First-order Reversible Kinetics Research Articles

Removal of hexavalent chromium from electroplating wastewater by ion-exchange in presence of Ni(II) and Zn(II) ions

This study presents the ion-exchange elimination of hexavalent chromium [Cr(VI)] from electroplated industrial wastewater. The effects of experimental factors such as pH, contact time, adsorbent dose, temperature, and co-ions on Cr(VI) removal were investigated. The metal ions were maximally removed (up to 96.7 %) and obtained with a resin dosage of 3 g L−1 at pH 2 for 70 min. Thermodynamic parameters, such as the standard Gibbs free energy change (ΔG0), standard enthalpy change (ΔH0),and standard entropy change (ΔS0), were calculated. The negative value of ΔG0(−8.031 kJ/mol K)indicates the spontaneity of the ion exchange process. The Freundlich and Langmuir isotherms fit the adsorption data well. The adsorption kinetics of Cr(VI) on the Amberlite IRA400 resin were analyzed using reversible first-order kinetics. The presence of Zn(II) and Ni(II) increased the efficiency of the adsorption process in the order Zn(II) > Ni(II). Column experiments were conducted to determine the breakthrough point of the packed-bed resin column, and a break-even concentration of 0.1 mgL−1 was deducted after the treatment of 4.5 L of the effluent. The adsorption data from the column studies were fitted using the Adam–Bohart adsorption model and the results fit the model well. A mathematical approach to the regeneration process is described in this study. The reusability of the resin was tested for 30 cycles and its efficiency of the regenerated resin was found to be above 97 % after the 30th cycle.

Enantioseparation and racemization of 3-fluorooxindoles.

Fluorinated oxindoles are frequently used building blocks in asymmetric synthesis and represent an important scaffold found in a variety of biologically relevant compounds. While it is understood that incorporation of fluorine atoms into organic molecules can improve their pharmacological properties, the impact on the configurational stability of chiral organofluorines is still underexplored. In this study, semipreparative HPLC enantioseparations of five oxindoles were carried out, and the resulting enantiomerically enriched solutions were used to investigate base promoted racemization kinetics at room temperature. It was found that incorporation of fluorine at the chiral center increases the configurational stability, while substitutions on the aromatic ring and at the lactam moiety also have significant effects on the rate of racemization, which generally follows reversible first-order reaction kinetics.

Analysis of reaction path and different lumped kinetic models for asphaltene hydrocracking

The product distribution of asphaltenes hydrocracking was studied in an autoclave with decalin as the liquid-phase system at different reaction temperatures and times to elucidate the relevant reaction mechanism. The results showed that the reaction products might be reversely condensed to generate secondary asphaltenes, resulting in a trend of first increasing and then decreasing the yields of some products at 420 °C. The significant yield increase of gas and gasoline at 420 °C might be due to the cracking of saturated and aromatic fractions to form light fractions. The conclusion was drawn the reaction behavior of asphaltenes hydrocracking under the research conditions followed the first-order reversible reaction kinetics by the reaction kinetic analysis, which further supported the inference that some products could recondense to form secondary asphaltenes. The four-lumped, five-lumped, and six-lumped models were constructed to study in depth the reaction behavior of asphaltene hydrocracking in the current system, and the results showed that the more similar the structure and composition of the reaction products to asphaltenes, the faster the reaction rate of their condensation to asphaltenes. Furthermore, the higher the temperature was more favorable to improve the selectivity and yield of transportation fuel diesel under the temperature of 380 °C-420 °C by the analysis of the ratio of rate constant. Although the applicability of lumped model was not positively correlated with the number of lumps, it is concluded that the six lumped model was the best model among the three models from the combined analysis of the applicability and the richness of the reaction information of the model.

Transport of Molecular Cargo by Interaction with Virus-Like Particle RNA.

Virus-like particles (VLPs) derived from Leviviridae virions contain substantial amounts of cellular and plasmid-derived RNA. This encapsidated polynucleotide serves as a reservoir for the efficient binding of the intercalating dye thiazole orange (TO). Polyethylene glycol (PEG) molecules and oligopeptides of varying length, end-functionalized with TO, were loaded into VLPs up to approximately 50 % of the mass of the capsid protein (hundreds to thousands of cargo molecules per particle, depending on size). The kinetics of TO-PEG binding included a significant entropic cost for the reptation of long chains through the capsid pores. Cargo molecules were released over periods of 20-120 hours following simple reversible first-order kinetics in most cases. These observations define a simple general method for the noncovalent packaging, and subsequent release, of functional molecules inside nucleoprotein nanocages in a manner independent of modifications to the capsid protein.

