Consecutive First-order Reactions Research Articles

A description of aggregate liberation and dispersion in A horizons of Australian Vertisols by ultrasonic agitation

A theory is proposed which is analogous to a first-order consecutive reaction to describe the stepwise breakdown of an aggregate hierarchy for Vertisols subjected to ultrasonic agitation. To explain the liberation and subsequent dispersion of microaggregates as increasing ultrasonic energy is applied the aggregate liberation and dispersion curve (ALDC) is developed. It is found that the prominence and shape of the curve is dependent on the rate constants, which explain the rate of microaggregate liberation and subsequent dispersion. From this curve it is possible to estimate the maximum mass of microaggregates, which is not only dependant on the rate constants, but also the availability of clay that form the microaggregates. The resulting ALDC for the sample also enables the estimation of the total energy applied needed to initiate dispersion of the liberated microaggregates. It is found that the relative stability of the micoraggregates are correlated with some of the chemical properties (ESP and CaCO 3) of the samples.

A Kinetic Study of Methanol Oxidation in Supercritical Water

The oxidation rate of methanol in supercritical water at 253 bar and temperatures between 673 and 773 K is investigated using an isothermal, isobaric plug-flow tubular reactor and GC/FID and GC/TCD chromatographic methods. Experiments are conducted at a nominal methanol feed concentration of 0.88 mol % (1.53 wt %) using H2O2 as an initial oxidant. In some experiments, the O2/MeOH molar ratios are varied from 1.5 to 3.0 and show that the rate of methanol oxidation is independent of the oxygen initial feed concentration. Overall first-order rate constants calculated from the data lead to Arrhenius parameters of A = 1011.8 s-1 and Ea = 178 kJ/mol (42.5 kcal/mol). The identified reaction products are mainly CO and CO2. The temporal variation of the CO yield exhibits a maximum at temperatures of 723 and 748 K, whereas the CO2 yield increases monotonically over the experimental range of residence time (3−50 s). The experimental data are consistent with a set of consecutive first-order reactions CH3OH → CO → CO2. The global rate-controlling step in the complete oxidation of methanol is the conversion of CO to CO2. The first-order rate constants calculated for CO oxidation to CO2 lead to A = 1010.8 s-1 and Ea = 172 kJ/mol (41.0 kcal/mol). Kinetics of this system may be useful to study supercritical water oxidation (SCWO) of polychlorinated biphenyls (PCBs) dissolved in methanol.

Using CBL Technology and a Graphing Calculator To Teach the Kinetics of Consecutive First-Order Reactions

This work proposes a demonstration to introduce first-order reactions using the CBL system. It then presents the analysis of two consecutive first-order reactions. The values of the rate constants that govern each reaction's rate are determined using the graphing and statistical capabilities of a TI-83 calculator.

Kinetic analysis of consecutive reactions using a non-linear least-squares error-compensation algorithm

An error-compensation algorithm based on a kinetic model of detecting intermediates in consecutive first-order reactions using the non-linear least-squares method was developed. A simulation study revealed that the algorithm performed well in compensating for the system error and eliminating random noise. It could offset the deficiency of low precision in kinetic analysis. The algorithm was applied to the determination of epinephrine, and the results were found to be reliable when the rate constants changed according to the variation of the experimental variables.

Emissions of odorous aldehydes from alkyd paint

Aldehyde emissions are widely held responsible for the acrid after-odor of drying alkyd-based paint films. The aldehyde emissions from three different alkyd paints were measured in small environ-mental chambers. It was found that, for each gram of alkyd paint applied, more than 2 mg of aldehydes (mainly hexanal) were emitted during the curing (drying) period. Since no measurable hexanal was found in the original paint, it is suspected that the aldehydes emitted were produced by autoxidation of the unsaturated fatty acid esters in the alkyd resins. The hexanal emission rate was simulated by a model assuming that the autoxidation process was controlled by a consecutive first-order reaction mechanism. Using the emission rate model, indoor air quality simulation indicated that the hexanal emissions can result in prolonged (several days) exposure risk to occupants. The occupant exposure to aldehydes emitted from alkyd paint also could cause sensory irritation and other health concerns.

Spectrophotometric Study of Hexanitrocobaltate(III) Ion Spontaneous Reduction in Water-Ethanol and Water-Acetone Mixtures

The kinetics of the spontaneous reduction of hexanitrocobaltate(III) ion have been investigated spectrophotometrically (λ=360 nm at 298 K) in ethanol or acetone water mixtures containing 0, 10, 25 and 50 % of organic solvents. The mechanism of this process was expressed by means of two consecutive first-order reactions. Both of the first-order rate constants decrease with the increasing nonaqueous species content. The reduction of hexanitrocobaltate(III) ion in the mixtures was much slower than the corresponding reaction in water.

