Consecutive First-order Reactions Research Articles

Simultaneous extraction and stripping of uranium ions via multi-dropped liquid membrane system

An investigation on the separation of U(VI) from aqueous solutions via a multi dropped liquid membrane (MDLM) and its model is presented. A new method that is more advantageous than other liquid membrane techniques is applied. Di(2-ethylhexyl) phosphoric acid was used as a highly selective carrier for the transport of U(VI) ions through the MDLM. Maximum percentages of U(VI) extraction and stripping achieved were 98.9 % using 1.459 × 10–3 M D2EHPA as the extractant, 1 M NH4HCO3 as the stripping solution. The influences of pH and temperature on donor and acceptor phases, the influence of carrier phase concentrations and membrane’s flow velocity were investigated. For the description of relationships of U(VI) concentration in particular phases with time, a model based on the assumption of consecutive first-order reactions was proposed. The kinetic parameters (k1, k2, Rmmax, tmax, Jdmax, Jamax) were calculated for the interface reactions assuming two consecutive, irreversible first-order reactions. The activation energy value was calculated as 10.2 kcal mol-1 for extraction. The value of calculated activation energy indicates that the process is chemically controlled by U(VI) ions. The experiments have demonstrated that D2EHPA derivative is a good carrier for U(VI) transport through MDLM in the study.

Bulk liquid pertraction of NaCl from aqueous solution using carrier-mediated transport

In the present work, removal of NaCl using the bulk liquid membrane (BLM) technique has been investigated, using a simple apparatus for conducting the experiments. Variables investigated were volume ratio of donor phase (DP) to receptor phase (RP), presence of sequestering agent (SA) in RP, type of organic liquid membrane (LM), quantity of mobile carrier (MC) in the LM. Stirring speed and volume of LM were kept constant at 100 rpm and 130 ml, respectively. The mass transfer of NaCl was analysed based on kinetic laws of two consecutive irreversible first-order reactions, and kinetic parameters (k1d, k2m, k2r, , tmax, , and ) for the transport of NaCl were investigated. The values obtained demonstrate that the process is diffusionally controlled. Results indicate that the membrane entrance and exit rate constants (k1, k2) increase with decreasing DP:RP ratio and with decrease in quantity of MC, and quantity of SA, and the presence of dichloroethane (DCE) is preferred to chloroform (CF) as LM.

Effect of peclet parameters of reacting components on their concentrations in consecutive reaction

The method of using two indicators with different molecular diffusion coefficients has been suggested, which allows one to estimate the dependence of the structure of flows and Peclet number of reacting components vs. the hydrodynamic mode of their flow in reactors. The mathematical model has been considered at various Peclet parameters on reacting components for the first-order consecutive reaction with new boundary conditions and the results of calculations have been compared with a standard one-parameter model.

Study of Co-pyrolysis Characteristics of Lignite and Rice Husk in a TGA and a Fixed-Bed Reactor

Abstract Co-pyrolysis characteristics of lignite and rice husk blend were determined in TGA and a fixed-bed reactor. From TGA results, the weight loss rate of lignite and rice husk blend increases at 250–400°C. In a fixed bed at programmed temperature condition, the synergistic effect to produce more volatiles is appeared at 500–700°C, and the maximum synergistic effect exhibits with a rice husk blending ratio of 0.8. The gas yield of co-pyrolysis of lignite and rice husk blend was higher than that of the sum of lignite and rice husk individually. The kinetic studies were performed according to Coats–Redfern method for first-order reaction. It was found that the pyrolysis process of lignite and rice husk could be described by one first-order reaction and two consecutive first-order reactions, respectively. However, for lignite and rice blends, this process can be described by three consecutive first-order reactions. The estimated kinetic parameters, viz., activation energies and pre-exponential factors for lignite, rice husk and their blends, were found to be in the range of 63.5–477.8 kJ/mol and 1.4 × 103–6.5 × 1047 min−1, respectively.

