First-order Reversible Reaction Research Articles

Kinetic modeling of glucose and fructose dissolution in 2-methyl 2-butanol

With the objective of developing simulation models for sugar bioconversion processes in non-aqueous media, the present study investigated the dissolution kinetics of glucose and fructose in 2-methyl 2-butanol at temperatures between 20 °C and 80 °C. For both sugars a two-phase dissolution process was observed, characterized by an initially fast dissolution lasting a few minutes, followed by a much slower dissolution phase extending up to 24 h. The experimental results are described by a combined sugar dissolution and mutarotation kinetic model that considers the dissolution of the sugar anomeric form present in the solid particles, namely α- d-glucopyranose and ß- d-fructopyranose, and its subsequent mutarotation in solution. The initial dissolution step is assumed limited by the solute transport from the surface to the bulk solution, and the corresponding sugar transport coefficient evaluated from established mass transport correlations. The second slower dissolution phase is solely controlled by the sugar mutarotation rate, and modeled as a first-order reversible reaction. The determined values of the mutarotation rate and equilibrium constants can be related to the solution temperature by an Arrhenius and Van’t Hoff relationship, respectively.

Stability of [6]-gingerol and [6]-shogaol in simulated gastric and intestinal fluids

The degradation kinetics of [6]-gingerol and [6]-shogaol were investigated in simulated gastric (pH 1) and intestinal (pH 7.4) fluids at 37 °C. Degradation products were quantitatively determined by HPLC (Lichrospher 60 RP select B column, 5 μm, 125 mm × 4 mm; mobile phase: methanol–water–acetic acid (60:39:1 v/v); flow rate: 0.6 ml/min; detection UV: 280 nm). In simulated gastric fluid (SGF) [6]-gingerol and [6]-shogaol underwent first-order reversible dehydration and hydration reactions to form [6]-shogaol and [6]-gingerol, respectively. The degradation was catalyzed by hydrogen ions and reached equilibrium at approximately 200 h. In simulated intestinal fluid (SIF) both [6]-gingerol and [6]-shogaol showed insignificant interconversion between one another. Addition of amino acids glycine, 3-amino propionic acid (β-alanine) and γ-amino butyric acid (GABA), and ammonium acetate at a range of concentrations of 0.05–0.5 mM had no effect on the rate of degradation of [6]-shogaol in SGF and 0.1 M HCl solution. However, at exceedingly high concentration (0.5 M) of ammonium acetate and glycine, significant amounts of [6]-shogaol ammonia and glycine adducts were detected. The degradation profile of [6]-gingerol and [6]-shogaol under simulated physiological conditions reported in this study will provide insight into the stability of these compounds when administered orally.

The stability of the amorphous form of cefuroxime axetil in solid state

The stability of the amorphous form of cefuroxime axetil was studied by means of the stress stability test. The degradation was evaluated using the HPLC method with UV detection (278 nm), as described in the monograph of Cefuroxime Axetil in European Pharmacopoeia. Liquid chromatography was performed with a H5 SAS Hypersil column (5 μm particle size, 250 mm × 4 mm), the mobile phase consisted of a mixture of 38 volumes of methanol and 62 volumes of a 23 g l −1 solution of ammonium dihydrogen phosphate, a flow rate of 1.2 ml min −1, and the internal standard was a solution of acetanilide in a mixture (1:1) of acetonitrile and water at a concentration of 0.2 mg ml −1. At an increased temperature at RH = 0%, the degradation of cefuroxime axetil (CFA) diastereoisomers is the reversible first-order reaction, while that occurring in humid air (RH > 25%) is the reversible first-order autocatalytic reaction with Δ 3-isomers and E-isomers of cefuroxime axetil and cefuroxime as the main products.

