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First-order Reaction (first-order + reaction)
Kinds of First-order Reaction Terms modified by First-order Reaction Selected AbstractsDevelopment and validation of a congener-specific photodegradation model for polybrominated diphenyl ethersENVIRONMENTAL TOXICOLOGY & CHEMISTRY, Issue 12 2008Xia Zeng Abstract With the phaseout of the manufacture of some polybrominated diphenyl ether (PBDE) formulations, namely penta-brominated diphenyl ether (BDE) and octa-BDE, and the continued use of the deca-BDE formulation, it is important to be able to predict the photodegradation of the more highly brominated congeners. A model was developed and validated to predict the products and their relative concentrations from the photodegradation of PBDEs. The enthalpies of formation of the 209 PBDE congeners were calculated, and the relative reaction rate constants were obtained. The predicted reaction rate constants for PBDEs show linear correlation with previous experimental results. Because of their large volume use, their presence in the environment, and/or importance in the photodegradation of the deca-BDE formulation, BDE-209, BDE-184, BDE-100, and BDE-99 were chosen for further ultraviolet photodegradation experiments in isooctane. The photodegradation model successfully predicted the products of the photochemical reactions of PBDEs in experimental studies. A gas chromatography retention time model for PBDEs was developed using a multiple linear regression analysis and, together with the photodegradation model and additional PBDE standards, provided a way to identify unknown products from PBDE photodegradation experiments. Based on the results of the photodegradation experiments, as well as the model predictions, it appears that the photodegradation of PBDEs is a first-order reaction and, further, that the rate-determining step is the stepwise loss of bromine. Our results suggest that, based on photodegradation, over time, BDE-99 will remain the most abundant penta-BDE, while BDE-49 and BDE-66 will increase greatly and will be comparable in abundance to BDE-47. [source] Degradation kinetics of ptaquiloside in soil and soil solutionENVIRONMENTAL TOXICOLOGY & CHEMISTRY, Issue 2 2008Rikke Gleerup Ovesen Abstract Ptaquiloside (PTA) is a carcinogenic norsesquiterpene glycoside produced in bracken (Pteridium aquilinum (L.) Kuhn), a widespread, aggressive weed. Transfer of PTA to soil and soil solution eventually may contaminate groundwater and surface water. Degradation rates of PTA were quantified in soil and soil solutions in sandy and clayey soils subjected to high natural PTA loads from bracken stands. Degradation kinetics in moist soil could be fitted with the sum of a fast and a slow first-order reaction; the fast reaction contributed 20 to 50% of the total degradation of PTA. The fast reaction was similar in all horizons, with the rate constant k1F ranging between 0.23 and 1.5/h. The slow degradation, with the rate constant k1S ranging between 0.00067 and 0.029/h, was more than twice as fast in topsoils compared to subsoils, which is attributable to higher microbial activity in topsoils. Experiments with sterile controls confirmed that nonmicrobial degradation processes constituted more than 90% of the fast degradation and 50% of the slow degradation. The lower nonmicrobial degradation rate observed in the clayey compared with the sandy soil is attributed to a stabilizing effect of PTA by clay silicates. Ptaquiloside appeared to be stable in all soil solutions, in which no degradation was observed within a period of 28 d, in strong contrast to previous studies of hydrolysis rates in artificial aqueous electrolytes. The present study predicts that the risk of PTA leaching is controlled mainly by the residence time of pore water in soil, soil microbial activity, and content of organic matter and clay silicates. [source] Kinetics and thermodynamic parameters of the thermal decomposition of imipramine hydrochloride and trimipramine maleateINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 4 2003Rafie H. Abu-Eittah Thermal decomposition of imipramine hydrochloride and trimipramine maleate has been investigated isothermally and nonisothermally. The kinetic parameters, namely the activation energy Ea and the Arrhenius preexponential term A, were calculated. Applying the theory of activated complex to the process of decomposition one calculated ,S,, ,H,, and ,G, for the reaction. The values of Ea as well as the thermodynamic functions did not vary significantly with temperature of the reaction whereas the preexponential term showed a significant dependence on the reaction temperature. Both imipramine hydrochloride and trimipramine maleate showed two main steps of decomposition. Each step proved to be a first-order reaction. The rate constant was calculated for each step, and the results were analyzed statistically. