Reaction Rate Equation Research Articles

Mathematical Model for the Kinetics of Heterogeneous Reaction of Carbonates Dissociation in the Process of Roasting in the Presence of Temperatures Gradients in Phosphate Raw Material

The paper deals with the investigation of the parameters for the structural and kinetic rate equation of the carbonates dissociation reaction, in accordance with the obtained results of the nonisothermic experiment, in the conditions of gradient temperature presence in the investigated samples. The most significant is the study of physicochemical transformations kinetic laws, which degree of completeness effects the quality of intermediate products directly, that is decarbonization and sintering. The main part of the process, when phosphorites are heated, takes place in a solid phase. The feature of topochemical reactions is their localization in the aria between a solid phase surface of the initial substance and the reaction products. This surface is formed and changed, as a result of chemical and power technological process for roasting, determining the dependence of the reaction rate on time. The method of thermal analytical experiments is used. The reverse kinetic problem is solved in the temperatures range of the chemical–technological process for roasting phosphate raw materials on conveyor indurating machines. The authors propose a method of approximate calculation for the parameters of kinetic equations which allows to reduce errors, caused by the heat exchange processes in a measuring cell, significantly. The obtained results and their accuracy are suitable for the practical application.

Abstract PO-062: Why drug and radiation combination synergism or antagonism can be quantitatively determined with the mass-action law based pharmacodynamics equation, algorithm and computer simulation

Abstract Biological system-analysis by the mass-action law with biophysical, biochemical and mathematical induction-and-deduction leads to the derivation of >300 reaction rate equations. These derived equations led to general biodynamics/pharmacodynamics and bioinformatics (MAL-BD/PD/BI) general paradigms for “Dose” and “Effect”. 1. Median-Effect Eq. (MEE) for single drug or entity, regardless, in vitro, in animals or in human, where Dm and m values signify the median-effect dose “potency” and “shape” (dynamic order), respectively. 2. Combination Index Eq. (CIE), where CI<1, =1, and >1 indicates synergism, additive effect and antagonism, respectively, in combinations. Since all terms in MEE and CIE are relativity ratios, they are dimensionless quantities. Therefore, MEE and CIE are fundamental MAL-BD/PD/BI/CI principle independent to entity’s physical nature (chemicals, biologicals, natural products, radiation, liquid, or gas); independent to unit (ug, nM, mg/ml. mg/kg, IU, rad or multiples of infection); and independent to mode or mechanism of actions (competitive, noncompetitive, uncompetitive, sequential, ordered, ping-pong or random). Comprehensive details are available in Chou TC, Pharmacol. Rev. 58: 621-681, 2006 (specifically on p.655 and p.660), It also discussed in Chou, Integrative Biol. 3: 548-559, 2011, and many more recent papers on chemotherapy and radiation therapy combinations, as indicated in Google scholars. The above 2006 Chou article, as of January 12, 2021, has 3,835 citations in 1,054 biomedical journals internationally, encompassing nearly all disciplines in biomedical sciences. Citation Format: Ting-Chao Chou. Why drug and radiation combination synergism or antagonism can be quantitatively determined with the mass-action law based pharmacodynamics equation, algorithm and computer simulation [abstract]. In: Proceedings of the AACR Virtual Special Conference on Radiation Science and Medicine; 2021 Mar 2-3. Philadelphia (PA): AACR; Clin Cancer Res 2021;27(8_Suppl):Abstract nr PO-062.

КИНЕТИКА СЕЛЕКТИВНОГО ГИДРАЗИНОЛИЗА МАЛЕИНОВОЙ КИСЛОТЫ НА КИСЛОТНОМ КАТАЛИЗАТОРЕ

For the first time, kinetics and the mechanism of the reaction of hydrazinolysis of maleic acid in the presence of cation exchanger resin KU-2-8 in H-form have been studied. The experiments were carried out in a static system in a thermostat glass reactor. It was found that cation exchanger shows high catalytic activity in the studied process - maleic acid conversion was 93%, and maleic hydrazide yield was 90%. The conversion selectivity of maleic acid to maleic hydrazide was 97,8%. The reaction rate was determined from the accumulation of maleic hydrazide. The apparent reaction rate constant (k) was calculated from the second-order reaction rate equation. The effect of initial concentrations of maleic acid and hydrazine hydrate, the temperature on the reaction rate was studied. The first order of maleic acid and hydrazine hydrate is determined. Activation energy of the process found from the Arrhenius dependence is 32,1 kJ/mol. On the basis of kinetic and IR spectroscopic methods, a probable reaction mechanism involving polymer-bound hydrogen ions is proposed.