Adsorption Kinetics of Platinum Group Elements in River Water

The uptake of platinum group elements (PGE) by different preparations of estuarine sediment suspended in filtered river water has been examined. For a given PGE, adsorption time courses to untreated sediment and to sediment whose hydrous metal oxides or organic matter had been removed by appropriate chemical treatments were similar. Adsorption of Rh(lll) and Pt(IV) proceeded via a first-order reversible reaction. For Rh, forward rate constants were 1 order of magnitude greater than reverse rate constants, but for Pt, forward and reverse constants were comparable. Respective system response times, required to attain 63% of the new equilibrium, ranged from about 10 to 30 h and 2 to 20 h. In contrast, rapid, initial uptake of Pd(ll) was succeeded, in most instances, by a protracted period of desorption, requiring a more complex mechanistic interpretation. In all cases, adsorption was reduced following a period of PGE equilibration with filtered river water, suggesting that complexation with natural organic ligands exerts a significant control on the adsorption process by, for example, stabilizing PGE in solution. Exchangeability of adsorbed PGE, evaluated by ammonium acetate extraction, decreased in the order Pd > Pt > Rh, in qualitative agreement with the proposed or modeled adsorption mechanisms. Experimental results, together with independent assessments of PGE mobility from secondary sources (e.g. road dust), indicate that Pd has the greatest potential for long-range transport and bioaccumulation in the aquatic environment.

Adsorption of Paraquat dichloride from aqueous solution by activated carbon derived from used tires

The removal of pesticide from wastewater under different batch experimental conditions, using a car tire derived activated carbon was investigated. The pesticide utilized in the study was Paraquat dichloride (1,1-dimethyl-4,4-bipyridyl dichloride), which is a well known herbicide. The adsorbent was produced from the pyrolysis and activation of used tires (TAC). The performances of this adsorbent and a commercial activated carbon F300 (CAC) have been compared. It was determined that the adsorption of Paraquat was weakly pH dependent. The effects of particle size, carbon dosage, temperature and the initial concentration of the Paraquat were studied. Further experiments investigating the regeneration capabilities of the tire-supplied carbon were performed. The regenerated carbons that were washed with basic pH solution were found to have the best sorption capacity recovery. It was found that the rate of sorption of Paraquat onto the carbon is very fast with almost 90% of the maximum possible adsorption taking place in the first 5 min. Nevertheless, the batch sorption kinetics was fitted for a first-order reversible reaction, a pseudo-first-order reaction and a pseudo-second-order reaction. The pseudo-second-order chemical reaction model appears to provide the best correlation. The applicability of the Langmuir isotherm for the present system has been evaluated at different temperatures. The isotherms show that the sorption capacity of CAC decreases with temperature and the dominant mechanism of CAC adsorption is physical sorption.

Modeling of Hydrodesulfurization (HDS), Hydrodenitrogenation (HDN), and the Hydrogenation of Aromatics (HDA) in a Vacuum Gas Oil Hydrotreater

A trickle-bed reactor model has been used in this work to simulate the catalytic hydrotreating of oil fractions. The most important reactions (hydrodesulfurization (HDS), hydrodenitrogenation (HDN), and the hydrogenation of aromatics (HDA)) are taken into account in the model. Kinetics of each reaction and reactor model was taken from different sources in the literature. HDS reaction was described by Langmuir−Hinshelwood kinetics. HDN was modeled as a consecutive reaction scheme in which nonbasic compounds are hydrogenated first to basic nitrogen compounds, which undergo further reactions to eliminate the N atom from the molecule. The kinetics of aromatics hydrogenation was represented by a first-order reversible reaction. The reactor model includes correlations for determining mass-transfer coefficients and is based on the two-film theory. The model was tested with experimental information obtained at pilot scale during the hydrotreating of vacuum gas oil. The pilot reactor was operated under isothermal conditions, and the effect of reaction temperature and space velocity on HDS, HDN, and HDA was studied in the ranges of 360−380 °C and 2 h-1, respectively. The predicted results showed good agreement with the experimental information. The model was also applied for simulating the behavior of a NiMo catalyst during commercial nonisothermal operation of an industrial hydrotreating plant.