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 166,179, 2003 [source] Thermal stability and molecular interaction of polyurethane nanocomposites prepared by in situ polymerization with functionalized multiwalled carbon nanotubesJOURNAL OF APPLIED POLYMER SCIENCE, Issue 5 2008R. N. Jana Abstract Polyurethane (PU) nanocomposites were prepared through conventional and in situ methods with multiwalled carbon nanotubes (MWNTs) functionalized with poly(,-caprolactone). The thermal degradation and stability of PU,MWNT nanocomposites were investigated with nonisothermal thermogravimetry and were explained in terms of the interaction between MWNTs and PU molecules with Fourier transform infrared spectroscopy. The difference in thermal stability between the conventional and in situ nanocomposites was also compared. The thermal degradation of all the nanocomposite samples took place in two stages and followed a first-order reaction. The degradation temperature of the in situ nanocomposites was higher than that of the conventional nanocomposites with the same loading of MWNTs. The activation energy at 10% degradation and the half-life period were also higher in the in situ nanocomposites compared to the conventional nanocomposites. Such higher thermal stability of the in situ nanocomposites was ascribed to covalent bond formation between MWNTs and PU chains, which could result in better dispersion of MWNTs in the PU matrix for the in situ nanocomposites than for the conventional nanocomposites. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008 [source] Combustion of chlorinated hydrocarbons in catalyst-coated sintered metal fleece reactors,JOURNAL OF CHEMICAL TECHNOLOGY & BIOTECHNOLOGY, Issue 2-3 2003K Everaert Abstract Incinerators emit chlorinated hydrocarbons, such as polychlorinated benzenes (PCBz) and phenols (PCPh), polychlorinated biphenyls (PCB) and polychlorinated dibenzodioxins and furans (PCDD/F), as very dilute streams. High temperatures (>1000,°C) are required in traditional oxidizers. From an energy-saving perspective and to avoid de novo synthesis of PCDD/F, exhaust gas clean-up must be performed at low temperatures (250,350,°C). Catalytic combustion can be applied in this temperature range and different reactor layouts are used (eg monoliths, honeycomb). The present investigation uses a novel catalyst-coated sintered metal fleece. Thin metal fibers are sintered (non-woven) to fleece of various thickness, structure and porosity. V,Ti,W catalysts are examined. The paper will briefly review the catalyst coating method suitable to provide a structured fleece reactor with adequate characteristics. Experiments were carried out in the temperature range of 260,340,°C with various hydrocarbons injected in a carrier air stream. The experimental investigations demonstrated: (i) that the conversion of the hydrocarbons (volatile organic compounds, VOC) is independent of the oxygen concentration, corresponding to a zero-order dependence of the reaction rate; (ii) that the conversion of the hydrocarbons is a first-order reaction in the VOC; (iii) that the oxidation of the VOC proceeds to a greater extent with increasing temperature, with chlorine substitution enhancing the reactivity, and (iv) that the reaction rate constant follows an Arrhenius-dependence with activation energies between 37.3 and 58.4,kJ,mol,1. An assessment of the results leads to a model expression with kinetic reaction control. This model can be used in a scale-up strategy. © 2003 Society of Chemical Industry [source] Estimation of Kinetic Parameters for Nonisothermal Food ProcessesJOURNAL OF FOOD SCIENCE, Issue 3 2003K.D. Dolan ABSTRACT This work deals with the hypothesis that kinetic parameters for nonisothermal processes can be reliably obtained using a 1-step method. Parameters were estimated for 3 typical processes: (1) no residence time distribution (RTD), (2) first-order reaction with RTD, and (3) nth-order reaction with RTD. When nonisothermal processes were approximated isothermally, k and ,E were underestimated 80% to 3 orders of magnitude, and 30% to 1 order of magnitude, respectively. Reaction order was overestimated by up to 0.81. Therefore, accounting for