Combining artificial neural networks and experimental design to prediction of kinetic rate constants

A “soft-modelling” computational approach of artificial neural networks (ANNs) combined with experimental design (ED) has been applied successfully in Chemical Kinetics for the prediction of kinetic rate constants. The system studied comprises two consecutive first-order reactions and the kinetic data were computed determining the values of both rate constants. The kinetic curves were distributed according to an ED, and the central star composite experimental design (CSCED) was chosen as the most appropriate. Computational treatments were performed on synthetic data endowed with noise, after which they were applied to the data measured in an experimental reaction between carbonyl cyanide 3-clorophenylhydrazone with 2-mercaptoethanol, computing the experimental kinetic data of absorbance acquired at 3 wavelengths. The combined ANN and ED approach applied in chemical kinetics proved to be robust and of general applicability and has the advantage of being a “soft-modelling” method such that it was not necessary to solve the system of ordinary differential equations to determine the explicit mathematical function between the data and the kinetic rate constants. Additionally, upon using the CSCED experimental design, it was possible to substantially reduce the number of experiments.

Reduction of chemical reaction networks through delay distributions

Accurate modelling and simulation of dynamic cellular events require two main ingredients: an adequate description of key chemical reactions and simulation of such chemical events in reasonable time spans. Quite logically, posing the right model is a crucial step for any endeavour in Computational Biology. However, more often than not, it is the associated computational costs which actually limit our capabilities of representing complex cellular behaviour. In this paper, we propose a methodology aimed at representing chains of chemical reactions by much simpler, reduced models. The abridgement is achieved by generation of model-specific delay distribution functions, consecutively fed to a delay stochastic simulation algorithm. We show how such delay distributions can be analytically described whenever the system is solely composed of consecutive first-order reactions, with or without additional "backward" bypass reactions, yielding an exact reduction. For models including other types of monomolecular reactions (constitutive synthesis, degradation, or "forward" bypass reactions), we discuss why one must adopt a numerical approach for its accurate stochastic representation, and propose two alternatives for this. In these cases, the accuracy depends on the respective numerical sample size. Our model reduction methodology yields significantly lower computational costs while retaining accuracy. Quite naturally, computational costs increase alongside network size and separation of time scales. Thus, we expect our model reduction methodologies to significantly decrease computational costs in these instances. We anticipate the use of delays in model reduction will greatly alleviate some of the current restrictions in simulating large sets of chemical reactions, largely applicable in pharmaceutical and biological research.

Efficient hydridoirida-β-diketone-catalyzed hydrolysis of ammonia- or amine-boranes for hydrogen generation in air

The dihydridoirida-β-diketone [IrH2{(PPh2(o-C6H4CO))2H}] (2) has been used as a homogeneous catalyst for the hydrolysis of ammonia- or amine-boranes to generate up to 3 equivalents of hydrogen in the presence of air. When using 0.5 mol% loading of 2, dimethylamine-borane is hydrolysed completely within 8 min at 30 °C and maintains its activity in consecutive runs. Ammonia-borane or tert-butylamine-borane is hydrolysed completely within 32 or 25 min respectively. Triethylamine-borane fails to be hydrolysed. Kinetic studies suggest a sequence of two consecutive first-order reactions, in which an intermediate builds up and finally falls, with the first step being the rate controlling step. ΔH1(‡) are in the range 65-85 kJ mol(-1) and negative values of ΔS1(‡) are obtained. A multinuclear NMR study of the catalyzed reaction shows the formation of a resting state (A) of the active catalyst proposed to be of the hydridodiacyl type [IrH(PPh2(o-C6H4CO))2(solvent)] with a hydride trans to the acyl group. In the absence of substrate a dormant species (B) is formed. By the reaction of hydridoirida-β-diketones with ammonia, the hydridoirida-β-ketoimine [IrHCl{(PPh2(o-C6H4CO))(PPh2(o-C6H4CNH))H}] (3) and the hydridobis(acylphosphane)aminoiridium(III) complex [IrH(PPh2(o-C6H4CO))2(NH3)] (4), with a hydride trans to phosphane, are formed. Aromatic amines such as aniline or anisidines afford cationic [IrH{(PPh2(o-C6H4CO))2H}(C6H4RNH2)]ClO4 (R = H (6); p-MeO (7); o-MeO (8)) hydridoirida-β-diketones with a coordinated amine group trans to the hydride. The dormant species B is proposed to be of the hydridobis(acylphosphine)aminoiridium(III) type with a hydride trans to the amine group.

