Reaction Equations Research Articles

Development of a self-test for undergraduate chemistry students: how do students solve tasks on basic content knowledge?

Abstract In this paper we describe the development of a self-test on content knowledge as one element of a digital learning environment. The self-test on prior knowledge consists of tasks in the categories Periodic Table of Elements, chemical bonding, chemical formulas, and chemical reactions (reaction equations and reaction mechanisms). For the study, tasks from all topics have been used in a paper-pencil multiple-choice and multiple response test on the task at hand and an accompanying questionnaire with closed and open items. The results of the study show that the students rated the tasks as suitable. Comments for improving the tasks regarding the wording or the design were implemented. Because of students’ lack of understanding regarding some of the technical terms, a glossary and games will be added to the digital learning environment. Many students overestimated their knowledge and their competences, therefore the self-test in the learning environment will include feedback to ensure that the students can improve their content knowledge and its application.

BioModME for building and simulating dynamic computational models of complex biological systems.

Molecular mechanisms of biological functions and disease processes are exceptionally complex, and our ability to interrogate and understand relationships is becoming increasingly dependent on the use of computational modeling. We have developed "BioModME," a standalone R-based web application package, providing an intuitive and comprehensive graphical user interface to help investigators build, solve, visualize, and analyze computational models of complex biological systems. Some important features of the application package include multi-region system modeling, custom reaction rate laws and equations, unit conversion, model parameter estimation utilizing experimental data, and import and export of model information in the Systems Biology Matkup Language format. The users can also export models to MATLAB, R, and Python languages and the equations to LaTeX and Mathematical Markup Language formats. Other important features include an online model development platform, multi-modality visualization tool, and efficient numerical solvers for differential-algebraic equations and optimization. All relevant software information including documentation and tutorials can be found at https://mcw.marquette.edu/biomedical-engineering/computational-systems-biology-lab/biomodme.php. Deployed software can be accessed at https://biomodme.ctsi.mcw.edu/. Source code is freely available for download at https://github.com/MCWComputationalBiologyLab/BioModME.

A numerical method for singularly perturbed convection–diffusion–reaction equations on polygonal meshes

A numerical method for singularly perturbed convection–diffusion–reaction equations on polygonal meshes

Unconditionally Positive, Explicit, Fourth Order Method for the Diffusion- and Nagumo-Type Diffusion–Reaction Equations

Unconditionally Positive, Explicit, Fourth Order Method for the Diffusion- and Nagumo-Type Diffusion–Reaction Equations

First principle based rate equation (1pRE) for reduction kinetics of Fe2O3 with syngas in chemical looping

Chemical looping combustion (CLC) of solid fuel is a promising technology with inherent CO2 separation and low energy penalty for CO2 capture. Syngas is main intermediate species of solid fuel conversion in CLC, the reduction kinetics of oxygen carriers with syngas play a crucial role in CLC systems. However, the current research obtains the reaction rate constants by fitting the apparent models with the experimental data, and cannot explain the reduction kinetics behavior from a microscopic level. It remains a challenge to compute the reduction kinetics of oxygen carriers with syngas directly from first-principles density functional theory (DFT) without fitting experimental data. This study proposes a first-principle-based rate equation (1pRE) theory and integrates it into the random pore model (RPM) to predict the kinetics of Fe2O3 reduction by syngas in CLC. The developed 1pRE theory utilizes DFT calculations to search for reaction pathways and energy barriers of elementary reactions. Then the DFT data are introduced into the statistical mechanics partition function and transition state theory (TST) to calculate the reaction rate constants. Microkinetic rate equations of elementary reactions occurring at the surface scale are developed to describe the change of surface coverage of different surface species. The 1pRE theory is integrated into the RPM to account for the influence of particle-scale structural changes on the overall conversion rate during the reduction process. The theory can predict the reduction kinetics of oxygen carriers without fitting experimental data and establishes a connection between microscopic insights and macroscopic phenomena. The accuracy was validated by experimental data of Fe2O3 oxygen carriers obtained from the thermogravimetric analyzer (TGA) in the atmosphere of syngas. The developed 1pRE predicts the reduction kinetics of oxygen carriers accurately and can be used to optimize the design of oxygen carrier materials and the scale up of CLC reactors.

