General Rate Law Research Articles

True Order Determination of Sonochemical Degradation Kinetics of Organic Contaminants in Water Using the Half-lives Method

In the literature, the modeling of the sonolytic decomposition kinetics of organic contaminants in water has been carried out using the pseudo-first and pseudo-second order equations. The results obtained with this method are totally biased because it requires the assumption of the order of the degradation reaction, which is a real limitation, and the sonochemical oxidation mechanism is a very complex phenomenon that cannot be described by such simple models. In this paper, for the first time, the true order of the sonochemical degradation kinetics of organic pollutants in aqueous solutions at various initial substrate concentrations was determined using the half-lives method combined with the general rate law model, i.e., the pseudo-nth order equation. Linear and nonlinear regression techniques were used to determine the order of the sonolytic destruction reaction. The half-life technique for the general rate law model can adequately describe the experimental results of the sono-destruction of the investigated pollutants. For rhodamine B and naphthol blue black, the sono-destruction mechanism for both contaminants does not change as the initial contaminant concentration varies over the range examined, while for 4-isopropylphenol and furosemide, the sono-destruction mechanism changes as the initial substrate concentration varies. A fractional order of the sonolytic destruction reaction was determined for all the pollutants tested. These fractional orders of sono-destruction reactions indicate the complex nature and behavior of the reactions, often involving multiple steps or mechanisms. They also reveal a more complex interaction between pollutant concentration and sonolytic destruction rate. In a word, the method developed in this paper should be used to determine the real order of the sono-oxidation reaction of nonvolatile organic pollutants in aqueous phase.

Kinetics, Mechanism, and Reactivity of the Cerium(IV)-Oxalatereaction in a Sulphate Medium

This work presents an approach for studying the kinetics, mechanism, and reactivity of intermediates in a wide class of the redox reactions for which the rate-limiting step is the redox-decomposition of an intermediate complex. This approach is applied to investigate the oxalic acid (H2Ox) oxidation by cerium(IV) in sulfuric acid medium, which is an integral part of the cerium-catalyzed oscillatory Belousov–Zhabotinsky (BZ) reaction. Using experimental, mathematical and computational techniques commonly used to study metal complexes in a stable oxidation state (OS), kinetically generalized by the authors for studying variable-valence metal complexes, the characteristics of intermediate complexes of the cerium(IV)-oxalate reaction were studied, the general rate law was derived on the basis of a set of equations describing the rapid establishment of preequilibria in the system and the subsequent nonequilibrium process. A quantitative reaction model is proposed that includes two parallel reaction pathways, for which two different intermediate cerium(IV)-oxalate complexes with close reactivity have been identified and characterized that may be due to the similarity in the structure of their inner coordination spheres and an inner sphere mechanism of electron transfer in the complexes. Based on the developed model, the distribution diagram was also constructed for the computed fractions of all the detectable cerium(IV) species under conditions of the BZ reaction, which testify to the necessity to take into account under these conditions the formation of intermediate complexes CeOHOx (n = 1, 2) during oxidation of oxalic acid. The main difference of the proposed model of the cerium(IV)-oxalate reaction as part of the BZ-reaction from the previous models is the explicit accounting of the formation of intermediate cerium(IV) complexes with anions of oxalic acid and sulfate background.

Application of the general rate law model to the sonolytic degradation of nonvolatile organic pollutants in aqueous media

The pseudo-first and pseudo-second order equations have been the most commonly used models to characterize the sonolytic disappearance kinetics of nonvolatile pollutants in aqueous media. In this work, the general rate law model, i.e., pseudo-nth order kinetics equation, was applied for the first time to the sono-decomposition of different nonvolatile organic pollutants, naphthol blue black (NBB), furosemide (FSM), 4-isopropylphenol (4-IPP), and rhodamine B (RhB), in water. It was shown that the general rate law for a chemical reaction would apply to the kinetics of sonochemical decomposition. It is not feasible to set the order of ultrasonic pollutant degradation kinetics to pseudo-first or pseudo-second, as is typically used in numerous studies. The sonochemical oxidation reaction has a fractional order, the order is often non-integer, which frequently indicates a complex sonolytic decomposition reaction mechanism. The degradation mechanism of NBB and RhB does not change with the initial substrate concentration. They are ultrasonically degraded by hydroxyl radicals both in the bulk liquid solution and at the liquid/bubble interfacial layer. The destruction mechanism of FSM and 4-IPP changes as the initial contaminant concentration changes. At low initial substrate concentrations, these pollutants are oxidized mainly by reaction with hydroxyl radicals in the bulk liquid solution and at the interfacial shell of the cavitation bubbles. At high initial substrate concentrations, FSM and 4-IPP are degraded by thermal destruction in the liquid/bubble interfacial layer and by •OH radicals both in the bulk liquid solution and at the liquid/bubble interfacial layer. Additionally, the pseudo-nth order model predicts very well the sonolytic degradation at various sonication frequencies and intensities. The general rate law expression should be used to assess the real kinetics order of the sonolytic destruction process without any predetermined assumptions or constraints.