Reactions of 1,?-bis(2-bromopyridinium)alkanes with hydroxide ion in aqueous solutions

The reaction of OH− ion with 1,ω-bis(2-bromopyridinium)alkanes, where the reaction centers are separated by a varying number of methylene groups, was investigated to model the increased velocity of OH− attack on premicellar aggregated N-alkylpyridinium compounds. 1,ω-Bis(2-bromopyridinium)alkanes (RPBr) [R = propane (I), butane (II), pentane (III), hexane (IV) and octane (V)] were synthesized and characterized by standard procedures. The kinetics of I–V with OH− ion fitted two consecutive first-order reactions. The intermediate products, 1-(2-pyridone)-ω-(2-bromopyridinium)alkane, and also the final products 1,ω-bis(2-pyridone)alkanes, were isolated. Deuterium isotope effects, activation parameters and salt effects on the reaction rates suggest that OH− attack is rate limiting and there is a through-space acceleration of the initial attack due to the proximity of the positive charges. These results place an upper limit of 20-fold for the electrostatic acceleration in OH− attack in premicellar aggregates. © 1998 John Wiley & Sons, Ltd.

Acid-catalysed hydrolysis kinetics of carbonato cobalt(III) complexes with nonlabile tripodal quadridentate ligands

Acid-catalysed hydrolysis reaction velocity was studied by the stopped-flow method at 25°C, ionic strength ( I) of 2.0 (NaClO 4) and [H +] = 0.02−1.0 M (M = mol dm −3) for seven cobalt(III) bidentate cabonato complexes [CoL(O 2CO)] n+ with a uninegative or a dinegative tripodal quadridentate ligand L of fac( N)-5-dptma, mer( N)-5-dptma, fac( N)-i-dtma, mer( N)-i-dtma, mer( N)-i-2,3-ma, cis( O)-aeida and trans( O)-aeida where 5-dptma stands for N, N-bis(3-aminopropyl)glycinato, i-dtmma for N, N-bis(2-aminoethyl)glycinato,i-2,3-ma for N-(2-aminoethyl)- N-(3-aminopropyl)glycinato, and aeida for N-(2-aminoethyl)- N-(carboxymethyl)glycinato. The time course of the absorbance of the acidic aqueous solution of the reactant complex was followed at relevant wavelength in the UV region and was analysed according to a program for the consecutive first-order reactions with two experimental rate constants K fast and k slow. In the cases of L = fac( N)-5-dptma, mer( N)-i-dtma and trans( O)-aeida, both the k fast and the k slow increase with the increasing acidity of the solution. These results are incompatible with the current mechanism predicting one acidity dependent and the other acidity independent rate constants. Therefore, we have assumed additionally the deprotonation equilibrium from the intermediate complex cis-[Col(OH 2)(O 2COH] n+1 giving rise to an inert monodentate carbonato complex cis-[CoL(OH 2)(O 2CO)] n+ and derived from the acidity dependences of the k fast and the k slow the relevant equilibrium and rate constants. In the case of L = mer( N)-5-dptma, the k slow changes slightly with the acidity attaining a flat maximum around [H +] = 0.2 M, which we have interpreted by assuming an amphoteric character of the mer( N)-[Co(5-dptma)(OH 2)(O 2COH)] +.

Acetosolv pulping of pine wood. Kinetic modelling of lignin solubilization and condensation

Experiments of delignification of Pinus pinaster wood by acetic acid at atmospheric pressure showed that acetic acid concentration is a primary factor in the process and that high concentrations (90%) significantly improve the delignification degree. The kinetics of the process were satisfactorily explained by a model of consecutive first-order reactions corresponding to lignin solubilization followed by lignin condensation and reprecipitation onto the lignocellulosic matrix, hydrolysis of α-aryl ether bonds being the dominant reaction of the delignification process. The selectivity of the lignin dissolution was practically independent of operating conditions. When the degree of delignification reached a value around 90% the selectivity decreased considerably due to lignin condensation.

Microcrystalline-Cellulose Hydrolysis with Concentrated Sulphuric Acid

The effects of temperature (25-40°C), H,SO, concentration (31-70% (w/v)) and the acid/substrate relationship (1-5 cm3 of H,SO, per g-' of cellulose) on the solubilization rate of microcrystalline cellulose and on the glucose production rate have been analysed. The solubilization process was by determining reducing groups present in solution. For acid/substrate relationships of more than 1 cm3 g-' and H,SO, concentrations of greater than 62% (w/v), the acid promoted the total solubilization of the cellulose in the form of chains with a low degree of polymerization within 4 h. The solubilization demonstrated zero-order kinetics in which the specific rate and time of total solubilization are a function of the variables in operation. Glucose was produced according to a mechanism of two consecutive first-order pseudo-homogeneous reactions. The values of the kinetic constants k, and k, have been correlated with temperature, the H,SO, concentration and the acid/substrate relationship.