Local Stability, Period-Doubling and 1:2 Resonance Bifurcation for a Discretized Chemical Reaction System

We investigate a discrete counterpart of planar dynamical system of nonlinear differential equations induced by kinetic differential equations for a two-species chemical reaction. Chemical reactions exhibit a wide range of dynamical behavior. We show how the theoretical analysis provides insight into the potential behavior of chemical reaction systems, determining the areas of parametric space which indicate scenarios for local stability, then for one type of bifurcation co-dimension one and one type of bifurcation co-dimension two. Precisely, we prove the existence of period-doubling bifurcation and 1:2 resonance bifurcation also, by using the center manifold theorem and the technique of normal forms. All mathematical investigations are illustrated with numerical examples, bifurcation diagrams, Lyapunov exponents and phase portraits.

Mathematical analysis of urea amperometric biosensor with Non-Competitive inhibition for Non-Linear Reaction-Diffusion equations with Michaelis-Menten kinetics

This article examines a mathematical model for stable urea amperometric biosensors with non-competitive inhibition under homogenous conditions. The system is based on reaction and diffusion equations with a non-linear component associated with the Michaelis-Menten kinetics of the enzyme reaction. Theoretical findings in this study can be used to examine the impact of various factors, including the Michaelis-Menten constant and the Thiele modulus. The steady-state non-linear reaction–diffusion equations were solved using two effective and widely used analytical approaches, the Akbari-Ganji method (AGM) and the differential transform method (DTM). The generalized approximation analytical solution for the concentrations of the substrate, inhibitor, and product, as well as the current for the experimental values of the parameter, is developed. The current can also be used to analyze the resistance and sensitivity of biosensors. The digital simulation was carried out utilizing MATLAB software. The numerical results help to validate the analytical results. The impact of membrane thickness, maximum enzymatic rate, and substrate concentration on biosensor response was evaluated.

Development of Electronic Portfolio Assessment Instruments to Improve Students’ Creative Thinking Skills in Chemical Reaction Equations Materials

Development of Electronic Portfolio Assessment Instruments to Improve Students’ Creative Thinking Skills in Chemical Reaction Equations Materials

Analysis of Cleaning Power Using New Cleaning Kinetics and Interfacial Science Studies on Aquatic Toxicity of Surfactants.

Studies devised through the fusion of cleaning and environmental sciences can be summarized as follows: new cleaning kinetics applying a probability density function and a surface chemical approach to the aquatic toxicity of surfactants. Cleaning power analysis using the probability density functional method combines conventional cleaning kinetics using a first-order reaction equation with a risk analysis method using a probability density function. It is possible to analyze the cleaning mechanism from the obtained parameter values. It is also possible to determine whether the interaction between two different cleaning elements corresponds to a synergistic, additive, or offsetting effect. Studies on the aquatic toxicity of surfactants have focused on the surface tension at which surfactants exhibit toxicity, changes in toxicity due to water quality, and biodegradation, and the presence of adsorbed substances have been identified.