thermal history and RTD is critical to obtain accurate estimates of kinetic parameters. The 1-step method was also used to solve for equivalent isothermal temperatures and times for an arbitrary nonisothermal process. [source] A bi-order kinetic model for poly(methyl methacrylate) decomposition in HNO3 using microwave irradiationAICHE JOURNAL, Issue 8 2009Chun-Chih Lin Abstract In this study, a novel bi-order model combined with zero- and first-order kinetics was proposed for the decomposition of PMMA (MW = 120,000 g/mol) in concentrated HNO3 by microwave irradiation. To develop and validate this model, Fourier Transform Infrared spectroscopy, scanning electron microscopy, fractional-life method, the gravimetric analysis and Newton's method were utilized. Rate constants, activation energies, the pre-exponential factors and the weight fractions (,) via main-chain scission for the decomposition at 423,453 K were derived from this model. The zero-order reaction was observed dominant at 423,443 K, while the first-order reaction dominated at 453 K and 473 K. The digestion efficiency increased as HNO3 was increased to >3 mL at 423 K,443 K. At 473 K, the digestion was almost 100% when HNO3 volume was >3 mL. The estimated , values increased with HNO3 volume at 423 and 443 K, but varied insignificantly at 453 and 473 K. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Room-Temperature Degradation of t -Zr(Pr)O2 in an Aqueous Suspension Revealed by Perturbed Angular CorrelationsJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 7 2008María C. Caracoche This paper deals with the phase stability of an aqueous suspension of tetragonal Zr0.9Pr0.1O2 (20 wt%/vol%) at room temperature as a function of the aging time. The suspension is investigated in situ using the highly localized Perturbed Angular Correlations technique. The results indicate that an almost fully reversible degradation process toward monoclinic zirconia takes place through a first-order reaction of rate constant k=0.7 day,1. Two successive diffusion mechanisms are observed that are interpreted as OH, ions' migration in the grain surface and then, as proton defects' diffusion into the bulk. [source] Study on the Kinetics for Enzymatic Degradation of a Natural Polysaccharide, Konjac GlucomannanMACROMOLECULAR SYMPOSIA, Issue 1 2004Guangji Li Abstract The enzymatic degradation of konjac glucomannan (KGM) was conducted using ,-mannanase from an alkalophilic Bacillus sp. in the aqueous medium (pH 9.0) at 30°C. The intrinsic viscosity ([,]), molecular weight (Mw) and molecular weight distribution (MWD) of the degraded KGM were measured. The mathematical relation between [,] and Mw, [,] = 5.06 × 10,4Mw0.754, was established. The kinetic analysis reveals a dependence of the rate constant (k) on the period of reaction and the initial substrate concentration (c0) over the range of substrate concentration (1.0,2.0%) used in this work. The results indicate that the enzymatic degradation of KGM is a complex reaction combining two reaction processes with different orders. In the initial phase of degradation k is inversely proportional to c0, which is characteristic of a zeroth-order reaction; while in the following phase k is independent of c0, implying the degradation follows a first-order reaction. The reactivity difference in breakable linkages of KGM, the action mechanism of an enzyme on KGM macromolecules, and the theory concerning the formation of an enzyme-substrate complex and ,substrate saturation' can be used to explain such a kinetic behavior. In addition, the enzymatic degradation of KGM was also carried out using the other enzymes like ,-mannanase from a Norcardioform actinomycetes, ,-glucanase Finizym and a compound enzyme Hemicell as a biocatalyst. By comparing and analyzing the degradation processes of KGM catalyzed by four different enzymes, it can be observed that there is a two-stage reaction with two distinct kinetic regimes over a certain range of degradation time for each of the degradation processes. These results are useful to realize controllable degradation of polysaccharides via an environmental benign process. [source] Relationship between sound pressure and reaction rate in sonochemical reactionTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 4 2009Yasuhiko Takuma Abstract Relationship between sound pressure in a sonochemical reactor and degradation rate of organic compounds, p -chlorophenol and p -nitrophenol, was investigated. Reaction rates were analyzed as first-order reaction. As a result, linear relationship was