Parameter Identification in Metabolic Reaction Networks by Means of Multiple Steady-State Measurements

In this work, we investigate some theoretical aspects related to the estimation approach proposed by Liebermeister and Klipp, 2006, in which general rate laws, derived from standardized enzymatic mechanisms, are exploited to kinetically describe the fluxes of a metabolic reaction network, and multiple metabolic steady-state measurements are exploited to estimate the unknown kinetic parameters. Further mathematical details are deeply investigated, and necessary conditions on the amount of information required to solve the identification problem are given. Moreover, theoretical results for the parameter identifiability are provided, and symmetrical and modular properties of the proposed approach are highlighted when the global identification problem is decoupled into smaller and simpler identification problems related to the single reactions of the network. Among the advantages of the proposed innovative approach are (i) non-restrictive conditions to guarantee the solvability of the parameter estimation problem, (ii) the unburden of the usual computational complexity for such identification problems, and (iii) the ease of obtaining the required number of measurements, which are actually steady-state data, experimentally easier to obtain with respect to the time-dependent ones. A simple example concludes the paper, highlighting the mentioned advantages of the method and the implementation of the related theoretical result.

Limited Mechanistic Link Between the Monod Equation and Methanogen Growth: a Perspective from Metabolic Modeling.

ABSTRACTThe Monod equation has been widely applied as the general rate law of microbial growth, but its applications are not always successful. By drawing on the frameworks of kinetic and stoichiometric metabolic models and metabolic control analysis, the modeling reported here simulated the growth kinetics of a methanogenic microorganism and illustrated that different enzymes and metabolites control growth rate to various extents and that their controls peak at either very low, intermediate, or very high substrate concentrations. In comparison, with a single term and two parameters, the Monod equation only approximately accounts for the controls of rate-determining enzymes and metabolites at very high and very low substrate concentrations, but neglects the enzymes and metabolites whose controls are most notable at intermediate concentrations. These findings support a limited link between the Monod equation and methanogen growth, and unify the competing views regarding enzyme roles in shaping growth kinetics. The results also preclude a mechanistic derivation of the Monod equation from methanogen metabolic networks and highlight a fundamental challenge in microbiology: single-term expressions may not be sufficient for accurate prediction of microbial growth.IMPORTANCE The Monod equation has been widely applied to predict the rate of microbial growth, but its application is not always successful. Using a novel metabolic modeling approach, we simulated the growth of a methanogen and uncovered a limited mechanistic link between the Monod equation and the methanogen’s metabolic network. Specifically, the equation provides an approximation to the controls by rate-determining metabolites and enzymes at very low and very high substrate concentrations, but it is missing the remaining enzymes and metabolites whose controls are most notable at intermediate concentrations. These results support the Monod equation as a useful approximation of growth rates and highlight a fundamental challenge in microbial kinetics: single-term rate expressions may not be sufficient for accurate prediction of microbial growth.

Analisis Pajak Penghasilan sebelum dan setelah Undang-Undang Nomor 7 Tahun 2021 bagi WP Orang Pribadi