Application of the extended Kalman filter for analysis of a consecutive first-order reaction

The extended Kalman filter was applied to determine kinetic parameters of a first-order consecutive reaction. The parameters were obtained with small standard errors and good variance of fit, and agree with those obtained by using the conventional non-linear least square regression. Equations for the extended Kalman filter algorithm for the first-order consecutive reaction were derived and adopted in data analysis.

On the validity of the steady-state approximation in non-isothermal kinetics. Part II

The authors discuss the steady-state approximation for variable temperature and, implicitly in time, kinetic constants, within the framework of the kinetic analysis of a sequence of two first-order consecutive reactions with an active intermediate. It is thus demonstrated that the steady-state approximation as used in isothermal kinetics may also be applied in the non-isothermal kinetics.

Use of spreadsheets in the kinetic analysis of two consecutive first-order reactions

The present author developed an expression in a previous report that could be applied to the determination of the two rate constants, k 1 and k 2, for two consecutive irreversible first-order reactions (2CIFR). This expression was solved utilizing various computer methods and rate data (which could be obtained from conversion (α) versus time ( t) curves). Thus, BASICA (IBM), Lotus spreadsheets, and the Paradox data base were employed. The usual expressions developed for 2CIFR can be converted into dimensionless parameters and variables (DPV). One investigator (to be mentioned subsequently) developed a procedure whereby these DPV could be used to solve for k 1 and k 2 in 2CIFR. His method was rather tedious in that it involved plotting, superposing, and displacement measurements. In the present paper, a Lotus spreadsheet will be utilized to analyze 2CIFR for k-values. By means of this analysis, which utilizes dimensionless variables, these k-values will be obtainable in a matter of seconds once the experimental data is provided.

A kinetic study of iron release from Azotobacter vinelandii bacterial ferritin

The kinetics of iron release from Azotobacter vinelandii bacterial ferritin (AVBF) was measured by reduction of core iron with S 2O 4 2− followed by chelation of Fe 2+ with α, α-bipyridine (bipy). The rate was first order in AVBF and one half order in S 2O 4 2−, suggesting that SO 2 − is the active reductant formed by S 2O 4 2− = 2SO 2 −. With zero-order conditions for tithionie and bipy, two consecutive first-order iron release reactions differing by a factor of about 14 were observed with rate constants of 0.0263 and 0.00184 sec −1, respectively, at 25°C and pH 7.0. The faster reaction corresponded to the loss of 1433 iron atoms (91%) and the slower second reaction corresponded to loss of 145 (9%) of the original 1575 iron atoms present. The first reaction increased about twofold with pH variation between 6.5 and 8.0, whereas the second reaction was unchanged in the pH range 5.5–8. Both dramatically increased at pH 5.0. Methyl viologen increased the rate of both reactions about tenfold. The biphasic behavior for iron loss is interpreted as two different populations of iron atoms present in the core of AVBF, the first representing the bulk iron, and the second a group of unique iron atoms released last which may represent iron attached to the interior of the protein shell or iron associated with the heme groups. Kinetic stopped-flow measurements show that the heme is first reduced, followed by reduction of the core iron by reduced heme, suggesting an electron transfer role for heme in AVBF function.

Kinetics and mechanism for the binding of HCN to cytochrome c oxidase

The kinetics of cyanide binding to cytochrome c oxidase were systematically studied as a function of [HCN], [oxidase], pH, ionic strength, temperature, type and concentration of solubilizing detergent, and monomer-dimer content of oxidase. On the basis of these results a minimum reaction mechanism is proposed in which the spectrally visible rapid and slow cyanide binding reactions are two consecutive first-order reactions, not parallel reactions with different conformers of cytochrome c oxidase. The fast reaction (k'obs) follows saturation type kinetics to form an HCN complex that subsequently undergoes a slow reaction (k'obs). The fast k'obs reaction is independent of ionic strength but is strongly dependent upon pH. Two pK values were evaluated from the bell-shaped rate versus pH profile; one is due to an ionizable group on the protein (pKa = 7.45), while the other is that of HCN (pKHCN = 9.15). Therefore, oxidase is reactive toward HCN only when the group on the protein is unprotonated. The slow k'obs reaction is not a reaction of oxidase with either CN- or HCN; in fact, the product formed by the fast k'obs reaction, the oxidase-HCN complex, still undergoes the slow k" process even if all of the excess KCN is removed. The apparent rate constant of the slower phase (k"obs) is independent of all the variations done in this study, and it probably corresponds to either a slow conformational change in the protein or a change in ligand coordination at one of the metal centers after HCN binds to the bimetallic center of oxidase. Based upon the bell-shaped pH dependence of the fast phase and the pH independence of the slow phase, the mechanism also predicts that a single conformer of cytochrome c oxidase can exhibit either monophasic or biphasic cyanide binding kinetics depending upon the pH. At either very low or very high pH, the two rates become comparable in magnitude, which makes the reaction appear to be monophasic even though both reactions still occur. The amount of monomeric or dimeric oxidase only slightly affects the magnitude of k'obs and k"obs values, and both processes are clearly present in both types of oxidase.