Folding and dimerization kinetics of bone morphogenetic protein-2, a member of the transforming growth factor-β family

The kinetics of folding and dimerization of bone morphogenetic protein-2 (BMP-2), a disulfide-connected, homodimeric cystine-knot protein and a member of the transforming growth factor-β superfamily, was analyzed under a variety of different conditions. Refolding and dimerization of BMP-2 were extremely slow under all conditions studied, and could be described by consecutive first-order reactions involving at least one long-lived intermediate. The rate constants vary from ~ 0.2 × 10(-5) to ~ 3.5 × 10(-5) s(-1), and were strongly dependent on temperature, redox conditions, and the presence of stabilizing or destabilizing ions. In particular, the combined impact of ionic strength and redox conditions on the rates indicates that electrostatic interactions control thiol-disulfide exchange reactions on the path from the unfolded and reduced monomers to the disulfide-connected growth factor in a rate-determining way.

Application of multivariate curve resolution-alternating least squares (MCR-ALS) for resolving pyrogallol autoxidation in weakly alkaline aqueous solutions

Abstract Multivariate curve resolution — alternating least squares (MCR-ALS) has been applied to data collected from UV/Vis spectrophotometric analysis of the autoxidation process of pyrogallol in weakly alkaline aqueous solutions. The MCR-ALS analysis was able to explain the autoxidation kinetics of pyrogallol at pH 7.4 and 8.0, allowing deduction of the pure spectra and concentration changes of different species present throughout the entire process. The autoxidation process at pH 7.4 was found to follow a first-order reaction model, with formation of purpurogallin as the sole and terminal product. Changing the pH to 8.0 not only accelerated autoxidation of pyrogallol to purpurogallin but also introduced a further autoxidation of purpurogallin. At pH 8.0 the process fits a model of two consecutive first-order reactions. The first step is formation of purpurogallin, which reacts in a further autoxidation to form a yellow colored substance, most probably purpurogallin polymer.

Hydrolysis Kinetics of Straw Biomass Catalyzed by Diluted Sulphuric Acid in the Present of Fe<sup>2+</sup>

This study focuses on kinetics of straw hydrolysis using sulfuric acid catalyst to produce fermentable sugars. The result shows the degradation of sugars is encountered during the hydrolysis of straw biomass. A consecutive first-order reactions kinetic model is proposed and the kinetic model well agrees with the experimental data. It turns out that rate of sugar formation and degradation is small at lower experimental temperature. The reactions rates constant k1 including the formation of sugar begins to increase rapidly when the Fe2+concentration increases from 0.125 to 0.500molL-1. However, the rate constant k2 relevant with the degradation of sugar varies unsensibly below 0.375molL-1 Fe2+and it is accelerated as the Fe2+concentration increases to 0.500molL-1. Thus the optimum yield is obtained at 0.375molL-1 Fe2+concentration.

The acetylation of glycerol over amberlyst-15: Kinetic and product distribution

Glycerol is a byproduct of biodiesel synthesis and it can be converted into high value-added bioadditives. The heterogeneous acetylation of glycerol with acetic acid was conducted over Amberlyst 15 using a slurry reactor. The influence of reaction conditions such as the temperature and the molar ratio of acetic acid to glycerol (AA:G) on the product distribution was investigated. The results indicated that glycerol acetylation was a consecutive reaction. The equilibrium time for the product distribution shortened with decreasing AA:G molar ratio but with increasing temperature. It was also shown that the equilibrium conversion of glycerol as well as the combined yield of di- and triacetylated glycerols (DAG+TAG) increased with the AA:G molar ratio. Moreover, the AA:G molar ratio was the more influential factor on the yield of DAG+TAG than the temperature, although increasing the temperature might also have a positive influence on this yield. Reasonable yields of mono-, di- and triacetylated glycerols could be obtained by varying the reaction time, the AA:G molar ratio, and the temperature. The kinetic model based on homogeneous first-order consecutive reaction showed that the overall apparent rate constants (k1, k2, and k3) as well as its corresponding activation energy (E1, E2, and E3) were found to be;k1=2.07×106β0.274exp−6890T,E1=57.26kJ/molk2=18.66β1.82exp−3830T,E2=31.87kJ/molk3=1.16β−0.474exp−1670T,E3=13.90kJ/mol