Research on income tax is still an interesting topic considering that the regulation is very dynamic with several policy changes, as on October 7, 2021, the government issued Law Number 7 of 2021 (referred to as the HPP Law) concerning the Harmonization of Tax Regulations. There are 6 (six) scopes (clusters) of regulatory changes, namely: 1) General Provisions and Tax Procedures (KUP), Income Tax (PPh), Value Added Tax (PPN), Voluntary Disclosure Program (PPS) Carbon Tax and Excise.
 The largest source of revenue is from income taxes, therefore the government continues to strive to increase the target of state revenues by various means, both tax intensification and extensification, such as sunset policy, tax amnesty, tax imposition for MSMEs with PP No. 46/2013, renewed by providing tax incentives with PP No. 23/2018. However, it is felt that this implementation still does not provide justice for taxpayers, so the 2021 HPP Law is stipulated which will take effect from the 2022 tax year.
 This research is a qualitative descriptive study. The data analysis technique is by describing and analyzing based on existing theory and in accordance with the reality that occurs in the field by using calculation illustrations, namely comparing the old regulations with the PPh Law, PP No. 23/2018 and the HPP Law. Techniques for collecting data using library research, data obtained from secondary data by extracting information from various sources, seminar materials (webinar), mass media, electronic media, various books, documents and relevant writings to develop research concepts and supported by literature review.
 This study focuses on the income tax cluster for individual taxpayers. The purpose of this study is to analyze Income Tax before and after Law Number 7 of 2021 is enacted. Is the tax burden paid by taxpayers more profitable before or after the enactment of the HPP Law.
 Based on the results of the illustrative analysis of the calculation that for individual taxpayers (as employees) with income up to Rp. 60 million, the tax burden paid is lower under the HPP Law than the PPh Law because it is only exposed to the first layer of tariffs. Income >Rp60 million – Rp5 billion, the tax burden is lower under the HPP Law than the PPh Law. But income above IDR 5 billion, the tax paid is higher under the HPP Law than the PPh Law. Limitation on gross turnover of <Rp 500 million a year with a tax rate of 0%, then MSMEs that are subject to tax are those with gross turnover > Rp 500 million a year. So that the MSME tax burden is lower. The government's policy regarding taxes with various regulations that have issued "goals" is aimed at encouraging taxpayers to carry out bookkeeping and business development because of these regulations the validity period is valid and the end of its application when it has been completed returns to the general rate (Law No.36 of 2008) concerning income tax in conjunction with Law No. 7 of 2021.
 The existence of a progressive rate breaket gives a sense of tax justice, namely taxes are charged to taxpayers according to their ability to pay. The higher the income, the higher the tax imposed. The implication of further research is to analyze the regulation of changes in tax laws which are the main points in the HPP Law.

Kinetics and mechanistics steps to the electron transfer reaction of peroxo-bridged binuclear cobalt(III) complex of succinimide by glycine in aqueous acidic medium

ABSTRACT. The kinetics and mechanistic steps to the electron transfer reaction of the peroxo-bridged binuclear cobalt(III) complex of succinimide [(suc)(en)2Co(O2)Co(en)2(suc)2+] hereafter called peroxo-bridged dicobalt(III) complex ‘[Co(O2)Co2+]’ by glycine have been carried out spectrophotometrically at λ = 420 nm and T = 26 ± 1 oC, [H+] = 1 x 10-3 M and ᶙ = 0.5 M (NaCl) in aqueous acidic medium. The reaction was found to be first order with respect to [Co(O2)Co2+] and [(Gly] and experimental data indicates a second-order overall. The reactions obeyed the general rate law: (d[Co(O2)Co2+]/dt) = (a +b)[H+])[Co(O2)Co2+][Gly]. Varying hydrogen ion concentration accelerated the reaction rate and shows first-order dependence while the reactions also affected by changes in the ionic strength of the reaction medium by giving a non-negative salt effect in the course of the reaction. Free radicals were not detected in the reactions. Spectroscopic investigation and Michaelis-Menten plots suggest the absence of intermediate complex formation. The experimental result obtained in this system is concluded in favor of the outer-sphere mechanism.
 
 KEY WORDS: Cobalt(III) complex, Kinetic, Electron transfer, Spectroscopic, Mechanistic steps, Michaelis-Menten, Glycine
 
 Bull. Chem. Soc. Ethiop. 2021, 35(2), 425-434.
 DOI: https://dx.doi.org/10.4314/bcse.v35i2.15

An epidemic model for non-first-order transmission kinetics.