Studies on thermokinetics of consecutive first-order reactions

The transformation equation for the thermokinetics of consecutive first-order reactions has been deduced, and a thermokinetic research method of irreversible consecutive first-order reactions, which can be used to determine the rate constants of two steps simultaneously, is proposed. The method was validated and its theoretical basis was verified by the experimental results.

Kinetic model for the biotransformation of tetrachloroethylene in groundwater

The biotransformation of tetrachloroethylene (PCE) to trichloroethylene (TCE) and then to cis-1,2-dichloroethylene (cis-DCE) under an anaerobic condition was studied using static soil microcosms. The kinetics of the biotransformation could be well approximated by the consecutive first-order reaction model, PCE →k1 TCE →k2 cis-DCE This model implied that the total amount of the above three compounds was always constant and was equal to the initial amount of PCE, even if the amount of each compound changed with time. Based on this stoichiometric relationship, two indices to characterize groundwater contamination with PCE were derived. The first was the total contamination level which was defined by the total molarity of the three compounds. The second was the degradation level which was defined by the total molar percentage of the products (TCE+DCE). These indices enabled us to evaluate the initial molarity of the pollutant PCE and the degree of the degradation. The kinetic theory also provided a useful rule such that the same time-concentration profile was obtained for the same ratio of the kinetic constants k2/k1, even if the scale of time changed. This rule enabled us to estimate the ratio of the kinetic constants, which suggested environmental fate of groundwater, from observed molarities of the three compounds.

Multivariate study of kinetic data for a two-step consecutive reaction using target factor analysis

Determination of reaction mechanism, rate constants and absorption spectra of reacting species are of primary interest in the investigation of a kinetic system. In this work, principal component analysis (PCA) and target factor analysis (TFA) were applied to deduce these kinetic parameters from synthetic multi-wavelength absorbance data of a two-step first-order consecutive reaction X 1 → k1 X 2 → k2 X 3. The Gaussian function was employed to generate absorption spectra of the constituting components. The effects of four variables, rate constant, peak height, resolution of absorption spectra and noise level, on the accuracy of the mathematical treatment were studied. PCA and TFA were found to be useful for investigating first-order consecutive reactions, even for noisy spectral data.

Determination of Initial Concentration of an Analyte by Kinetic Detection of the Intermediate Product in Consecutive First-Order Reactions Using an Extended Kalman Filter

Many analytical reagents react with analytes according to a rate law described by a consecutive first-order reaction mechanism, A [yields][sup k(1)] B [yields][sup k(2)] C, where a product formation step is followed by a product degradation step. In many cases, consecutive first-order reactions are used to determine the initial concentration of analyte A by kinetic detection of the intermediate product B. In this work, the factors that affect the determination of the initial concentration of analyte and the kinetic parameters for this class of reactions have been investigated by computer simulations using an extended Kalman filter. The flip-flop phenomenon exhibited by this kinetic model is discussed, and a unique approach for the determination of the initial concentration of analyte is proposed. Empirical and residual methods for obtaining initial estimates for the rate constants and the initial concentration from the kinetic data, based on the model for consecutive first-order reactions, the initial concentration of analyte, the mismatch between the measured time and the real time, the data density, the fitting range, and the initial estimate for the background signal have been evaluated by using synthetic data with Gaussian-distributed noise. 15 refs., 6 figs.

Pharmacodynamics of the Hydrolysis-Activation of the Cardioprotective Agent (+)-1,2-Bis(3,5-dioxopiperazinyl-1-yl)propane

The hydrolysis of the cardioprotective agent ICRF-187 [(+)-1,2-bis(3,5-dioxopiperazinyl-1-yl)propane] to its presumed active form under conditions of physiologic pH and temperature were followed by HPLC chromatography. Successful chromatography of all of the hydrolysis products required the use of EDTA in the aqueous eluant to prevent metals in the HPLC flow system from binding to the strongly metal ion-binding product ADR-925. The kinetics of the hydrolysis was followed to approximately 200 h. The ring closest to the methyl group on ICRF-187 was observed to open at about twice the rate of the other ring. This product accumulates in the reaction mixture not only because it is produced more quickly but also because it decays more slowly. ICRF-187 is lost from the reaction mixture with a half-life of 9.3 h, whereas the final hydrolysis product ADR-925 is produced with a half-life of 23.0 h. Rate constants for ring opening to one-ring and two-ring opened hydrolysis products were obtained with a reaction scheme that assumed parallel and consecutive first-order reactions for these steps.