Initial Reaction Rate Constants Research Articles

SAWI TRANSFORMATION FOR SOLVING A SYSTEM OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS

There are many problems in nature whose solutions are obtained through mathematical concepts. One of the most common mathematical concepts is a mathematical concept that is classified under initial value problems, such as a system of linear ordinary differential equations equipped with initial values. One tool that can solve the initial value problem is the Sawi transformation. This article describes the study of the initial value problem as a system of linear ordinary differential equations and its solution using the Sawi transformation. In addition, as part of applying the resulting theory, 2 (two) case examples are given (a first-order chemical reaction system with three certain chemicals and a mass-spring system with forced motion) to be solved using the Sawi transformation. So that problem solving can be interpreted and easily understood, in the 2 (two) case studies discussed and focused on the concentration of the chemical reactants, simulations were carried out for several different initial values and reaction rate constants. Compared to other methods (Laplace transform), the results obtained from using the Sawi transformation for the cases discussed show that the analytical solutions for the selected initial values have similar solutions.

Theoretical Study on the Mechanisms, Kinetics, and Toxicity Evaluation of OH-Initiated Atmospheric Oxidation Reactions of Coniferyl Alcohol

In this paper, we investigated the mechanisms, kinetics, and toxicity evaluation of the OH-initiated reaction of coniferyl alcohol (4-(3-hydroxy-1-propenyl)-2-methoxyphenol) in the atmosphere using theoretical calculations. The initial reaction of coniferyl alcohol with OH radicals had two pathways, H-abstraction and OH-addition reactions. The total reaction rate constants were 2.32 × 10−9 cm3 molecule−1 s−1 (in gas-phase) and 9.44 × 109 s−1 M−1 (in liquid-phase) for the preliminary reactions of coniferyl alcohol with OH radicals at 298 K, respectively, and the half-lives of the total reaction (including all initial H-abstraction and OH-addition reactions) of coniferyl alcohol with OH radical in the atmosphere, urban and remote clouds were 8.3 × 10−2 h, 5.83 × 103 h and 9.27 × 102 h, respectively. The temperature had a strong and positive influence on the initial reaction rate constant. The branching ratios of H-abstraction and OH-addition reactions were 3.68% and 97.69%, respectively, making the OH-addition reactions become dominant reactions. The ecotoxicity evaluation revealed that the toxicity levels of coniferyl alcohol and its products were similar and non-toxic. However, all these products have developmental toxicity, with most of them having no mutagenicity. Therefore, further attention should be paid to the oxidation process and product toxicity evaluation of coniferyl alcohol in the atmosphere.

An amphiphilic nitrogen-doped graphene prepared by ammonia cold plasma and its supported platinum nanocatalyst for aqueous-phase hydrogenation of cinnamaldehyde

Herein, a nitrogen-doped graphene (NPGR) with amphiphilic surface was efficiently synthesized by radio-frequency cold plasma under low vacuum, using ammonia as plasma source. NPGR supported platinum nanocatalyst (Pt/NPGR) was then prepared for aqueous-phase hydrogenation of cinnamaldehyde (CAL) and effects of nitrogen doping on the reaction were investigated. Results indicated the formation of a Pickering emulsion catalytic system, exhibiting the high catalytic performance. Apparent initial reaction rate constant (k) over it arrived at 1.07 h−1, higher than that over Pt catalysts supported on pristine graphene (Pt/ GR, 0.62 h−1) and graphene oxide (Pt/GO, 0.15 h−1), respectively. On the other hand, the selectivity to cinnamyl alcohol kept high (84%) at 95% CAL conversion. In addition, the catalyst showed good recyclability for the reaction. The high catalytic performance of Pt/NPGR in aqueous-phase CAL hydrogenation was thanks to the enhanced surface properties of graphene after doping a small amount of nitrogen in it.

Using formaldehyde as a novel chemical actinometer for 185 nm vacuum ultraviolet photon flux quantification in water

Quantifying ultraviolet (UV) photon flux is important for water photolysis practice. However, it is currently challenging to quantify the photon flux of 185 nm vacuum UV (VUV185) emitted by low-pressure mercury lamp (LPML) because of the interference of coexisting 254 nm UV (UV254). Given that formaldehyde (FA) is insensitive to UV254 within the time scale of interests whereas vulnerable to VUV185, this study for the first time evaluated the possibility of using FA as a chemical actinometer to determine the VUV185 photon flux under varying conditions. Experimental results revealed that the photodegradation of FA followed a pseudo-1st-order reaction kinetic under VUV185 irradiation, and the products of initial concentration (C0) and reaction rate constants (i.e., C0 × k) were proportional to the numbers of LPMLs (under C0 of 50–300 mg/L), suggesting that C0 × k is an excellent indicator for photon flux determination. Increasing dissolved oxygen concentration from 1.0 to 7.8 mg/L, pH from 4.0 to 10.4, and temperature from 22 to 44 °C all imposed negligible interferences (variation ≤ 10%) on the C0 × k values, proving that FA is a good actinometer for VUV185 photon flux detection. Because FA can be measured readily by spectrophotometry method, its use as an actinometer is more convenient than conventional actinometers. Therefore, this study demonstrates that FA is a promising candidate of actinometer for VUV185 quantification in the copresence of UV254.