Efficient Simulation of Arbitrary Multicomponent First-Order Binding Kinetics for Improved Assay Design and Molecular Assembly.

Traditional enzyme-linked immunosorbent assay (ELISA), long the workhorse for specific target protein detection using microplate wells, is nearing its fundamental limit of sensitivity. New opportunities in health care call for in vitro diagnostic tests with ultrahigh sensitivity. Magnetic bead-based sandwich immunoassay formats have been developed that can reach unprecedented sensitivities, orders of magnitude better than are allowed for by the rate constants for a single ligand–receptor interaction. However, these ultrahigh sensitivity assays are vulnerable to a host of confounding factors, including nonspecific binding from background molecules and loss of low-abundance target to tube walls and during wash steps. Moreover, the optimization of workflow is often time-consuming and expensive. In this work, we present a simulation tool that allows users to graphically define arbitrary binding assays, including fully reversible first-order binding kinetics, timed addition of extra components, and timed wash steps. The tool is freely available as a user-friendly webapp. The framework is lightweight and fast, allowing for inexpensive simulation and visualization of arbitrarily complex assay schemes, including but not limited to digital immunoassays, DNA hybridization, and enzyme kinetics, for validation and optimization of assay designs without requiring any programming knowledge from the user. We demonstrate some of these capabilities and provide practical guidance on assay simulation design.

Enantioseparation and racemization of α-aryl-α-fluoroacetonitriles.

The 2-Aryl-2-fluoroacetonitriles have garnered increasing interest as versatile building blocks in asymmetric synthesis. However, the configurational stability of these organofluorines is poorly understood and analytical methods that can be used to differentiate between their enantiomers remain underdeveloped. In this study, baseline high performance liquid chromatography (HPLC) enantioseparation of ten 2-aryl-2-fluoroacetonitriles was achieved by screening frequently used chiral stationary phases. While Chiralcel OD, Chiralpak AD, and Chiralpak AS proved to be most broadly useful, preparative separation of the enantiomers of 2-(2-naphthyl)-2-fluoroacetonitrile was possible on Chiralcel OJ. This enabled racemization studies at various temperatures and in the presence of organic bases which showed that this compound is configurationally stable under neutral conditions upon heating to 130°C for 6 h but undergoes complete racemization within 10 h in the presence of stoichiometric amounts of a guanidine base at room temperature. The racemization is likely to proceed via formation of an achiral keteniminate intermediate and obeys reversible first-order reaction kinetics with a half-life time of 87.7 min in ethanolic hexanes at 23.2°C. Racemization is significantly slower and occurs with a half-life time of 23.1 h at 22.4°C when the guanidine is replaced with a weaker amidine base.

Solid-state reduction of an Indonesian iron sand concentrate using subbituminous coal

ABSTRACT The reduction of an Indonesian iron sand concentrate was studied using TG/DTA and XRD analyses. The iron sand concentrate was mixed with coal and formed into a cylindrical pellet. The experimental results show that magnetite was reduced into wustite at 700–800°C and into metallic iron at temperature above 800°C. The transformation of titanomagnetite into ulvospinel and ilmenite occurred between 900 and 1000°C, and ulvospinel transformed into ilmenite and iron at 1000–1100°C. To simulate the reduction process in a rotary kiln, iron sand concentrate pellets were hardened at 1250°C and reduced using coal, which was added to cover the surface of the pellet at a temperature range of 800–1100°C for 150 min. The reduction degree was calculated based on the weight loss and the metallization degree was determined by wet chemical analysis. Quasi-equilibrium values of the reduction and metallization degrees were obtained at a certain temperature. The reversible first-order kinetics equation was proposed to analyse the experimental data to predict the metallization degree as a function of the reduction time and temperature.

Matrix Isolation Spectroscopy and Nuclear Spin Conversion of Propyne Suspended in Solid Parahydrogen.