Intermediates and the folding of proteins L and G.

We use a minimalist protein model, in combination with a sequence design strategy, to determine differences in primary structure for proteins L and G, which are responsible for the two proteins folding through distinctly different folding mechanisms. We find that the folding of proteins L and G are consistent with a nucleation-condensation mechanism, each of which is described as helix-assisted beta-1 and beta-2 hairpin formation, respectively. We determine that the model for protein G exhibits an early intermediate that precedes the rate-limiting barrier of folding, and which draws together misaligned secondary structure elements that are stabilized by hydrophobic core contacts involving the third beta-strand, and presages the later transition state in which the correct strand alignment of these same secondary structure elements is restored. Finally, the validity of the targeted intermediate ensemble for protein G was analyzed by fitting the kinetic data to a two-step first-order reversible reaction, proving that protein G folding involves an on-pathway early intermediate, and should be populated and therefore observable by experiment.

Effect of dissolved organic carbon on the photoproduction of dissolved gaseous mercury in lakes: potential impacts of forestry.

The production of dissolved gaseous mercury (DGM) in freshwater lakes is induced by solar radiation and is also thought to be linked to processes mediated by dissolved organic carbon (DOC). Studies investigating these processes using comparisons between lakes are often confounded by differences in DOC content and structure. In this study, we investigated the link between DOC concentrations and DGM production by using tangential ultrafiltration to manipulate DOC concentrations in water samples taken from a given lake. In this way, a range of samples with different DOC concentrations was produced without substantial changes to DOC structure or dissolved ions. This was repeated for four lakes in central Quebec: two with highly logged drainage basins and two with minimally logged drainage basins. On two separate days for each lake, water samples (filtered to remove >99% of microorganisms) with varying DOC concentrations were incubated in clear and dark Teflon bottles on the lake surface. DGM concentrations were measured at 3.5-h intervals over the course of 10.5 h. Levels of DGM concentrations increased with increasing cumulative irradiation for all lakes until approximately 4000 kJ m(-2) (400-750 nm, photosynthetically active radiation (PAR)), when DGM concentrations reached a plateau (between 20 and 200 pg L(-1)). When we assumed that DGM production was limited by the amount of photoreducible mercury, reversible first-order reaction kinetics fitted the observed data well (r2 ranging between 0.59 and 0.98, p < 0.05 with the exception of N70 100% DOC, 0% DOC, and K2 0% DOC with p = 0.06, 0.10, and 0.11, respectively). The DGM plateaus were independent of DOC concentrations but differed between lakes. In contrast, photoproduction efficiency (DGMprod) (i.e., the amount of DGM produced per unit radiation (fg L(-1) (kJ/m2)(-1)) below 4000 kJ m(-2) PAR) was linearly proportional to DOC concentration for both logged lakes (r2 = 0.97, p < 0.01) and nonlogged lakes (r2 = 0.52, p = 0.018) studied. Furthermore, logged lakes had a lower DGMprod per unit DOC (p < 0.01) than the nonlogged lakes. In these four lakes, the rate of DGM production per unit PAR was dependent on the concentration of DOC. The DGM plateau was independent of DOC concentration; however, there was a significant difference in DGM plateaus between lakes presumably due to different DOC structures and dissolved ions. This research demonstrates an important mechanism by which logging may exacerbate mercury levels in biota.

The water–gas-shift reaction at short contact times

We have examined the water–gas-shift reaction over noble metals and metals with ceria for catalyst contact times between 0.008 and 0.05 s for temperatures from 300 to 1000 °C. With reactants of CO, H 2, and H 2O at a 1/2/4 composition, the reaction approached equilibrium at these contact times for temperatures as low as 380 °C, which corresponds to a 50/1 H 2/CO ratio. All results follow the equilibrium conversion versus temperature curve at high temperatures and then the rate decreases rapidly as temperature decreases. All metals show considerable promotion upon ceria addition, with Pt/ceria showing the most promise in terms of promotion, stability, and lack of methanation activity. A simple kinetic model that assumes first-order reversible reaction in all species fits all data at all temperatures from equilibrium to low conversions. The rate is nearly independent of surface area over a wide variation of parameters, and rates indicate that mass-transfer limitations are not dominant.