Numerical modeling of the working process in an oxygen-methane combustion chamber operating on gaseous fuel

A method for three-dimensional numerical modeling of the working process in the oxygen-methane combustion chamber of a heat engine operating on gaseous fuel is presented. The advantages and disadvantages of the method based on the gross reaction equation written for the stoichiometric ratio are considered. The vortex dissipation model is used as a combustion model, and the ideal gas model is used for the working body. A justification is given for the effects in the combustion chamber obtained as a result of modeling. The results of three-dimensional numerical modeling and thermodynamic calculations are compared. Recommendations are given for improving the design of the combustion chamber and increasing its effectiveness. Keywords heat engine, combustion chamber, vortex dissipation model, combustion, numerical modeling, thermodynamic calculation, gross reaction

Факторы, влияющие на базовые ставки центральных банков в контексте неопределенности экономической политики

The relevance of the research topic is determined by the current unstable state of the world economy and the increasing role of central banks, which have the ability to positively influence countries’ economic development. Central banks, when implementing monetary policy, adhere to a certain strategy and accepted methods, including using monetary policy rules. The aim of this study is to evaluate the Taylor rule linking the central bank’s benchmark interest rate, the inflation rate, and the deviation of a country’s economic development from its trajectory. Developing the Taylor rule, we add a factor to the central bank reaction equation that reflects the level of uncertainty. The econometric assessment is based on statistics for two countries, the USA and the Russian Federation, whose central banks currently adhere to different monetary policy regimes introduced at different times. Despite differences between the countries’ economies and central banks’ monetary policies, uncertainty-related indices have shown their significance.

Reaction mechanism and mechanical properties of SiC joint brazed by in-situ formation of Ti3SiC2

This study undertakes vacuum pressureless brazing of SiC ceramics with TiSi2 powder, achieving MAX bonding. Microscopic characterization elucidates the microstructural evolution of the joined seam across various brazing temperatures and durations. The formation process of Ti3SiC2 is detailed through thermodynamic and kinetic analyses. At 1550 ℃ for 30 min or 1600 ℃ for 15 min, the filler undergoes in-situ reaction with SiC, yielding a dense, continuous Ti3SiC2 (MAX) phase, with no other phases observed. This suggests that increased temperature reduces MAX synthesis time. However, prolonged brazing causes voids in the center of the joined seam. Si volatilization was key for Ti3SiC2 in-situ formation, and this reaction equation was proposed. Maximum average shear strength at room temperature is 127.15 MPa at 1550 ℃ for 30 min and 118.15 MPa at 1600 ℃ for 15 min.

Electronic Portfolio Assessment Instruments in Improving Students' Creative Thinking Skills

The objective of the study is to determine the stage of the process of developing electronic portfolio assessment instruments and obtain a valid and reliable electronic portfolio assessment instrument that can be used as an alternative effective assessment in improving students’ creative thinking on redox reaction materials. The research method employed was Research and Development (RD) with a 4-D development model: define, design, develop, and disseminate. The data sources for this study were obtained from chemistry education lecturers, chemistry teachers, and eleventh-grade students in one of the high schools in Bandung. The instruments used in this study were interview guidelines, instrument content validation sheet, task assessment observation sheet, creative thinking skills assessment task and rubric, portfolio assessment rubric, pre-test and post-test questions and rubrics on chemical reaction equations that have tested for validity. The developed electronic portfolio assessment instrument was realized in a task and assessment rubric based on 21st-century creative thinking indicators. The results reveal that the developed electronic portfolio assessment instrument has good quality because it fulfils the valid requirements with a CVR value of 1.00 and fulfils the reliable requirements with a Cronbach Alpha value of 0.702-0.982. Electronic portfolios can be used as one of the assessment tools for science learning. The developed electronic portfolio assessment instrument may promote students’ creative thinking on redox reaction material based on the N-Gain 0.72 with the high category and has good effectiveness based on the N-Gain 0.61 with the medium category. Based on the category of mastery learning, the effectiveness is 9.66%.

Rate Equations for Reversible Disproportionation Reactions and Fitting to Time-Course Data.

Integrated rate equations are straightforward to fit to experimental data to verify a proposed mechanism and to extract kinetic parameters. Such equations are derived for reversible disproportionation/comproportionation reactions with any set of initial concentrations. Extraction of forward and reverse rate constants from experimental data by fitting the rate law to the data is demonstrated for the disproportionation of 2,2,6,6-tetramethyl-1-piperidinyl-N-oxyl (TEMPO) under acidic conditions where the approach to equilibrium is observed.