Kinetics of hydrogenation of acrylonitrile butadiene rubber: a latex-based in situ and low-temperature approach

The kinetics of hydrogenation of acrylonitrile butadiene rubber (NBR) latex by the action of diimide generated by hydrazine hydrate and hydrogen peroxide in the presence of copper sulfate at low temperature was studied by calculating the initial reaction rate constants. Altering reaction parameters of different reactant dosages such as carbon-carbon double bonds, hydrazine hydrate, hydrogen peroxide, and copper sulfate can be designed to calculate the initial reaction rate constant in a hydrazine hydrate/hydrogen peroxide/copper sulfate reaction system. The method of initial reaction rate constants gives rate constant and reaction order in the hydrogenation reaction of NBR latex calculated from the hydrogenation kinetic data. Based on these kinetic values, the kinetic equation of hydrogenation of NBR latex in this catalytic system at the temperature ranged from 5 to 65 °C and the hydrogenated reaction activation energy were studied in this paper. Graphical abstract

Theoretical investigation on the contribution of HO[rad], SO4[rad]- and CO3[rad]- radicals to the degradation of phenacetin in water: Mechanisms, kinetics, and toxicity evaluation

Indirect oxidation induced by reactive free radicals, such as hydroxyl radical (HO), sulfate radical (SO4-) and carbonate radical (CO3-), plays an important or even crucial role in the degradation of micropollutants. Thus, the coadjutant degradation of phenacetin (PNT) by HO, SO4- and CO3-, as well as the synergistic effect of O2 on HO and HO2 were studied through mechanism, kinetics and toxicity evaluation. The results showed that the degradation of PNT was mainly caused by radical adduct formation (RAF) reaction (69% for Г, the same as below) and H atom transfer (HAT) reaction (31%) of HO. For the two inorganic anionic radicals, SO4- initiated PNT degradation by sequential radical addition-elimination (SRAE; 55%), HAT (28%) and single electron transfer (SET; 17%) reactions, while only by HAT reaction for CO3-. The total initial reaction rate constants of PNT by three radicals were in the order: SO4- > HO > CO3-. The kinetics of PNT degradation simulated by Kintecus program showed that UV/persulfate could degrade target compound more effectively than UV/H2O2 in ultrapure water. In the subsequent reaction of PNT with O2, HO and HO2, the formation of mono/di/tri-hydroxyl substitutions and unsaturated aldehydes/ketones/alcohols were confirmed. The results of toxicity assessment showed that the acute and chronic toxicity of most products to fish increased and to daphnia decreased, and acute toxicity to green algae decreased while chronic toxicity increased.

Development of an educational tool aimed at designing ideal chemical reactors

AbstractThis project aims at developing an educational tool, named REAJA, for simulating ideal chemical reactors according to the continuous stirred‐tank reactor, plug flow reactor, and batch reactors. The software was developed using the Python programming language, following the Agile methodology and test‐driven development. It has a main interface that introduces the objective and its functionalities through the images, texts, and buttons for three reactor modules: isothermic, adiabatic, and with the thermal exchange. Initial concentration, equilibrium constant, and reaction rate constant can also be calculated by specific modules. We present the results in a separate screen containing comparative graphs of concentration, temperature, and conversion, allowing the user to choose the best option among the simulated reactors. The software Aspen Plus and Excel/Runge–Kutta fourth‐order method was applied to verification testing with REAJA obtaining <5% and 10–90%, respectively. The last case could be justified by the simplifications made for educational purposes. Finally, the software was applied at the minicourse of the 21st week of Chemical Engineering of UNICAMP and in the undergraduate course of Topics in Chemical Processes with problem‐based learning methodology. We use a questionnaire to validate the usefulness of our software, which results are promising and indicate the success of our educational tool as a complement in the classroom since it facilitated the understanding of contents related to kinetics, thermodynamics, and chemical reactors.