Species of dissolved Cu and Ni and their adsorption kinetics in turbid riverwater

Time-dependent sorption experiments have been carried out under controlled laboratory conditions, using filtered river water and particles from the turbidity maximum zone (TMZ) of the Tamar Estuary (UK). Adsorptive cathodic stripping voltammetry (ACSV) was used to determine ACSV labile and total dissolved Cu and Ni, without prior sample handling and/or pre-concentration. The ACSV metal lability is theoretically defined and is dependent upon the α-coefficient ( α MAL) of the added ACSV ligand. The fraction of labile dissolved Cu in the river water was in the range 28–41% of the total, while labile Ni was 80–90% of the total dissolved Ni. After 24 h incubation with the particles, the concentration of total dissolved Cu was reduced to half the original value and involved the removal of 40% of labile Cu and 70% of the non-labile Cu. Removal of total dissolved Ni after 24 h ranged from 40 to 60% and the uptake kinetics were dominated by adsorption of labile Ni. The kinetics of adsorption for the different chemical forms of Cu and Ni were interpreted by assuming a first-order reversible reaction between the dissolved components and the particulate phase. The chemical response time for the removal of labile Cu was 1.1 and 0.5 h for non-labile Cu. The chemical response time for labile Ni was in a range from 0.7 to 0.3 h. The results are interpreted in terms of the role played by chemical kinetics in determining the phase transport of metals in the reactive zones of estuaries.

Stochastic Model of the n-Stage Reversible First-Order Reaction: Relation between the Time of First Passage to the Most Probable Microstate and the Mean Equilibrium Fluctuations Lifetime

Using the stochastic model of

Adsorption kinetics for the removal of chromium(VI) from aqueous solution by adsorbents derived from used tyres and sawdust

The batch removal of hexavalent chromium (Cr(VI)) from wastewater under different experimental conditions using economic adsorbents was investigated in this study. These adsorbents were produced from the pyrolysis and activation of the waste tyres (TAC) and from the pyrolysis of sawdust (SPC). The performance of these adsorbents against commercial activated carbon F400 (CAC) has also been carried out. The removal was favoured at low pH, with maximum removal at pH=2 for all types of carbon. The effects of concentration, temperature and particle size have been reported. All sorbents were found to efficiently remove Cr(VI) from solution. The batch sorption kinetics have been tested for a first-order reversible reaction, a first-order and second-order reaction. The rate constants of adsorption for all these kinetic models have been calculated. The applicability of the Langmuir isotherm for the present system has been tested at different temperatures. The thermodynamic parameters (Δ G 0, K c) obtained indicate the endothermic nature of Cr(VI) adsorption on TAC, SPC and CAC.

Kinetics for the reversible isomerization reaction of trans-astaxanthin

Abstract The isomerization of cis -astaxanthins in organic solvents, a reverse reaction of the isomerization of trans -astaxanthin, was investigated. HPLC analysis revealed that cis -astaxanthins could be also isomerized to produce trans -astaxanthin and the other cis -astaxanthin. The results showed that the isomerization of trans -astaxanthin to cis -astaxanthin was a reversible reaction and followed first-order reversible reaction kinetics. The effect of temperature on the isomerization reaction of trans -astaxanthin, dissolved in dimethyl sulfoxide at 20–70°C or in a mixture of dichloromethane and methanol (25:75) at 10°C, respectively, was also studied. The results indicated that increasing temperature could markedly increase the reaction rate of trans -astaxanthin isomerization. Temperature-dependence of the isomerization rate constants of trans -astaxanthins could be described by the Arrhenius equation with activation energy ( E a ) of 105.8±4.2 kJ/mol.