shown for each compound. Slope indicating the first reaction rate constant was remarkably affected by the position of the reaction flask. The sound pressure profile was measured and the relationship between the averaged pressure in a flask and the rate constant was shown. The relation was found to be remarkably different between the two. The threshold values were observed as 67kPa for p -chlorophenol and 22kPa for p -nitrophenol, respectively. From these results, it was shown that nature of compounds affects the dependency on sound pressure. On a étudié la relation entre les vitesses de dégradation des composés organiques, le p-chlorophénol et le p-nitrophénol, et la pression acoustique dans une réaction sonochimique. Les premières constantes de vitesse de réaction se sont avérées fortement influencée par la position de la cellule de réaction dans notre installation. Le profil de pression acoustique dans l'installation a été mesuré et la relation entre la pression moyennée dans la cellule et la constante de vitesse a été déterminée. On a trouvé que la relation était significativement différente entre les deux composés et que les valeurs seuils étaient de 100,kPa pour le p-chlorophénol. On a montré également que la nature des composés avait une influence sur leur dépendance à la pression acoustique. [source] Synergistic cellulose hydrolysis can be described in terms of fractal-like kineticsBIOTECHNOLOGY & BIOENGINEERING, Issue 2 2003Priit Väljamäe Abstract A fractal-like kinetics model was used to describe the synergistic hydrolysis of bacterial cellulose by Trichoderma reesei cellulases. The synergistic action of intact cellobiohydrolase Cel7A and endoglucanase Cel5A at low enzyme-to-substrate ratios showed an apparent substrate inhibition consistent with a case where two-dimensional (2-D) surface diffusion of the cellobiohydrolase is rate-limiting. The action of Cel7A core and Cel5A was instead consistent with a three-dimensional (3-D) diffusion-based mode of action. The synergistic action of intact Cel7A was far superior to that of the core at a high enzyme-to-substrate ratio, but this effect was gradually reduced at lower enzyme-to-substrate ratios. The apparent fractal kinetics exponent h obtained by nonlinear fit of hydrolysis data to the fractal-like kinetics analogue of a first-order reaction was a useful empirical parameter for assessing the rate retardation and its dependence on the reaction conditions. © 2003 Wiley Periodicals, Inc. Biotechnol Bioeng 84: 254,257, 2003. [source] CFD Modeling of a Bubble Column Reactor Carrying out a Consecutive A , B , C ReactionCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 4 2004J.M. van Baten Abstract In this paper, we develop a CFD model for describing a bubble column reactor for carrying out a consecutive first-order reaction sequence A , B , C. Three reactor configurations, all operating in the homogeneous bubbly regime, were investigated: (I) column diameter DT = 0.1 m, column height HT = 1.1 m, (II) DT = 0.1 m, HT = 2 m, and (III) DT = 1 m, HT = 5 m. Eulerian simulations were carried out for superficial gas velocities UG in the range of 0.005,0.04 m/s, assuming cylindrical axisymmetry. Additionally, for configurations I and III fully three-dimensional transient simulations were carried out for checking the assumption of cylindrical axisymmetry. For the 0.1 m diameter column (configuration I), 2-D axisymmetric and 3-D transient simulations yield nearly the same results for gas holdup ,G, centerline liquid velocity VL(0), conversion of A, ,A, and selectivity to B, SB. In sharp contrast, for the 1 m diameter column (configuration III), there are significant differences in the CFD predictions of ,G, VL(0), ,A, and SB using 2-D and 3-D simulations; the 2-D strategies tend to exaggerate VL(0), and underpredict ,G, ,A, and SB. The transient 3-D simulation results appear to be more realistic. The CFD simulation results for ,A and SB are also compared with a simple analytic model, often employed in practice, in which the gas phase is assumed to be in plug flow and the liquid phase is well mixed. For the smaller diameter columns (configurations I and II) the CFD simulation results for ,A are in excellent agreement with the analytic model, but for the larger diameter column the analytic model is somewhat optimistic. There are two reasons for this deviation. Firstly, the gas phase is not in perfect plug flow and secondly, the liquid phase is not perfectly mixed. The computational results obtained in this paper demonstrate the power of CFD for predicting