Compartmental models in epidemiology characterize the spread of an infectious disease by formulating ordinary differential equations to quantify the rate of disease progression through subpopulations defined by the Susceptible-Infectious-Removed (SIR) scheme. The classic rate law central to the SIR compartmental models assumes that the rate of transmission is first order regarding the infectious agent. The current study demonstrates that this assumption does not always hold and provides a theoretical rationale for a more general rate law, inspired by mixed-order chemical reaction kinetics, leading to a modified mathematical model for non-first-order kinetics. Using observed data from 127 countries during the initial phase of the COVID-19 pandemic, we demonstrated that the modified epidemic model is more realistic than the classic, first-order-kinetics based model. We discuss two coefficients associated with the modified epidemic model: transmission rate constant k and transmission reaction order n. While k finds utility in evaluating the effectiveness of control measures due to its responsiveness to external factors, n is more closely related to the intrinsic properties of the epidemic agent, including reproductive ability. The rate law for the modified compartmental SIR model is generally applicable to mixed-kinetics disease transmission with heterogeneous transmission mechanisms. By analyzing early-stage epidemic data, this modified epidemic model may be instrumental in providing timely insight into a new epidemic and developing control measures at the beginning of an outbreak.

Insights into adsorption rate constants and rate laws of preset and arbitrary orders

Adsorption kinetics is of great significance in a variety of scientific and engineering applications, for example, removal of toxic metal ions from aqueous solution by adsorption. The pseudo-first-order (PFO) and pseudo-second-order (PSO) models are most popularly used and the latter is claimed applicable to most experimental adsorption data. The aim of the present study is to explain the reason behind the claim, provide a quantitative understanding of these preset-order models and general ones of arbitrary orders by rigorously deriving their relationship. It is proven that the ratios of the adsorption time required to reach 0.95 of the fractional surface coverage (or adsorption progress factor) to the half-time are around 4.32, 19, 133, and 1143 for the 1st, 2nd, 3rd, and 4th orders, respectively. For the general rate laws of nth order (n ≥ 2), t0.95/t0.5 ≈ 1/(0.1n−1 − 0.05n−1). Adsorption progress factor curves for different rate orders cross each other at the half-time point. When the time is shorter than the half-time, the adsorption progress factor increases with an increase in the rate order. However, this trend is opposite when the time passes over the half-time point. The higher the rate order, the longer the time is needed to reach equilibrium. We provide a guideline to determine the order of rate equation for describing the experimental data by deriving the relationship between the saturation time and the rate order. In addition, we propose a method and show how to employ it to validate the results obtained from the linearized PSO model and point out that the claimed wide applicabilityof the PSO might be caused by the ignorance or insufficient data points on the steep rising edge of the adsorption curve.

Density Functional Theory (DFT) approach for kinetic and thermodynamic study of reaction mechanism of copper (II) complex from 2-hydrazinyl-4,5-dihydro-1h-imidazole and anthracene-9-carbaldehyde

Abstract: A computational approach was employed to study the reaction mechanism for the copper (II) complex from 2-hydrazinyl-4,5-dihydro-1H-imidazole and anthracene-9-carbaldehyde at DFT (B3LYP) theory level. The reaction mechanism was proposed and found to have five elementary steps which involve intermediate elementary step and three transition state. The reaction mechanisms are observed to have bimolecular and unimolecular steps which give rise to two-step reaction pathway. The bimolecular step appeared to be rate determining step with highest energy barrier (2925.75kJ/mol) at the third transition state (TS3). The geometrical variations in bond length of the intermediate and the transition states during the course of the reaction was also studies which signified that transformation has occurred from the initial state to final state of product formation. The rate equation and general rate law for the reaction pathways were also established. The kinetics study shows that the reaction mechanism for the formation of copper (II) complex follows pseudo-first order and second order reaction with high correlation while the thermodynamic study indicates that the overall reaction is non-spontaneous and endothermic.

Immobilization of biosorbent in hydrogel as a new environmentally friendly fertilizer for micronutrients delivery

Abstract The aim of this work was to study the use of alginate-carboxymethyl cellulose-eggshell biocomposites as a material with controlled release of Cu2+ ions. The composition of biocomposites was optimized with Response Surface Methodology (5.0 wt% sodium alginate, 1.2 wt% carboxymethyl cellulose, 10.0 wt% eggshells). Physicochemical properties of biocomposites, kinetics and equilibrium of copper(II) ion sorption on structures were investigated. The General Rate Law model best described the kinetics data and the values of kinetic rate constants were 0.259, 0.358 min −1 for wet and dry capsules. The description of the sorption kinetics was also presented with the Weber-Morris diffusion model, which indicated a multi-stage process. The maximum sorption capacities for wet and dry biocomposites were 281 and 49 mg g−1. The composites presented a slow release of ions in the model soil solution (9 wt%/14 days). Studied biocomposites have a good potential as controlled release fertilizers fitting into the concept of sustainable development and precision agriculture. The new fertilizer formulations have the potential to by used as a new type of slow-release fertilizer that delivers micronutrient ions according to the plants uptake pattern with minimization of losses into the environment.