Model and simulation analysis of fire development and gas flowing influenced by fire zone sealing in coal mine

Fire zone sealing is an important approach to fire extinguishment and disaster relief. The study is aimed at investigating the distributions and evolutions of temperature and CH4 concentration fields during fire zone sealing and revealing the mechanism of sealing-induced gas explosion accidents. Firstly, the models of O2 consumption, heat production and products of coal combustion were constructed based on the Arrhenius equation of chemical reaction rate, and meanwhile the mathematical models of gases and temperature field in the sealing process were established. Besides, the variations of airflow volume, temperature and CH4 and O2 concentrations during and after fire zone sealing were numerically simulated. The results show that in the sealing process, the airflow into the fire zone gradually decreases, and air begins to flow out through the air intake at the later stage. After the completion of fire zone sealing, the temperature at fire source decreases briefly, then gradually increases and finally goes down. The temperature in the whole fire zone, except the fire source, also decreases first, then rises and finally falls gradually. The sealing raises the overall CH4 concentration in the fire zone, and the CH4 concentration at the air return side is always higher than that at the air intake side. When the sealed flow field gradually recovers to a steady flow field, the CH4 concentration goes up slowly under the influence of CH4 release. The research is of great significance for grasping the development of mine fire and the evolution of flow field in the sealing process and can provide guidance for the prevention of gas explosion accidents.

Contributions to the kinetics of the iodide–iodate test reaction for micromixing time calculation with extended incorporation models

In order to characterize the efficiency of micromixing in chemical reactors, Villermaux used a borate buffer in the reaction system named after him. For micromixing time calculations, kinetic data of the Dushman reaction are essential. The choice of the acid and the influence of the salt on the reaction rate constant has led to a debate on the kinetics of the Dushman reaction. In the present work, a comprehensive kinetic study was performed to obtain the reaction rate equation of the Dushman reaction. A fifth-order rate equation with the partial reaction rate orders: H+2;IO3-1;I-2 could be confirmed.Furthermore, the influence of ionic strength μ was investigated using sodium perchlorate as the ion source. The reaction rate constant k for the Dushman reaction was determined as a function of the ionic strength k=k0·fDushmanlogfDushman=-1.93(±0.06)·μ1+μ+0.40±0.02·μ.The impact of the newly obtained reaction rate constant on micromixing time calculations was investigated using the incorporation model. It could be shown, that micromixing times can differ by a power of ten depending on the chosen reaction rate constant. Moreover, an extension of the incorporation model for sulphuric acid is provided, which includes the acid dissociation constants. This model unites the obtained reaction rate constant from this work and the equilibrium reactions of sulphuric acid. Micromixing experiments can now be performed independent of the acid choice, since similar micromixing times are calculated.According to the CLP Regulation and REACH, boric acid is classified as toxic for reproduction. Therefore, non-toxic chemicals have recently been preferred which has led to the implementation of a phosphate buffer by Pinot et al. and Baqueiro et al. This has risen questions about the definition of the segregation index and micromixing time calculations. Comprehensive micromixing time calculations have been performed with an extended incorporation model for a phosphate buffer. The results suggest that both HPO42- and H2PO4- species only take partially part in the acid–base reaction.

Kinetic analysis of the spontaneous thermal polymerization of acrylic acid

Acrylic acid is a monomer that has been responsible for a number of severe explosions worldwide as a result of thermal runaway. The present work was intended to lead to an improved understanding of the kinetics of the thermal polymerization and Michael addition reaction (MAR) of acrylic acid. Sealed cell differential scanning calorimetry was carried out, and the kinetics of the thermal polymerization of acrylic acid were assessed on the basis of the model-free Friedman method. In addition, microcalorimetry using a Thermal Activity Monitor IV apparatus was conducted to determine the kinetic parameters for the MAR. The rate constant for the MAR was found to be k (s−1) = 3.45 × 105 × exp (− 9.48 × 103/T (K)), while the activation energy was 78.8 kJ mol−1. The progress of the MAR was fitted with an n-order reaction model, and the reaction order as well as the rate constant was determined to be linearly proportional to temperature. By employing a modified n-order reaction model in which the reaction order was a linear function of temperature, we obtained a reaction rate equation for the MAR that closely reproduced the experimental results over a wide temperature range.