Parahydrogen (pH2) quantum solids are excellent matrix isolation hosts for studying the rovibrational dynamics and nuclear spin conversion (NSC) kinetics of molecules containing indistinguishable nuclei with nonzero spin. The relatively slow NSC kinetics of propyne (CH3CCH) isolated in solid pH2 is employed as a tool to assign the rovibrational spectrum of propyne in the 600-7000 cm-1 region. Detailed analyses of a variety of parallel (ΔK = 0) and perpendicular (ΔK=±1) bands of propyne indicate that the end-over-end rotation of propyne is quenched, but K rotation of the methyl group around the C3 symmetry axis still persists. However, this single-axis K rotation is significantly hindered for propyne trapped in solid pH2 such that the energies of the K rotational states do not obey simple energy-level expressions. The NSC kinetics of propyne follows first-order reversible kinetics with a 287(7) min effective time constant at 1.7 K. Intensity-intensity correlation plots are used to determine the relative line strengths of individual ortho- and para-propyne rovibrational transitions, enabling an independent estimation of the ground vibrational state effective A″ constant of propyne.

Calculating the first-order kinetics of three coupled, reversible processes

Calculation of the concentration-time profile in four consecutive, well-mixed compartments that are connected by diffusional transport is a frequently occurring problem for chemists and engineers. Mathematically this is equivalent to many other problems such as the concentration profiles of a parent compound and its three consecutive reaction products resulting from reversible first-order kinetics. Here we present an analytical solution to this problem implemented in a Microsoft Excel spreadsheet (available for download) and we discuss various examples of how this simple-to-use tool can be applied to very different scenarios from various fields of science.

Compact model for parametric instability under arbitrary stress waveform

A deterministic compact model of the parametric instability of elementary devices is further developed. The model addresses the device instability class that can be traced back to microscopic reactions obeying reversible first-order kinetics. It can describe the response to any periodic stimulus waveform and it is suitable for the implementation in commercial electronic circuit simulators (Eldo UDRM). The methodology is applied to model the negative-bias-temperature threshold voltage instability of a p-channel MOSFET. A simple circuital example is shown where the simulation of threshold voltage recovery is crucial for circuit design.

Adsorptive removal of acid red from aqueous solutions by cationic surfactant-modified bentonite clay

AbstractThe performance of hexadecyltrimethylammonium chloride (HDTMA)-intercalated bentonite clay (organoclay) for the removal of acid red (AR) from aqueous solutions has been evaluated in this study. The adsorbent HDTMA-modified bentonite clay was prepared by the reaction of Na-bentonite with (HDTMA+) cations equal to twice the cation exchange capacity of the Na-bentonite. The adsorbent characterization was done with the surface area analyzer, FTIR, SEM, XRD, TGA and potentiometric titrations. Maximum adsorption of AR onto organoclay has been found to be at pH 3.0. The Langmuir isotherm model was found to be the best fit model. The maximum adsorption capacity was found to be 140.84 μmol/g at 30°C. Adsorption has been found to be endothermic and follows first-order reversible kinetics.

Dating Human Bone: Is Racemization Dating Species-Specific?

Our recently developed dating technique based on the racemization rate of aspartic acid was applied to dating human bone, as well as that of other mammals, utilizing capillary electrophoresis mass spectrometry. First, several well-dated (mostly (14)C-dated and with strong archeological evidence) human bones ranging in age from 150 to ~10,000 years were used to develop a calibration curve for human bone. The D/L ratio of aspartic acid for these specimens ranged from 2.4% to ~10%, with a correlation coefficient of better than 0.99, indicating a strong linear relationship between the d/l ratio of aspartic acid and the age of the specimens. This calibration curve can now be used to date human archeological specimens of unknown age, up to ~10,000 years. However, when the technique was applied to well-dated mixed species of larger mammal bones such as bison, whale, llama, etc., the calibration curve showed a slower rate of racemization with a lower correlation (0.88). As additional large mammal bones with less certain age (i.e., using archeological evidence alone with no (14)C-dating) were dated the correlation coefficient decreased to 0.70. The correlation coefficient decreased further to 0.58 when the racemization data from all mammals (including human) were added to the calibration curve, indicating the importance of using well-dated, species-specific specimens for forming a calibration curve. This conclusion is consistent with our previously published calibration curve for a single species of silk (Bombyx mori), which followed the expected reversible first-order kinetics. These results support species specificity of amino acid racemization dating.