Hydrogel capsules with alfalfa as micronutrients carrier

The aim of this work was to study the properties of biocomposite based on sodium alginate and carboxymethyl cellulose with immobilized alfalfa as a material with controlled release of Cu2+ ions. Physicochemical (swelling, pHZPC) and sorption (kinetics, equilibrium) properties of the produced structures were investigated. Kinetic data were best described using a general rate law model, and the value of kinetic rate constant was 5.34 × 10−6. The sorption kinetics are also described using the Weber–Morris model, and the analysis revealed a three-step sorption. The maximum sorption capacity was determined using the Sips model and amounted to 9 mg g−1. Desorption of Cu2+ ions in soil solution (NaNO3 1 wt%) was carried out, and biocomposites released micronutrients in a slow way. The results showed that biocomposites with immobilized alfalfa are a very good material for potential applications in the agrochemical industry as a controlled released fertilizer.

An upscaled rate law for magnesite dissolution in heterogeneous porous media

Spatial heterogeneity in natural subsurface systems governs water fluxes and residence time in reactive zones and therefore determines effective rates of mineral dissolution. Extensive studies have documented mineral dissolution rates in natural systems, although a general rate law has remain elusive. Here we fill this gap by answering two questions: (1) how and to what extent does spatial heterogeneity affect water residence time and effectively-dissolving surface area? (2) what is the upscaled rate law that quantifies effective dissolution rates in natural, heterogeneous media? With data constraints from experimental work, 240 Monte-Carlo numerical experiments of magnesite dissolution within quartz matrix were run with spatial distributions characterized by a range of permeability variance σ2lnκ (0.5–6.0) and correlation length (2–50cm). Although the total surface area and global residence time (τa) are the same in all experiments, the water fluxes through reactive magnesite zones varies between 0.7 and 72.8% of the total water fluxes. Highly heterogeneous media with large σ2lnκ and long λ divert water mostly into non-reactive preferential flow paths, therefore bypassing and minimizing flow in low permeability magnesite zones. As a result, the water residence time in magnesite zones (i.e., reactive residence time τa,r) is long and magnesite dissolution quickly reaches local equilibrium, which leads to small effective surface area and low dissolution rates. Magnesite dissolution rates in heterogeneous media vary from 2.7 to 100% of the rates in the equivalent homogeneous media, with effectively-dissolving surface area varying from 0.18 to 6.83 m2 (out of 51.71 m2 total magnesite surface area). Based on 240 numerical experiments and 45 column experiments, a general upscaled rate law in heterogeneous media, RMgCO3,ht=kAe,hm1-exp-τaτa,rα, was derived to quantify effective dissolution rates. The dissolution rates in heterogeneous media are a function of the rate constants k being those measured under well-mixed conditions, effective surface area in equivalent homogeneous media Ae,hm, and the heterogeneity factor 1-exp-τaτa,rα. The heterogeneity factor quantify heterogeneity effects and depends on the relative magnitude of global residence time (τa) and reactive residence time (τa,r), as well as the shape factor α=5σlnκ2 of the gamma distribution for reactive residence times. Exponential forms of rate laws have been used at the micro-scale describing direct interactions among water and mineral surface, and at the catchment scale describing weathering rates and concentration-discharge relationships. These observations highlight the key role of mineral-water contact time in determining dissolution rates at different scales. This work also emphasizes the importance of critical interfaces between reactive and non-reactive zones as determined by the details of spatial patterns and effective surface area as a scaling factor that quantifies dissolution rates in heterogeneous media across scales.

Oxidations at Sulfur Centers by Aqueous Hypochlorous Acid and Hypochlorite: Cl+ Versus O Atom Transfer.