Reaction Kinetics of Ammonium Removal from Cow Urine by Struvite Formation Using a Baffle Column Reactor

Reaction kinetics is the study of reaction rates and reaction mechanisms, which refers to determining the order and reaction rate constants of a given material. This study will examine the kinetics of the reaction of ammonium removal from cow urine by struvite formation. Cow urine contains NH 4 which is high enough so that it can be used as material for the manufacture of struvite. Struvite (MgNH 4 PO 4 .6H 2 O) is a white crystalline material consisting of magnesium, ammonium, and phosphate in equimolar. The experiment was conducted with a temperature setting of 25, 35, 45, and 65 ËšC. The flow rates used were 8.8, 11, 14.67, 22, and 44 mL/min. The process of making struvite was carried out by crystallization at pH 9, molar ratio of 3:1:1, also air rate of 0.4 L/min. The study carried out following the first order with the best conversion was 0.7797 at 8.8 ml/min and 65 ËšC. The activation energy is 3123.82 J/mol and the collision frequency is 0.0379. The equation of reaction rate k = 0.0379 e -375,73/T (K -1 ).

Three-component reaction involving isoquinoline and dimethyl acethylenedicarboxylate in the presence of indole: Theoretical and experimental investigations of the reaction mechanism

The reaction kinetics among isoquinoline, dimethyl acetylenedicarboxylate, and indole (as NH-acid) were investigated using ultraviolet (UV) spectrophotometry. The reaction rate equation was obtained, the dependence of the reaction rate on different reactants was determined, and the overall rate constant ( kov) was calculated. By studying the effects of solvent, temperature, and concentration on the reaction rate, some useful information was obtained. A logical mechanism consistent with the experimental observations was proposed. Also, comprehensive theoretical studies were performed to evaluate the potential energy surfaces of all structures that participated in the reaction mechanism. Finally, the proposed mechanism was confirmed by the obtained results and the probable and logical reaction paths and also a correct product configuration were suggested based on the theoretical results.

New Thermonuclear Reaction Rate Equations for Radiative Neutron Capture

The radiative neutron capture reaction rates have been studied at very low energies which are of interest for nuclear astrophysics. The rates for many of these reactions have remained independent of temperature so far. The temperature dependence of the thermonuclear reaction rates have been explored within the statistical model. Apart from the compound nuclear contribution, the pre-equilibrium as well as the direct effects have been taken into account. The corresponding Maxwellian-averaged thermonuclear reaction rates of relevance in astrophysical plasmas at temperatures in the range from 10$^6$ K to 10$^{10}$ K have been calculated. Analytical expression as a function of $T_9$ has been provided for $^6$Li(n,$\gamma$)$^7$Li by fitting the calculated reaction rate.

The Mini Blast Furnace Process: An Efficient Reactor for Green Pig Iron Production Using Charcoal and Hydrogen-Rich Gas: A Study of Cases

The mini blast furnace process is an efficient route to produce pig iron based on the burden with granulated charcoal. New, improved technologies have recently been introduced in the mini blast furnace process, such as pulverized charcoal and gas injections, new burden materials, and peripheral devices that improve the overall process efficiency. In this paper, we revise the new injection possibilities and discuss new aspects for further developments. The analysis is carried out with a comprehensive multiphase multicomponent mathematical model using mass, momentum, and energy conservation principles coupled with the rate equations for chemical reactions, multiphase momentum, and heat exchanges. We analyze new technological possibilities for the enhancement of this process as follows: (i) a base case of pulverized charcoal injection with industrial data comparison; (ii) a set of scenarios with raceway injections, combining pulverized charcoal with hydrogen-rich fuel gas, replacing granular charcoal in the burden; (iii) a set of scenarios with hydrogen-rich gas injection at the shaft level, replacing reducing gas in the granular zone of the reactor; and the possible combination of both methodologies. The simulated scenarios showed that a considerable decrease in granular charcoal consumption in the burden materials could be replaced by combining a pulverized charcoal injection of 150 kg/tHM and increasing rich gas injections and oxygen enrichment values, decreasing the specific blast injection and granular charcoal. The productivity of the mini blast furnace process was increased for all scenarios compared with the reference case. We review the aspects of these operational conditions and present an outlook for improvements on the process efficiency.

Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures

We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary Gamma -convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.

Kinetics of Sequential Protopectin Degradation in a Flowing Reaction Solution

The degradation mechanism of protopectin was studied using beet pulp, pomelo albedo, and sunflower calathides as examples. Experimental data were processed according to sequential irreversible reactions (PP → MG → PS) occurring in a flowing reaction solution. This approach enabled evaluation of the main kinetic parameters of the reduced equation and calculation of the reaction rate constant and activation energy of secondary phytomass protopectin degradation. The results made it possible to regulate the production of pectinic polysaccharides with given physicochemical parameters.