Reactivation kinetics of guanidine hydrochloride-denatured creatine kinase measured using the substrate reaction.

Guanidine hydrochloride-denatured creatine kinase (CK) can very quickly form a dimer with reactivity when the denaturant is diluted into the reaction system in the presence of DTT or EDTA. Tsou's method and its applied equation [Tsou (1988), Adv. Enzymol. Rel. Areas Mol. Biol. 61, 381-436; Yang and Zhou (1998), Biochim. Biophys. Acta 1388, 190-198] were used to measure the kinetic reactivation rate constants and the reactivation degree for reassociated CK dimers. Partial reactivation (about 50% at best) occurred following a monophasic course during the substrate reaction when compared with previous time interval measurements. The reactivation degree increased with increasing DTT (0.1-5 mM) and EDTA (0.1-1 mM) concentrations. The apparent forward rate constants do not change with concentration, showing that the reactivation is a reversible first-order reaction, but not of complex formation type. However, the apparent forward rate constants do change with EDTA concentration, showing that the reactivation with EDTA is a reversible first-order reaction as well as of complex formation type. Excess DTT concentrations have an inhibitory effect, indicating that the excessive EDTA acts as a metal chealate not only for free Mg2+, but also for MgATP during the enzyme catalysis. This study shows that additional information about the reactivation of CK can be obtained from examining the substrate reaction. The possible refolding pathway of CK is discussed.

Effects of Light Intensity, n-Alcohols, Water-Soluble Colorants, and Solution Viscosity on Photoisomerization of Sorivudine

Effects of various factors, such as light intensity, polarizability of n-alcohol solvents, addition of colorants, and viscosity of solutions on the kinetics of the photoisomerization of therapeutically effective E-isomer of sorivudine to its less effective Z-isomer were studied. Solutions of known concentrations of E-isomer or Z-isomer in water or in a series of n-alcohols were directly exposed to ultraviolet (UV) A light, or visible light of 400 or 900 foot candles (fc). E-isomer solutions containing various colorants at 1% w/v, or in a series of poloxamer solutions of different viscosities, were also exposed to 400 or 900 fc light. Using the stability-indicating HPLC assay, which showed mass-balance between the starting isomer and the converting isomer, the kinetics of photoisomerization were monitored. The photoisomerization reaction, which takes place on the vinyl side chain, was found to be a first-order reversible reaction. In water, the rate of conversion of E-isomer to Z-isomer was faster than that of Z-isomer to E-isomer, since, E-isomer with higher extinction coefficient absorbed substantially more light than Z-isomer. The rate of photoisomerization increased with the intensity of the visible light and was very rapid in the presence of UV A light (300 to 400 nm), which is to be expected based on the 239 nm and 283 nm absorption maxima of sorivudine. Addition of water-soluble colorants retarded the photoisomerization process significantly, especially as the maximum absorption wavelengths (λmax) of the colorants approached the UV region. The rate of photoisomerization increased with increasing polarizability (αs) of the n-alcohol solvents. Polarizable solvents such as alcohols could compensate for the electron density built up in the excited state, and thus facilitated the photoisomerization process. The rate of photoisomerization decreased as the viscosity of solution increased. This may be attributed to the fact that the twisting of the C=C bond in the excited state can be inhibited by the friction imposed by the viscous medium.

Rate and equilibrium constants for the epimerization of the endothelin receptor antagonist J-104,132 in aqueous solution.