Nonclonal growth of preneoplastic cells positive for glutathione S-transferase P-form in the rat liver

We investigated the process of induction of preneoplastic cells positive for glutathione S-transferase P-form (GST-P) in the rat liver. AAF (2-Acetylaminofluorene) mixed with normal rat chow at high concentration (0.04%) induced 517 000 ± 86,000 GST-P(+) single hepatocytes/g liver after 2 weeks followed by induction of a few foci and nodules after 4-6 weeks. Overproduction of GST-P(+) single hepatocytes was dose- and time-dependent, and the induction kinetics were typical of first-order consecutive reaction, by which induction of the positive cells was nongenetic. Quantitative analysis indicated that the estimated numbers of cells in foci and nodules at 4-6 weeks after exposure to AAF ranged from 2.7 × 10(4) (2(14.7)) to 3.6 × 10(6) (2(21.7)) cells, and 2.0 × 10(4) (2(14.3)) to 2.7 × 10(6) (2(21.4)) cells, respectively, when analyzed by using two equations. According to the initiated cell theory of Farber, foci and nodules are formed through sequential cell division of 14 to 21-times or more within a short time period. The rapid growth exceeded the rate of cell division, indicating that the growth of preneoplastic cells is based on a nonclonal penetration mechanism.

Self-oscillations in a flow ideal mixing reactor in the region of multiplicity of stationary equilibrium states: a consecutive reaction

A model of a flow ideal mixing reactor for a consecutive two-stage exothermic first-order reaction was considered. The presence of a region of multiplicity of stationary states was established. This multiplicity region can contain regions of three and five stationary states; the region of five states always appears inside the region of three stationary states. Changes in the type of stationary state stability in each of these regions are analyzed. Numerical calculations of phase trajectories in the regions of stationary state stability and instability were performed. A mechanism of the creation of a stable limiting cycle was suggested for the case of three stationary states.

Transport and Fate of Nitrogen-Containing Compounds in Gas-Phase Biofilters: A Swing Test to Mitigate Ammonia

This work carried out a three-month experiment to study the transport, transformation, and fate of nitrogen (N) in two gas-phase ammonia mitigation biofilters using agricultural products (a mixture of wood chips and compost) as the packing media. Two nitrogen enriching steps and one nitrogen depleting step were included as a swing test. In the first nitrogen enriching step, a high ammonia inlet concentration (~70 ppm) was applied. The ammonia removal efficiencies reached 94%, and 73.5% to 86.6% of N-NH3 was transformed into NH4+-N, NO2--N, or NO3--N. The nitrogen depleting step partially cleaned nitrogen compounds with limited disturbance to the media and restored ammonia removal efficiency for a short time. The second nitrogen enriching step used a lower (40 ppm) ammonia inlet concentration. Only 33.4% to 46.2% of NH3-N was transformed into NH4+-N, NO2--N, or NO3--N in the media, and the ammonia removal efficiency fell quickly after ten days. The pH values in the biofilter media were high and changed only slightly during the test (8.5 to 8.2). The free ammonia concentration reached 784 mg L-1 in the media moisture. The nitrogen mass balance analysis showed that the NH4+-N, NO2--N, and NO3--N accumulated in the media accounted for 50% to 100% of the nitrogen captured from the inlet gas. The nitrification process was modeled as consecutive first-order reactions. The kinetic time constants of the two first-order reactions decreased with time and with accumulated nitrogen in the media, suggesting a decline of the nitrogen transformation rates. One very likely reason that caused the decrease of ammonia removal efficiency and kinetic time constants is the accumulated free ammonium in the biofilter media.