the performance of bubble column reactors. Of particular use is the ability of CFD to describe scale effects. [source] Hard-modelled trilinear decomposition (HTD) for an enhanced kinetic multicomponent analysisJOURNAL OF CHEMOMETRICS, Issue 5 2002Yorck-Michael Neuhold Abstract We present a novel approach for kinetic, spectral and chromatographic resolution of trilinear data sets acquired from slow chemical reaction processes via repeated chromatographic analysis with diode array detection. The method is based on fitting rate constants of distinct chemical model reactions (hard-modelled, integrated rate laws) by a Newton,Gauss,Levenberg/Marquardt (NGL/M) optimization in combination with principal component analysis (PCA) and/or evolving factor analysis (EFA), both known as powerful methods from bilinear data analysis. We call our method hard-modelled trilinear decomposition (HTD). Compared with classical bilinear hard-modelled kinetic data analysis, the additional chromatographic resolution leads to two major advantages: (1) the differentiation of indistinguishable rate laws, as they can occur in consecutive first-order reactions; and (2) the circumvention of many problems due to rank deficiencies in the kinetic concentration profiles. In this paper we present the theoretical background of the algorithm and discuss selected chemical rate laws. Copyright © 2002 John Wiley & Sons, Ltd. [source] On the continuum approximation of large reaction mixturesAICHE JOURNAL, Issue 7 2010Teh C. Ho Abstract In analyzing a reaction mixture of very many components, treating the mixture as a continuum can produce results of generality. In many practical situations (e.g., hydrodesulfurization), it is highly desirable to predict the overall behavior of the mixture at large times (high conversions) with minimum information on the mixture property. For irreversible first-order reactions in a plug-flow reactor, it was previously shown that the continuum approximation cannot be valid at arbitrarily large times. This work is an investigation of the validity of the approximation for mixtures with complex kinetics. It is found that the approximation can be conditionally or universally valid, depending on kinetics, reactor type, pore diffusion, and mixture properties. The validity conditions for a variety of situations, nontrivial as they may seem, take a power-law form. Backmixing and pore diffusion widen the range of validity. The underlying physics and some dichotomies/subtleties are discussed. The results are applied to catalytic hydroprocessing in petroleum refining. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Optimal bimodal pore networks for heterogeneous catalysisAICHE JOURNAL, Issue 4 2004Stefan Gheorghiu Abstract A practical problem in the rational design of a heterogeneous catalyst is to optimize its structure at all scales. By optimizing the large-pore network of a bimodal porous catalyst with a given nanoporosity (for example, zeolite or mesoporous catalyst) for the yield of diffusion-limited first-order reactions, it is found that catalysts typically benefit from a hierarchical pore network with a broad pore-size distribution. When comparing the performance of the optimal structures to that of self-similar, fractal-like pore hierarchies, it is found that the latter can be made to have the same effectiveness factor as the optimal ones, suggesting that fractal-like catalysts operate very near optimality, even if their structure is considerably different from that of the true optima. This is useful, because fractal-like structures have the advantage of being organized in a modular, natural way, potentially easy to reproduce by templating. © 2004 American Institute of Chemical Engineers AIChE J, 50: 812,820, 2004 [source] Ring-opening polymerization of substituted ,-caprolactones with a chiral (salen) AlOiPr complexJOURNAL OF POLYMER SCIENCE (IN TWO SECTIONS), Issue 3 2007Mark R. Ten Breteler Abstract The ring-opening polymerization (ROP) of ,-caprolactone (,-CL), 4-methyl-,-caprolactone (4-MeCL), and 6-methyl-,-caprolactone (6-MeCL) with a single-site chiral initiator, R,R,-(salen) aluminum isopropoxide (R,R,-[1]), was investigated. The kinetic data for the ROP of the three monomers at 90° in toluene corresponded to first-order reactions in the monomer and propagation rate constants of k,-CL > k4-MeCL , k6-MeCL. A notable stereoselectivity with a preference for the R -enantiomer was observed in the ROP of 6-MeCL with R,R,-[1], whereas for 4-MeCL, no stereoselectivity was found. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 429,436, 2007. [source] Reaction kinetics of graft copolymerization and thermochemical studies of the degradation of poly(vinyl alcohol) graft copolymerPOLYMER INTERNATIONAL, Issue 3 2001Yassin A Aggour Abstract Poly(vinyl alcohol) (PVA) is a water-soluble and biomedical polymer. 2-Acrylamido-2-methyl-1-propanesulfonic acid was grafted onto PVA using ammonium persulfate as radical initiator. The influences of synthesis conditions such as temperature, concentrations of initiator, PVA and monomer were investigated. Both the initial rate of grafting and the final percentage of grafting were increased by an increase in reaction temperature. The reaction kinetics were studied to determine the rate constants of the first-order reactions. An activation energy of 16.3,kJ,mol,1 was found for the grafting reaction. The graft copolymers were characterized by IR and intrinsic viscosity measurements. A proposed mechanism of the grafting reaction is discussed. Kinetics of the thermal degradation were studied using a thermogravimetric method and the order of thermal stabilities are given. The apparent activation thermodynamic parameters, Ea, ,H*, ,S* and ,G* were determined and correlated to the thermal stabilities of the homo- and grafted polymers. © 2001 Society of Chemical Industry [source] Modeling of Product Removal during Enzymatic Conversions by Using Affinity MoleculesBIOTECHNOLOGY PROGRESS, Issue 6 2007Daniël G. R. Halsema The feasibility of using magnetic particles for in-line product isolation during enzymatic conversion was studied. A comparison was made between a process based on magnetic particles and a conventional adsorption column. The enzymatic reaction was described by two consecutive first-order reactions (synthesis and subsequent hydrolysis), while the adsorption of substrate and product was described by multicomponent Langmuir isotherms. The yield as well as synthesis/hydrolysis ratio were calculated for various system characteristics. The results show that magnetic particles are very effective when the affinity with the particles is specific and for enzymatic conversions involving low ratios of the rate of synthesis versus the rate of hydrolysis. For slow conversions and for low specific affinity molecules column separations are more appropriate. [source] Effect of Amino Acids on Acrylamide Formation and Elimination KineticsBIOTECHNOLOGY PROGRESS, Issue 5 2005Wendie L. Claeys The effect of amino acids other than asparagine on acrylamide (AA) formation/elimination kinetics was studied in an asparagine-glucose model system (0.01 M, pH 6) heated at temperatures between 140 and 200 °C. Addition of cysteine or lysine to the model significantly lowered the AA yield, whereas addition of glutamine had a strong promoting effect and of alanine a rather neutral effect on the AA formation. This was also reflected by AA formation/elimination kinetics, which for all model systems studied could be modeled by two consecutive first-order reactions. The ratio of the elimination to the formation rate constant increased from the systems to which glutamine or alanine was added, over the control model system, to the model systems that contained lysine or cysteine. [source] Kinetic Modeling of Breweryapos;s Spent Grain AutohydrolysisBIOTECHNOLOGY PROGRESS, Issue 1 2005Florbela Carvalheiro Isothermal autohydrolysis treatments of breweryapos;s spent grain were used as a method for hemicellulose solubilization and xylo-oligosaccharides production. The time course of the concentrations of residual hemicelluloses (made up of xylan and arabinan) and reaction products were determined in experiments carried out at temperatures in the range from 150 to 190 °C using liquid-to-solid ratios of 8 and 10 g/g. To model the experimental findings concerning to breweryapos;s spent grain autohydrolysis several kinetic models based on sequential pseudo-homogeneous first-order reactions were tested. Xylan and arabinan were assumed to yield oligosaccharides, monosaccharides (xylose or arabinose), furfural, and other decomposition products in consecutive reaction steps. The models proposed provide a satisfactory interpretation of the hydrolytic conversion of xylan and arabinan. An additional model merging the two proposed models for xylan and arabinan degradation assuming that furfural was formed from both pentoses was developed and the results obtained are discussed. The dependence of the calculated kinetic coefficients on temperature was established using Arrhenius-type equations. [source] | ||||||||||||||||