Sulfur-containing compounds are known to be susceptible to oxidation by aqueous HOCl, but the factors affecting the rates of these reactions are not well-established. Here we report on the kinetics of oxidation of thiosulfate, thiourea, thioglycolate, (methylthio)acetate, tetrathionate, dithiodiglycolate, and dithiodipropionate at 25 °C and 0.4 M ionic strength. These reactions obey the general rate law -d[OCl-]/dt = (kOCl-[OCl-] + kHOCl[HOCl])[substrate] with some exceptions: tetrathionate and the two disulfides undergo rate-limiting hydrolysis at high pH, and dithiodiglycolate has an additional term in the rate law that is second order in [substrate]. The reactions of HOCl are believed to have a Cl+ transfer mechanism, and in the case of thiosulfate the rate of hydrolysis of the ClS2O3- intermediate was determined. In the case of thiourea evidence was obtained for thiourea monoxide as a long-lived product. It is shown that sulfite and species with terminal sulfur atoms have kHOCl values in the vicinity of 1 × 109 M-1 s-1, while SCN- and thioethers react somewhat more slowly; tetrathionate, trithionate, and disulfides react much more slowly. Comparison of the rate constants with those for oxidation of these sulfur substrates by H2O2 and [Pt(CN)4Cl2]2- shows that HOCl reacts a few orders of magnitude more rapidly than [Pt(CN)4Cl2]2- and ∼9 orders of magnitude more rapidly than H2O2. Many of the kHOCl values are leveled by the high electrophilicity of HOCl. It is proposed that the kOCl- values correspond to oxygen-atom transfer mechanisms, as supported by LFERS (linear free energy relationships) relating these rate constants to those for reactions of H2O2 and [Pt(CN)4Cl2]2-.

Primary weathering rates, water transit times, and concentration‐discharge relations: A theoretical analysis for the critical zone

AbstractThe permeability architecture of the critical zone exerts a major influence on the hydrogeochemistry of the critical zone. Water flow path dynamics drive the spatiotemporal pattern of geochemical evolution and resulting streamflow concentration‐discharge (C‐Q) relation, but these flow paths are complex and difficult to map quantitatively. Here we couple a new integrated flow and particle tracking transport model with a general reversible Transition State Theory style dissolution rate law to explore theoretically how C‐Q relations and concentration in the critical zone respond to decline in saturated hydraulic conductivity (Ks) with soil depth. We do this for a range of flow rates and mineral reaction kinetics. Our results show that for minerals with a high ratio of equilibrium concentration ( ) to intrinsic weathering rate ( ), vertical heterogeneity in Ks enhances the gradient of weathering‐derived solute concentration in the critical zone and strengthens the inverse stream C‐Q relation. As decreases, the spatial distribution of concentration in the critical zone becomes more uniform for a wide range of flow rates, and stream C‐Q relation approaches chemostatic behavior, regardless of the degree of vertical heterogeneity in Ks. These findings suggest that the transport‐controlled mechanisms in the hillslope can lead to chemostatic C‐Q relations in the stream while the hillslope surface reaction‐controlled mechanisms are associated with an inverse stream C‐Q relation. In addition, as decreases, the concentration in the critical zone and stream become less dependent on groundwater age (or transit time).

Mathematical Formalism of Nonequilibrium Thermodynamics for Nonlinear Chemical Reaction Systems with General Rate Law

This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with $N$ species, $M$ reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs' macroscopic chemical thermodynamics under G. N. Lewis' kinetic law of entire equilibrium (detailed balance in nonlinear chemistry kinetics). In doing so, the equilibrium thermodynamics is then naturally generalized to nonequilibrium settings without detailed balance. The kinetic models are represented by a Markovian jumping process. A generalized macroscopic chemical free energy function and its associated balance equation with nonnegative source and sink are the major discoveries. The proof is based on the large deviation principle of this type of Markov processes. A general fluctuation dissipation theorem for stochastic reaction kinetics is also proved. The mathematical theory illustrates how a novel macroscopic dynamic law can emerges from the mesoscopic kinetics in a multi-scale system.

An experimental investigation of substituent effects on the formation of 2,3-dihydroquinazolin-4(1H)-ones: a kinetic study

The effect of different substituents on the kinetics of the reactions between 2-amino-benzamide and some of benzaldehyde derivatives have been spectrally investigated in the presence of formic acid. The proposed mechanism were challenged due to the determination of rate-determining step (RDS) and also, to obtain the general rate law of the reaction. For all substituents, the reactions followed the second-order kinetics and the partial orders of reactions were recognized with respect to each reactant. Electron withdrawing substituents on benzaldehyde ring increased the rate of reaction. Kinetic values (k and Ea) and associated activation parameters (ΔH‡, ΔG‡ and ΔS‡) of the reactions were determined. Both the Arrhenius and the Eyring equations were used to calculate activation energy. Comparison of magnitude of and T showed that the reactions were enthalpy controlled. Isokinetic plots for the reactions were plotted and linear relationship between and recognized that relative contribution of enthalpy and entropy to the overall free energy was the same in the reactions.

