Inc.     

Kinetics and mechanism of the benzenethiolysis of 2,4-dinitrophenyl and 2,4,6-trinitrophenyl methyl carbonates and S-(2,4-dinitrophenyl) and S-(2,4,6-trinitrophenyl) ethyl thiolcarbonates

The reactions of 2,4-dinitrophenyl and 2,4,6-trinitrophenyl methyl carbonates (DNPC and TNPC, respectively) and S-(2,4-dinitrophenyl) and S-(2,4,6-trinitrophenyl) ethyl thiolcarbonates (DNPTC and TNPTC, respectively) with a series of benzenethiolate anions were subjected to a kinetic investigation in water, at 25.0 degrees C, and an ionic strength of 0.2 M (KCl). These reactions obey pseudo-first-order kinetics, under excess of benzenethiolate, and are first order in the latter reactant. However, comparable reactant concentrations were used in the reactions of 4-nitrobenzenethiolate anion with TNPC and TNPTC, which showed second-order kinetics. The nucleophilic rate constants are pH independent, except those for the reactions of TNPC with 4-methoxy- and pentafluorobenzenethiolates, and TNPTC with benzenethiolate and 4-chloro- and 3-chlorobenzenethiolates, which show acid dependence. The Br?nsted-type plots for the nucleophilic rate constants are linear with slopes beta = 0.9, 1.0, 0.9, and 0.9 for the reactions of DNPC, TNPC, DNPTC, and TNPTC, respectively. No break in the Br?nsted plot was found for the reactions of DNPC and DNPTC at pK(a) ca. 4.1 and 3.4, respectively, consistent with concerted mechanisms. TNPC is more reactive toward benzenethiolate anions than DNPC, and TNPTC more than DNPTC due to the better leaving groups involved. Comparison of the kinetic results obtained in this work with those for the concerted phenolysis of the same substrates shows that benzenethiolate anions are better nucleophiles toward carbonates than isobasic phenoxide anions. This is explained by Pearson's "hard and soft acids and bases" principle.     

The conditional constant as error variable in the evaluation of stability constants from combined pH and pM measurements

Combined pH and pM measurements are useful in studies of chelate complexes. A plot of a conditional constant as a function of pH will indicate the species present in the solution and will give good estimates of the unknown stability constants. The values of the constants can be refined by non-linear regression analysis with the conditional constant as error variable. The approach enables programmable pocket calculators to be used in the optimization process.     

Kinetics and mechanism of ninhydrin reaction with copper(II) complexes of glycine and α-alanine. Elucidation of the template mechanism

Ninhydrin has been found to react with Cu(glycine)⁺ and Cu(alanine)⁺ in the ratio of 1:1. The kinetic studies of the reaction were carried out at different concentrations of the reactants at 80°C (pH = 5.0). The reaction proceeds through the formation of a ternary labile complex of ninhydrin with Cu(II) complexes of glycine and alanine. The kinetics were found to follow pseudo-first-order reaction path with respect to Cu(II)-complex in presence of excess [Ninhydrin]. Formation of a ternary labile complex indicates a template reaction mechanism based on the reactions with coordinated ligands. The variation of pseudo-first-order rate constants with [ninhydrin] was found to be in good agreement with equation where B₁ and B₂ are the unknown empirical parameters. The [acetate ion] has no significant effect on the rate constants. On the basis of observed data a probable mechanism has been proposed. © 1993 John Wiley & Sons, Inc.     

New differential techniques for evaluating rate constants and ratios of rate constants. The behaviors of irreversible first-and pseudo-first-order reactions

A record of the time dependence of the difference between two signals, one proportional to the concentration of a reactant or product in one reaction mixture and the other proportional to the concentration of the same or a corresponding substance in another mixture in which the reaction is initiated at the same time as the first, makes it possible to obtain not only the ratio, but also the individual values, of the rate constants for the two reactions. The effects of the experimental variables on a number of measurable parameters are examined, the errors associated with a number of different ways of evaluating the rate constants and their ratio are discussed, and it is shown how conditions can be selected that should provide values whose precisions compare favorably with those attainable by other techniques.