Mechanism and kinetic analysis of vacuum aluminothermic reduction for preparing TiAl intermetallics powder

This work investigates the mechanism and kinetics of an aluminothermic reduction process using Na2TiF6 as the raw material for preparing TiAl alloy powder. The experiment was carried out at 1100 °C with a 3:7 M ratio of Na2TiF6 to Al. Quasispherical TiAl alloy powder with an oxygen content of 0.32% could be achieved after vacuum ball milling of the reduction product. The thermal analysis results demonstrated that the aluminothermic reduction reaction was an exothermic process. Moreover, the kinetic parameters and the equation for the exothermic reaction rate of the reduction process were calculated by a thermoanalytical technique. According to XRD, SEM, and EDS analyses, the reduction mechanism and the evolution process of the products were discussed. Experimental evidence indicated that TiAl3 and TiF3 could be generated as intermediate products during reduction. TiAl could be produced through further reduction reactions between TiAl3 and TiF3.

Time Fractional Fisher-KPP and Fitzhugh-Nagumo Equations.

A standard reaction–diffusion equation consists of two additive terms, a diffusion term and a reaction rate term. The latter term is obtained directly from a reaction rate equation which is itself derived from known reaction kinetics, together with modelling assumptions such as the law of mass action for well-mixed systems. In formulating a reaction–subdiffusion equation, it is not sufficient to know the reaction rate equation. It is also necessary to know details of the reaction kinetics, even in well-mixed systems where reactions are not diffusion limited. This is because, at a fundamental level, birth and death processes need to be dealt with differently in subdiffusive environments. While there has been some discussion of this in the published literature, few examples have been provided, and there are still very many papers being published with Caputo fractional time derivatives simply replacing first order time derivatives in reaction–diffusion equations. In this paper, we formulate clear examples of reaction–subdiffusion systems, based on; equal birth and death rate dynamics, Fisher–Kolmogorov, Petrovsky and Piskunov (Fisher–KPP) equation dynamics, and Fitzhugh–Nagumo equation dynamics. These examples illustrate how to incorporate considerations of reaction kinetics into fractional reaction–diffusion equations. We also show how the dynamics of a system with birth rates and death rates cancelling, in an otherwise subdiffusive environment, are governed by a mass-conserving tempered time fractional diffusion equation that is subdiffusive for short times but standard diffusion for long times.

A novel chemo-mechanical model for fracture toughness of mortar under sulfate attack

It is widely believed that the mechanical properties of concrete structures gradually deteriorate in a corrosive environment. However, it has been observed that the fracture toughness of concrete strengthens during the initial stage of sulfate attack. With the increase in the corrosion time, the fracture toughness gradually weakens. The main reasons for this contrasting response are as follows: (1) The strengthening effect is caused by the continued hydration of concrete materials; (2) sulfate ions lead to delayed ettringite formation (DEF) in the pores of mortar, which causes filling and compaction effect during the early stage of corrosion and pore swelling during the later stage that damages the concrete structure. In this paper, the effect of sulfate corrosion on the fracture toughness of mortar is investigated, and the relationship between strengthening-weakening effects of fracture toughness and corrosion time is obtained. Subsequently, the displacement and strain in the fracture process zone are analyzed by digital image correlation, which clarifies the critical influence of solution concentration and corrosion time on the mortar. Finally, based on the chemical reaction rate equations of DEF, a novel chemo-mechanical model of fracture toughness is established for mortar under sulfate attack.

Heavy oil hydrocracking kinetics with nano-nickel dispersed in PEG300 as slurry phase catalyst using batch reactor

The kinetics of slurry phase heavy oil hydrocracking with nickel nanoparticles dispersed in PEG300 as the slurry phase catalyst was investigated. Colloidal metal nanoparticles were synthesized using a chemical reduction method. Catalytic evaluations were performed in a batch reactor with 7.0 MPa H2 and varying temperatures (310–370 °C) and reaction times (4–72 h). A five-lump kinetic model was used to obtain kinetic parameters using the R software with the Levenberg-Marquardt nonlinear least-squares algorithm. The order of the residue hydrocracking reaction rate equation was 2.5. The activation energies were determined, and the calculated product compositions were in agreement with the experimental values (<5%). The residue exhibited high selectivity towards naphtha. High residue conversion was accomplished, even at low reaction times.