β-Lactoglobulin heat denaturation: A critical assessment of kinetic modelling

Bovine whey protein β-lactoglobulin (β-lg) will denature above 70 °C. Denaturation may contribute positively or negatively to food functionality, so it is important to control the degree of denaturation during milk processing. This work critically examined the kinetic modelling of β-lg denaturation in water, buffer or milk at 70–150 °C using the general rate law for a single-species reaction and the Arrhenius equation. Several published datasets, originally analysed in linearised form, were re-analysed with nonlinear regression, which preserves the error structure of data and estimates the precision of parameters. This work discusses statistical best practice for modelling the heat denaturation of β-lg, explores the criteria for using 2- or 3-parameter regression equations, and proposes new approaches for modelling the concentration- and temperature-dependence of denaturation rates. These new approaches improved the accuracy and precision of kinetic parameter estimates, and revealed new details of how solution conditions influence β-lg denaturation rates.

Iron oxidation kinetics and phosphate immobilization along the flow-path from groundwater into surface water

Abstract. The retention of phosphorus in surface waters through co-precipitation of phosphate with Fe-oxyhydroxides during exfiltration of anaerobic Fe(II) rich groundwater is not well understood. We developed an experimental field set-up to study Fe(II) oxidation and P immobilization along the flow-path from groundwater into surface water in an agricultural experimental catchment of a small lowland river. We physically separated tube drain effluent from groundwater discharge before it entered a ditch in an agricultural field. Through continuous discharge measurements and weekly water quality sampling of groundwater, tube drain water, exfiltrated groundwater, and surface water, we investigated Fe(II) oxidation kinetics and P immobilization processes. The oxidation rate inferred from our field measurements closely agreed with the general rate law for abiotic oxidation of Fe(II) by O2. Seasonal changes in climatic conditions affected the Fe(II) oxidation process. Lower pH and lower temperatures in winter (compared to summer) resulted in low Fe oxidation rates. After exfiltration to the surface water, it took a couple of days to more than a week before complete oxidation of Fe(II) is reached. In summer time, Fe oxidation rates were much higher. The Fe concentrations in the exfiltrated groundwater were low, indicating that dissolved Fe(II) is completely oxidized prior to inflow into a ditch. While the Fe oxidation rates reduce drastically from summer to winter, P concentrations remained high in the groundwater and an order of magnitude lower in the surface water throughout the year. This study shows very fast immobilization of dissolved P during the initial stage of the Fe(II) oxidation process which results in P-depleted water before Fe(II) is completely depleted. This cannot be explained by surface complexation of phosphate to freshly formed Fe-oxyhydroxides but indicates the formation of Fe(III)-phosphate precipitates. The formation of Fe(III)-phosphates at redox gradients seems an important geochemical mechanism in the transformation of dissolved phosphate to structural phosphate and, therefore, a major control on the P retention in natural waters that drain anaerobic aquifers.

Concentration-independent rate constant for biodiesel synthesis from homogeneous-catalytic esterification of free fatty acid

Dependence of the second-order rate constant (SRC) on the reactants’ concentration, for esterification of fatty acids, is found empirically in the published reports. Taguchi method is used to study dependency of the rate constant on temperature, reactants’ concentration, and catalyst loading for the synthesis of biodiesel from sulfuric acid-catalyzed esterification of free fatty acid (FFA) with methanol. On the basis of general literature on dependency of rate constant on reactants’ concentration and the esterification-rate determining step, concentration term embedded in the units of SRC has been identified as catalyst concentration. Accordingly SRC has been modified to include the catalyst concentration in the rate law, which is consistent with the general mass-action rate law reported by Blum and Luus (1964) and Pekař (2011). Analysis of the modified rate constant showed it to be independent of the reactants’ concentration. It is thus named as 'concentration independent rate constant (CIRC)'. The predictions of kinetics of the esterification of FFA are better using CIRC than other commonly used rate forms. The modified rate constant is shown to be equivalent to Brønsted–Bjerrum relation. Moreover, the modified rate constant is more general than the reported ones for esterification of fatty acids and it predicts kinetics well over a wide range of reaction parameters.