A reversible first-order dispersive model of parametric instability

A general purpose instability model is derived for the variation of device parameters which is related to the activation–deactivation of statistically independent microscopic defects, with reversible first-order reaction kinetics and distributed rate constants. The model is aimed at predicting the parametric instability of electronic devices under periodic AC stimulus of arbitrary waveform over a wide time-scale range covering the whole device lifetime. As a practical application, we extracted a model for the negative-bias temperature instability of a p-channel type silicon MOSFET, including both the recovery effects and the voltage–temperature dependence. The model can be implemented in commercially available tools for the compact simulation of integrated circuits.

Characterizing the dynamics of amino acid racemization using time-dependent reaction kinetics: A Bayesian approach to fitting age-calibration models

Robust estimates of specimen age and associated precision are critical to the study of many palaeobiological and sedimentological processes. While recent work has explored a variety of methods for calibrating the rate of amino acid racemization using paired radiocarbon analyses, and for assessing the precision of age estimates obtained using these models, the calibration models themselves, and the underlying assumptions used to construct them, have not yet been rigorously evaluated. Here we use a Bayesian model fitting procedure to compare three previously proposed calibration functions (“apparent parabolic kinetics” [APK], “simple power-law kinetics” [SPK], and “constrained power-law kinetics” [CPK]), and we propose a new function, “time-dependent reaction kinetics” (TDK), which has a mechanistic basis in first-order reversible kinetics. We then evaluate which of three statistical distributions – normal, lognormal, gamma – best describes the prediction uncertainty associated with each age-calibration function. The Bayesian fitting method outlined here is superior to the least-squares fitting approach commonly used because it allows greater flexibility in modelling this uncertainty and its effects on the precision of age estimates. To facilitate the adoption of this methodology, we provide an analytical script that can be implemented on a variety of computer platforms using freely available software.Regardless of the fitted calibration function, we find that the gamma and lognormal distributions more accurately describe prediction uncertainty than to the normal distribution. Three of the four calibration functions perform well (the exception being APK), but no single function performs best in all situations. In general, TDK and CPK (which we show to be a special case of TDK) yield superior model fits to SPK when d/l is close to saturation, and moreover provide useful mechanistically-based functions for calibrating amino acid racemization datasets.

Mathematical modeling of high-pressure oil-splitting reactor using a reduced population balance model

A reduced non-equilibrium bivariate population balance model is developed to model simultaneous reversible chemical reaction and extraction of an industrial scale high-pressure oil-splitting reactor with a first-order reversible kinetics. The model includes details about the reacting mixture by considering the discrete (particulate) nature of the dispersed phase. This, however; increases the mathematical complexity of the model and results in a coupled system of partial differential equations (PDE) of hyperbolic type with nonlinear source terms. The characteristics analysis shows that these hyperbolic PDEs have two dominant and distinct characteristic speeds: The mean droplet speed and the mean continuous phase (oil) speed. This generates a set of contact waves moving along the reactor height in opposite directions. Therefore, modern numerical methods based on CFD literature are applicable to provide a numerical solution of the developed model. As a first step in the numerical investigation, a finite volume method with a first-order upwind scheme is developed and implemented. Also, sufficient conditions of stability are derived and implemented. The numerical model is validated against analytical solution of a special case, where numerical convergence in the sense of l2-norm is established. Numerical simulation results showed that the unreacted oil concentration profile decreased exponentially along the reactor height. On the other hand, the glycerine concentration in the oil phase passes through a maximum due to the simultaneous reaction and extraction processes. Three operating parameters: temperature, mean droplet diameter and excess water flow rate were studied to highlight their effect on the reactor performance. The most important parameter was the reactor operating temperature, where 240 °C was found sufficient for complete oil conversion. This agrees with the operating temperature in industrial practice.

AMIDE FUNCTIONALIZATION OF MULTIWALLED CARBON NANOTUBES AND THEIR EVALUATION FOR Hg(II) REMOVAL FROM WATER

This paper deals with the amide functionalization of multiwalled carbon nanotubes (MWNTs) and its evaluation for mercury removal from water. The functionalized MWNTs were characterized using FTIR for structural modification. The properties of MWNTs such as hydrophilic character, nature of surface, selective chemical interaction with mercury, etc., were significantly improved after functionalization making them promising adsorbents for mercury removal. The equilibrium is achieved in short time of 5 h resulting in up to 80% removal of Hg (II). Kinetics of adsorption was established and found to follow first-order reversible kinetics with forward and backward reaction rate constants 0.6648 and 0.1662, respectively.