A step forward on NETmix reactor for heterogeneous photocatalysis: Kinetic modeling of As(III) oxidation

This study focuses on the kinetic modeling of As(III) oxidation by heterogeneous TiO2 photocatalysis, assisted by ultraviolet light emitting diodes, using a static mixer – NETmix reactor – in two different configurations: back-side illumination and front-side illumination. First, preliminary experimental assays were performed varying the load of TiO2-P25 and the incident radiation flux for each configuration, and the observed pseudo-first-order kinetic constants were obtained. A model was built based on a mechanistic reaction pathway for As(III) oxidation, taking into account the radiation absorption by the catalytic surface. Three kinetic parameters were estimated considering the solution of the material balance for the existing chemical species and the evaluation of the radiation field inside the reactor by solving the Radiative Transfer Equation. The incident radiation flux was determined at every point on the catalyst surface. It was concluded that the initial reaction rate per unit area is similar in both reactor configurations. However, when compared per unit volume, front-side illumination exhibits twice the reaction rate as the back-side illumination. Moreover, according to the obtained parameters, the front-side configuration showed higher As(V) adsorptivity when compared to the back-side. In addition, the dependence of the reaction rate upon the incident radiation level proved to be the same regardless of the illumination mechanism. Nevertheless, considering that the radiation field is not uniform, the complete expression of the dependence with the local incident radiation flux in the reaction rate equations must be used. The results obtained with the model predictions were contrasted with the experimental data regarding As(III) concentrations and showed a good agreement for both reactor configurations.

Tuning smaller Co3O4 nanoparticles onto HZSM-5 zeolite via complexing agents for boosting toluene oxidation performance

Tunable smaller Co3O4 nanoparticles onto HZSM-5 zeolites were prepared by the addition of various rich-hydroxyl complexing agents. The physicochemical properties including the crystalline size, surface dispersion, reducibility and acidity of Co3O4 active component and the catalytic performance for toluene oxidation were extensively investigated by numerous characterization techniques and catalytic experiments. It was found that the smaller particle size and the better dispersion of Co3O4 nanoparticles on HZSM-5 zeolite after complexing agents addition lead to remarkable reducibility enhancement and higher abundance of surface acidity, which were proved to be the key factors for the elevation of toluene oxidation activity. Among all, the catalyst with β-cyclodextrin as the complexing agent (designated as Co3O4/HZSM-5/β-CD) exhibited not only the optimum catalytic activity, but also high catalytic stability under dry condition and good regeneration capacity under humid conditions. Based on the results of reaction order determination, a first-order reaction rate equation with respect to toluene concentration was derived under rich-oxygen atmospheres, which was in good accordance with the conclusion in previous research.

Thermal Stability and Thermodynamics in the Process of Synthesising 1, 3-dimethylurea

The present work aims to study the thermal stability and thermodynamics in the process of synthesizing 1, 3-dimethylurea. The HPLC spectrograms were used to study the impacts of reaction time and temperature on the thermal behaviour of the ammonolysis reaction system. Rate equation of the ammonolysis reaction can be summed up as c(t) = 1016.24*e-(t/47.9403) +16.1935. Thermal stability curve also can be determined. Experimental results revealed that the process of synthesizing 1, 3-dimethylurea was of pseudo-first-order reaction kinetics and k value was 0.0163 min-1. Thermodynamics results indicated that enthalpy was -1.92 kJ/mol, Gibbs free energy was -8.51 J/mol, and entropy was 15.96 J/mol*K. The reaction was an exothermic, spontaneous and entropy increasing process. Based on thermal stability and thermodynamics study, synthesis of 1, 3-dimethylurea was unfavourable at higher temperature as well as long reaction time.

Phase behaviors and curcumin encapsulation performance of Gemini surfactant microemulsion

Protection of environment-sensitive bioactive component is an important issue in biological and pharmaceutical applications. The aim of this study is to provide an alternative for the solubility enhancement and the controlled release of curcumin by encapsulation with the microemulsion formed with Gemini surfactant. Pseudo-ternary phase diagrams for the surfactant/cosurfactant/oil/water (S/C/O/W) systems are obtained and the phase behaviors are systematically investigated. Less amount of water can be solubilized in the microemulsion containing alcohol with a longer carbon chain or surfactant with a longer spacer. A lower mass ratio of S/C or a higher temperature also leads to a smaller microemulsion area. As a representative, the oil-in-water microemulsion of the 14-4-14/1-propanol/n-heptane/water system is applied to encapsulate curcumin. High drug loading capacity and encapsulation efficiency are achieved higher than 7 mg·g−1 and 99%, respectively. Moreover, the in vitro release data are adequately described by the first-order reaction rate equation at both fast and mild release stages. A higher content of oil causes a slower release and a lower stable concentration for the packaged curcumin. The free radical scavenging activity is somewhat reduced when compared with that of free curcumin in ethanol due to gradual release.