The degradation of [5S-[5alpha,6beta,7alpha(R*)]]-2-butyl-5-(1,3-benzodioxol-5-yl)-7-[(2-carboxypropyl)-4-methoxyphenyl]-6-dihydro-5H-cyclopenta[b]pyridine-6-carboxylic acid (J-104,132) was studied in aqueous solution as a function of temperature and pH. The degradation reaction does not proceed to completion; rather, a stable equilibrium is attained in which approximately 2% of the degradate is produced. Kinetic data for the formation of the degradate are analyzed using an integrated form of the rate law for a reversible first-order reaction, and the forward and reverse rate constants and overall equilibrium constants are presented. Isolation and spectroscopic structural determination indicate that the degradate is the C7 beta-epimer of the drug. A mechanism for the epimerization reaction involving a novel enamine-like intermediate is proposed and shown to be consistent with the kinetic data. The rate and equilibrium constants are used to predict the room temperature stability of an injectable formulation of J-104,132, and these predictions are compared to actual data from long-term stability studies. It is concluded that the preformulation kinetic studies provide essential data needed for optimum drug product development.

Simulating Dynamic Equilibria: A Class Experiment

A first-order reversible reaction is simulated on an overhead projector using small coins or discs. A simulation is carried out in which initially there are 24 discs representing reactant A and none representing reactant B. At the end of each minute half of the reactant A discs get converted to reactant B, and one quarter of the reactant B discs get converted to reactant A discs. Equilibrium is established with 8 A discs and 16 B discs, and no further net change is observed as the simulation continues. Another simulation beginning with 48 A discs and 0 B discs leads at equilibrium to 16 A discs and 32 B discs. These results illustrate how dynamic equilibria are established and allow the introduction of the concept of an equilibrium constant. Le Châtelier's principle is illustrated by further simulations.

Nonequilibrium thermodynamics of heat waves in a catalytic bed. Functional of an autowave solution

The thermodynamic description of the physicochemical processes in a fixed catalytic bed is considered in the approximation of the simplest (quasihomogeneous) model in the presence of a first-order reversible reaction. It is shown that the physical nature of slow heat waves is amenable to the second law of thermodynamics, and the total entropy production in a distributed open and strongly nonequilibrium system is a functional of the autowave solution of a mathematical model. Of the one-parameter family of autowave solutions, the minimum value of the functional corresponds to the unique physically valid solution. The methods of nonequilibrium thermodynamics are used to substantiate the technique of “cutting off” the reaction function. At the same time, a variational problem that is solved without using this technique is formulated.

酸性染料によるナイロン染色布の摩擦堅牢度

Several acid dyes whose molecular sizes were far different were used in this work. They were dyed with nylon fabrics and the characteristics of their rubbing-fastness were investigated. The amount of removed dyes were different from dye to dye and it had nothing to do with molecular size of dye. From kinetic analysis, the removal process of acid dyes could be treated as a reversible reaction of first order. The rate constant of transfer of acid dyes from dyed nylon fabrics to white cloth (k1) and the rate constant of reverse process (k-1) mostly increased with molecular weight of dyes but the equilibrium constant (K) did not depend on it. So far with cotton fabrics, the constants k1 and K generally depended on load weight on white cloth but k-1 did little, while with nylon fabrics dyed with acid dyes all those constants did. The dependence of k1 on load weight was the biggest, k-1 was the second and K was the third.

Removal of metal ions by nonliving water hyacinth roots

Nonliving dried water hyacinth (Eichhornia crassipes (Mart.) Solms) roots were investigated/or the biosorption of cadmium, lead and other heavy metal ions from aqueous solutions. Dried water hyacinth roots, when suspended in solution, strongly and rapidly sorb several different metal ions. Factors such as reaction time, pH, the initial concentration of metal ions, the presence of other metal ions and biomass concentration were investigated. The adsorption was shown to follow the generalized Langmuir adsorption equation. The relative affinity of the roots for lead is greater than that for cadmium. The batch sorption kinetics of the uptake of cadmium and lead can be described by an apparent first-order reversible reaction model. The roots could be regenerated after the metal ions were stripped. Successful de sorption of Cd and Pb from the biomass by acidic CaCl2 solutions revealed that the metal uptake phenomenon is reversible, implying physical sorption of Cd and Pb.