Taguchi method for optimizing the cation exchange resin catalyzed esterification of oleic acid with ethanol and adsorption kinetics study

In this study, solid acid catalysts (cation exchange resins) were used to catalyze the esterification reaction of acidified oil and ethanol for the preparation of biodiesel. The catalyst was characterized by SEM, BET, XRD, and FTIR. The esterification reaction was studied under various conditions using one-way analysis. Process optimization was performed by the Taguchi method, revealing that the optimal conditions for maximum oleic acid conversion (91.63%) were a catalyst dosage of 20 wt%, ethanol/oleic acid molar ratio of 9:1, reaction time of 5 h, and reaction temperature of 80 ℃. In addition, the adsorption behavior of cation exchange resin (S-CER) on oleic acid and ethanol during the esterification process was investigated. The Freundlich and Langmuir adsorption kinetic models of the resin were also established. This study focused on the dynamic equilibrium of oleic acid and ethanol adsorption on the S-CER catalyst surface. The adsorption process was found to align better with the Freundlich isotherm equation. According to this equation, oleic acid's maximum adsorption capacity was found to be 371.24 mg/g. Lastly, a pseudo-primary kinetic equation for the esterification reaction was formulated, and the calculated activation energy for the reaction was 35.59 kJ/mol.

A computational approach to heat transfer and ablation in space capsule insulation

In this article, the heat transfers and ablation phenomena of thermal insulations utilized in manned space capsules are investigated. In this regard, by collecting and solving the equations related to ablation insulations, a computer program has been developed that is able to predict the thermal response of these insulations under various operating conditions. This approach considers mass and heat transfer equations in two-dimensional solid bodies. To solve these equations, finite volume method and implicit formulation for time dependence have been used. The reaction equation, written in the form of Arrhenius, is solved using the Runge-Kutta method, and the density and the flux of the gas produced at each step are obtained. Furthermore, a practical model with low computational requirements and execution time and execution time is presented to consider the regression rate based on determining the identifier for destroyed cells, charred cells, and virgin material. The research results demonstrate that increasing the thickness of the layers, the heat of decomposition and ablation, the intensity of the reaction, and reducing the thermal diffusion coefficient, density of char, and temperature of ablation enhance the efficiency of thermal insulation. Validation of the model with experimental results in silica-phenolic insulation reveals a good agreement between simulation and experimental observations. Additionally, it was shown that for a carbon-phenolic insulation with a thickness of 5 mm in the specified space capsule under the given conditions, the maximum recession rate is 1.9 mm at a maximum temperature of 1000 K and 4.9 mm at a maximum temperature of 1300 K.

Study of the kinetics of aviation oils thermal conversion under non-isothermal conditions

The paper discusses the results of a kinetic study of the thermal decomposition of MS-8P, TN-98, and TN-600 aviation oils under conditions of continuous heating at a constant rate of 5 K/min to a temperature of 1 073 K. An integral method was used to describe the reaction mechanism and determine the macrokinetic parameters. It has been established that, from a phenomenological point of view, the average reaction of aviation oils conversion under the experimental conditions corresponds to the reaction model described by the surface-limited reaction equation (MS-8P), the power law (TN-98) and the model described by the three-dimensional diffusion-limited reaction equation (TN-600). When dividing the averaged reaction into two reactions (the first is completed at a temperature of 550–600 K, the second at a temperature of 638–655 K), it is determined that the first reaction is described by the reaction equation of the 2nd order (MS-8P), the first order (TN-98) and the reaction equation of one-dimensional diffusion (TN-600), and the second the reaction equation of the first order (three types of oil). The activation energy of the first reaction was 99 kJ/mol (MS-8P), 145.6 kJ/mol (TN-98) and 57.4 kJ/mol (TN-600), the value of the pre-exponential factor was – 144 241 567 min–1 (MS-8P), 62 161 395 942 min–1 (TN-98) and 236.16 min–1 (TN600). The activation energy of the second reaction is 160 kJ/mol (MS-8P), 91.6 kJ/mol (TN-98) and 127.1 kJ/mol (TN-600), the pre-exponential factor is 8.81 ‧ 1011 min–1 (MS-8P), 1.26 ‧ 104 min–1 (TN-98) and 2.04 ‧ 108 min–1 (TN-600). It is shown that the use of these values of the activation energy and the pre-exponential factor leads to agreement between the calculated values of the degree of decomposition of the studied oil samples and the experimental ones in the range of values of the degree of decomposition from 0 to 1.