Adsorptive removal of congo red dye from aqueous solution using bael shell carbon

This study investigates the potential use of bael shell carbon (BSC) as an adsorbent for the removal of congo red (CR) dye from aqueous solution. The effect of various operational parameters such as contact time, temperature, pH, and dye concentration were studied. The adsorption kinetics was modeled by first-order reversible kinetics, pseudo-first-order kinetics, and pseudo-second-order kinetics. The dye uptake process obeyed the pseudo-second-order kinetic expression at pH 5.7, 7 and 8 whereas the pseudo-first-order kinetic model was fitted well at pH 9. Langmuir, Freundlich and Temkin adsorption models were applied to fit adsorption equilibrium data. The best-fitted data was obtained with the Freundlich model. Thermodynamic study showed that adsorption of CR onto BSC was endothermic in nature and favorable with the positive Δ H° value of 13.613 kJ/mol.

Removal of chromium (VI) from aqueous solutions using Lewatit FO36 nano ion exchange resin

The removal of the chromium (VI) ion from aqueous solutions with the Lewatit FO36 ion-exchange resin is described at different conditions. The effects of adsorbent dose, initial metal concentration, contact time and pH on the removal of chromium (VI) were investigated. The batch ion exchange process was relatively fast and it reached equilibrium after about 90 min of contact. The ion exchange process, which is pH dependent showed maximum removal of chromium (VI) in the pH range 5.0–8.0 for an initial chromium (VI) concentration of 0.5 mg/dm3. The equilibrium related to Lewatit FO36 ion- exchange capacity and the amounts of the ion exchange were obtained using the plots of the Langmuir adsorption isotherm. It was observed that the maximum ion exchange capacity of 0.29 mmol of chromium (VLVg for Lewatit FO36 was achieved at optimum pH value of 6.0. The ion exchange of chromium (VI) on this cation-exchange resin followed first-order reversible kinetics.

Study of kinetic and fixed bed operation of removal of sulfate anions from an industrial wastewater by an anion exchange resin

Sulfate anions represent very important wastewater pollutants, which appear in the effluents discharged from copper mines. In this study, for the first time, an attempt has been made on the removal of sulfate anions by an ion exchange resin. This work is focused on the removal of sulfate anions from the Sarcheshmeh copper complex (Kerman province, Southeast of Iran) wastewater by an anion exchange resin. Batch experiments of sulfate anions adsorption on Lewatit K6362 resin were carried out to determine the adsorption equilibrium data and the relation of adsorption isotherms. Isothermal data can be fitted with Freundlich adsorption isotherms better than Langmuir equation. The results show that maximum removal of sulfate anions take places in the resin dosage of 1000 mg/100ml and the adsorption of sulfate anions on the resin follows reversible first-order kinetics. The overall adsorption rate constants were compared for different initial concentrations. Finally, the effects of parameters such as the flow rate, bed height and inlet adsorbate concentration on the breakthrough curve in a fixed bed column were studied in detail.

Removal of chromium from aqueous solution by using oxidized multiwalled carbon nanotubes

The batch removal of hexavalent chromium (Cr(VI)) from aqueous solution by using oxidized multiwalled carbon nanotubes (MWCNTs) was studied under ambient conditions. The effect of pH, initial concentration of Cr(VI), MWCNT content, contact time and ionic strength on the removal of Cr(VI) was also investigated. The removal was favored at low pH with maximum removal at pH <2. The adsorption kinetics was modeled by first-order reversible kinetics, pseudo-first-order kinetics, pseudo-second-order kinetics, and intraparticle diffusion models, respectively. The rate constants for all these kinetic models were calculated, and the results indicate that pseudo-second-order kinetics model was well suitable to model the kinetic adsorption of Cr(VI). The removal of chromium mainly depends on the occurrence of redox reaction of adsorbed Cr(VI) on the surface of oxidized MWCNTs to the formation of Cr(III), and subsequent the sorption of Cr(III) on MWCNTs appears as the leading mechanism for chromium uptake to MWCNTs. The presence of Cr(III) and Cr(VI) on oxidized MWCNTs was confirmed by the X-ray photoelectron spectroscopic analysis. The application of Langmuir and Freundlich isotherms are applied to fit the adsorption data of Cr(VI). Equilibrium data were well described by the typical Langmuir adsorption isotherm. Overall, the study demonstrated that MWCNTs can effectively remove Cr(VI) from aqueous solution under a wide range of experimental conditions, without significant Cr(III) release.