The structures of the dicationic tetranitrosyl iron complex with cysteamine [Fe2S2(CH2CH2NH3)2(NO)4]2+ and its decomposition products in protic media: an experimental and theoretical study

Decomposition products of [Fe2S2(CH2CH2NH3)2(NO)4]SO4·2.5H2O (1′) were studied by electrochemistry and mass spectrometry. The structures of the dicationic tetranitrosyl iron complex with cysteamine of the composition [Fe2S2(CH2CH2NH3)2(NO)4]2+ (1) and possible products of its decomposition and NO replacement by an aqua ligand were studied by quantum chemical methods at the density functional theory level. Taking into account the solvation effects, the replacement of the nitrosyl ligand in dication 1 by an aqua ligand was found to be less favorable in aqueous solution than in the gas phase. The pK value was calculated for the proton abstraction from the NH3 group of compound 1 (7.2), and the removal of NO from the deprotonated form of the complex was found to be much easier. This result is consistent with the experimental data on an increase in the rate of NO formation in aqueous solutions of 1 with increasing pH from 6 to 8 assuming that the increase in pH is accompanied by an increase in the percentage of the less stable deprotonated form of the complex and that OH− does not participate in the elementary step of NO formation. The kinetic curves of NO formation are well described by a two-step scheme of consecutive first-order reactions of the NO formation and consumption. In the gas phase, dication 1 was found to be unstable to decomposition into two mononuclear cationic dinitrosyl iron complexes with cysteamine. This result is consistent with the fact that these cations are observed in the electrospray ionization mass spectrometric experiment. The major peak in the mass spectra is associated with the [Fe2S2(CH2CH2NH3)2(NO)4 − H]+ ion. As follows from the calculations, this is due to the deprotonation of the dication as it gets rid of the hydration shell, because even the dimer of water molecules is more basic than dication 1.

Kinetics of methoxy-NNO-Azoxymethane hydrolysis in strong acids

The kinetics of methoxy-NNO-azoxymethane (I) hydrolysis in concentrated solutions of strong acids (HBr, HCl, HClO4, and H2SO4) has been investigated by a manometric method. The gas evolution rate is described by the equation corresponding to two consecutive first-order reactions, with the rate constant of the second reaction considerably exceeding the rate constant of the first reaction, i.e., k 2 {ie17-1} k 1. The temperature dependences of k 1 (s−1) in 47.59% HBr in the temperature range from 60 to 90°C and in 64.16% H2SO4 between 80 and 130°C are described by Arrhenius equations with IogA= 12.7 ± 1.5 and 13.6 ± 1.4 and E a = 115 ± 10 and 137 ± 10 kJ/mol, respectively. The parameters of the Arrhenius equation for the rate constant k 2 for the reaction in 64.16% H2SO4 between 80 and 130°C are IogA= 9.1 ± 2.5 and E a = 91 ± 18 kJ/mol. An analysis of the UV spectra of compound I in concentrated H2SO4 shows that I is a weak base \( (pK_{BH^ + } \approx - 6) \). The rate-determining step of the hydrolysis of I is the attack of the nucleophile on the carbon atom of the MeO group of the protonated molecule of I. The resulting methyldiazene dioxide decomposes via a complicated mechanism to evolve N2, NO, and N2O. The pseudo-first-order rate constant k 1 of the reaction at 80°C depends strongly on the acid concentration and on the type of nucleophile (Br−, Cl−, or H2O). The relationship between k 1 and the rate constant k of the bimolecular nucleophilic substitution reaction (SN2) is given by the linear equation log\( [k_1 /(C_H + C_{Nu} )] = m^ \ne m*X_0 + \log (k/K_{BH^ + } ) \), where \( C_{H^ + } \) and C Nu are the concentrations of H+ and nucleophile, respectively; X 0 is the excess acidity; and m ≠ and m* are coefficients. The Swain-Scott equation log\( (k_{Nu} /k_{H_2 O} ) = ns \), where n is the nucleophilicity factor and s is the substrate constant (s = 0.72), is applicable to the rate constants k of the SN2 reactions of the protonated molecule of I with Br−, Cl−, and H2O.