On the Constitutive Equations for Coupled Flow, Chemical Reaction, and Deformation of Porous Media

AbstractDeformation, chemical reactions, fluid flow in geological formations, and many engineering materials are coupled processes. Most existing models of chemical reactions coupled with fluid transport assume the dissolution‐precipitation process or mineral growth in rocks. However, these models have limitations, such as predicting restricted reaction extent due to pore clogging or disregarding porosity changes resulting from mineral growth. Recent studies indicate mineral replacement involves coupled dissolution‐precipitation, maintaining porosity while altering the solid volume. This has multiple practical implications for natural geological processes and within petroleum and environmental engineering. We present a novel model for reaction‐driven mineral expansion that preserves porosity and allows solid volume change. First, we look at fluid‐rock interaction at the pore scale and derive effective rheology of a reacting porous media. On a larger scale, we adopt a two‐phase continuum medium approach to investigate the coupling between reaction, deformation, and fluid flow. Our micromechanical model based on observations assumes that rock or cement consists of an assembly of solid reactive grains, initially composed of a single, pure phase. The reaction occurs at the fluid‐solid contact and progresses into the solid grain material. We approximate the pores and surrounding solid material as an idealized cylindrical shell to simplify the problem and obtain tractable results. We derive macroscopic stress‐strain constitute laws that account for chemical alteration and viscoelastic deformation of porous rocks. Our model explains the possibility of achieving a complete reaction, preservation of porosity during chemical reactions, and dependence of mechanical rock properties on fluid chemistry.

Hyena neural operator for partial differential equations

Numerically solving partial differential equations typically requires fine discretization to resolve necessary spatiotemporal scales, which can be computationally expensive. Recent advances in deep learning have provided a new approach to solving partial differential equations that involves the use of neural operators. Neural operators are neural network architectures that learn mappings between function spaces and have the capability to solve partial differential equations based on data. This study utilizes a novel neural operator called Hyena, which employs a long convolutional filter that is parameterized by a multilayer perceptron. The Hyena operator is an operation that enjoys sub-quadratic complexity and enjoys a global receptive field at the meantime. This mechanism enhances the model’s comprehension of the input’s context and enables data-dependent weight for different partial differential equation instances. To measure how effective the layers are in solving partial differential equations, we conduct experiments on the diffusion–reaction equation and Navier–Stokes equation and compare it with the Fourier neural operator. Our findings indicate that the Hyena neural operator can serve as an efficient and accurate model for learning the partial differential equation solution operator. The data and code used can be found at https://github.com/Saupatil07/Hyena-Neural-Operator.

Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations

An arbitrary order finite difference method for solving non-linear convection Diffusion Reaction equations in curved boundary domains with Cartesian grid is proposed. Ghost points' values are determined with the Reconstruction Off-Site Data based on a polynomial interpolation using the least square method with constraints to enforce the boundary conditions. We propose a second-, fourth-, and sixth-order schemes for linear non-constant coefficients problem in both the conservative and non-conservative scalar equations. Extensions to non-linear scalar problems and systems are then implemented while preserving the optimal orders. Numerical simulations are carried out to provide evidence about the convergence order and the stability of the method.