Kinetic studies of nitrofurazone photodegradation by multivariate curve resolution applied to UV-spectral data

This work aims at describing the kinetic model of nitrofurazone photodegradation by a novel chemometric technique, hybrid hard–soft multivariate curve resolution (HS-MCR). The study was applied to UV-spectral data from the photolysis of nitrofurazone solutions at different concentrations and exposed under varying illuminance power. The HS-MCR method was able to elucidate the kinetics of the photodegradation process and to determine the rate constants, and estimating at the same time the pure spectra of the degradation products. Exposure to light of the drug gave a first rapid isomerization to the syn-form that in turn underwent degradation furnishing a mixture of yellow-red products. The photodegradation process could be explained with a kinetic model based on three consecutive first-order reactions (A > B, B > C and C > D). These results were confirmed by application of the MCR procedure to the analysis of the data obtained from HPLC-DAD analysis of the nitrofurazone samples at different reaction times. The kinetic model was observed to be dependent on experimental conditions. The samples at higher concentrations showed rate constants lower than the diluted samples, whereas an increase of the rate of all degradation processes was observed when the light power also increased. This work shows the power of the hybrid hard- and soft-multivariate curve resolution as a method to deeply study degradation processes of photolabile drugs.

Kinetic Study of Hydrodechlorination of Chlorobiphenyl with Polymer-Stabilized Palladium Nanoparticles in Supercritical Carbon Dioxide

Hydrodechlorination of 4-chlorobiphenyl in supercritical fluid carbon dioxide (SF-CO(2)) catalyzed by palladium nanoparticles stabilized in high-density polyethylene beads proceeds by consecutive reactions to the final product bicyclohexyl. Each step of the reaction sequence, that is, 4-chlorobiphenyl --> biphenyl --> cyclohexylbenzene --> bicyclohexyl, follows pseudo-first-order kinetics. Arrhenius parameters of each reaction step were determined separately in SF-CO(2) by in situ absorption spectroscopy using a high-pressure fiber-optic cell. A simulation of product distributions using the first-order consecutive reaction equations was performed and compared with the experimental results obtained by GC/MS analysis of the 4-chlorobiphenyl reaction system. The differences are explained in terms of adsorption/desorption behavior of the intermediates on the catalytic metal surface with respect to the stereostructures of the molecules generated by a molecular mechanics method.

Efficient hydrolysis of chitosan in ionic liquids

Effective hydrolysis of chitosan, the N-deacetylated product of chitin, remains challenging. Here, we report acid-promoted hydrolysis of chitosan in imidazolium based ionic liquids with good total reducing sugars (TRS) yield under mild conditions. TRS yield reached over 60% in the presence of about 6.0 wt% concentrated hydrochloric acid at 100 °C within 7 h. Kinetic modeling of a typical experimental data set suggested that the hydrolysis most likely followed a consecutive first-order reaction sequence, where k 1 and k 2, the rate constants for TRS formation and degradation, were determined to be 0.01372 and 0.00015 min −1, respectively. Our method may be useful to explore new applications of natural chitin resources.

Process intensification using a two-phase system and micromixing for consecutive and reversible reactions

This study aimed to find reaction conditions that improve the yield of target intermediate products, using a two-phase system and a microspace for first-order consecutive and reversible reactions. As a result, the yield of target products with a two-phase system can be surpassed by that of a single-phase system through selecting the organic phase such that the partition coefficient of the raw material to the aqueous phase is large, and that of the target product to the organic phase is also large. In addition, the volume ratio of two phases and the liquid–liquid interfacial area are also important factors for improving the target product yield. In a microspace, the microfluid segments can be designed both arbitrarily and precisely, and thus it is possible to control the interfacial area and mass transfer rates accurately. Utilization of a microspace can play a significant role in intensifying a two-phase system. © 2009 American Institute of Chemical Engineers AIChE J, 2009