The effects of the vibrational excitation on H + ND(a1Δ, j0 = 2, v0 = 0,1,2) reaction

Reactions of vibrationally excited ND (a1Δ, j0 = 2, v0 = 0,1,2) molecule with H atom have been carried out on the modified NH2 potential energy surface (PES) for the 2A′ excited state using Centrifugal Sudden approximation. The chemical reaction of ND (a1Δ) with H can proceed via the depletion ND + H → N + HD and the exchange pathways ND + H → NH + D. So, we present the time-dependent wave packet quantum scattering calculations of initial-state-resolved reaction probabilities, integral cross sections and initial state-selected reaction rate constants for exchange and depletion channels of the title reaction. For exchange reaction, it was found that vibrational excitation plays a very important role in the integral cross sections and rate constants.

The oxidation mechanism of 3,4-dihydroxy-2-butanone in the aqueous phase for secondary organic aerosols formation

3,4-dihydroxy-2-butanone (DHBO) is a major oxidation product of IEPOX and can easily be oxidized in tropospheric aqueous phase. The aqueous oxidation mechanism of DHBO has investigated by DFT and initial reaction rate constants also have calculated through TST. In the aqueous phase, the following trend in reactivity of initial reaction can be obtained: OH ≫ SO4− > NO3, which bases on the calculated rate constants (k(OH) = 1.20 × 108 L mol−1 s−1, k(SO4−) = 8.51 × 105 L mol−1 s−1 and k(NO3) = 2.86 × 105 L mol−1 s−1) at 298 K and 1 atm. After initial reaction, the major products of DHBO further react with OH radical at presence of O2. The final products include acetic acid and methylglyoxal, which are important SOA precursors. This work provides a reference for oxidation mechanism of dihydroxycarbonyl of isoprene-driven in aqueous and help understand SOA formation.

Hybrid soft sensor modeling for bisphenol‐A synthesis reaction process

AbstractTo online estimate the concentrations of key components at the outlet of bisphenol‐A (BPA) synthesis reactor, a hybrid modeling approach is proposed in this paper. First, the simplified mechanism model for the synthesis of BPA in an industrial fixed‐bed reactor is deduced on the basis of mass and energy balance. Second, considering that the initial concentrations of reactants at the inlet of BPA synthesis reactor cannot be measured in real‐time, the modified stochastic gradient boosting‐Gaussian process regression approach previously proposed by the authors is employed to online estimate the initial concentrations of reactants. Furthermore, modified stochastic gradient boosting‐Gaussian process regression method is also adopted to model the nonlinear influence of the reaction factors ( i.e., initial concentrations of reactants and inlet temperature) on the reaction rate constants in the simplified mechanism model. Finally, the hybrid modeling approach for BPA synthesis process is achieved by integrating the simplified mechanism model with the estimation models of initial concentrations and reaction rate constants. The feasibility and validity of the proposed hybrid model is verified through an industrial BPA synthesis process. On the basis of the hybrid model, the sensitivity analyses of the initial concentrations and inlet temperature are conducted, which can provide theoretical guidance for the operation optimization study in future work.

Born oppenheimer and renner teller quantum dynamics of the ND + D reaction

The Born Oppenheimer (BO) and Renner Teller (RT) time dependent quantum dynamics are investigated for the reaction NDa1Δ+D′(2S), considering the NH2 electronic states X∼2B1 and A∼2A1. The introduction of RT effects opens the possibility of studying not only the adiabatic reactions (depletion- A N(2D) + D2(a1Δ) and Exchange ND’+(a1Δ) + D) but also non-adiabatic ones (quenching + exchange ND′(X3Σ-)+D, depletion- X N(4S) + D2(a1Δ)). The initial state resolved reaction probabilities, cross sections, and rate constants are obtained considering the Coriolis Coupling (CC) interactions for all the reactions above. To point out the role of RT and CC effect, we compared our results with experimental and semi- classical data.

High-sulfur capacity and regenerable Zn-based sorbents derived from layered double hydroxide for hot coal gas desulfurization.

The Zn-Al mixed metal oxide (ZnAl-MMO) with a plate-like structure was derived from Zn-Al layered double hydroxide. The ZnAl-MMO with a Zn/Al molar ratio of 3:1 exhibits superior absorption ability for H2S in a simulated coal gas at 600 ℃ due to the special structure of the ZnAl-MMO. Besides ZnS, elemental sulfur is also produced during the desulfurization process. The deactivation model could well simulate the absorption behavior of H2S. The sulfidation reaction over the sorbent shows large initial reaction rate constants (1110-5390 m3 min-1 kg-1) and low activation energy (29.5 kJ mol-1). The regeneration rate of the used sorbent can reach 99.8% under the optimum conditions. The regenerated sorbents still show high sulfur capacity (ca. 30%), implying its great application potential for industrial-scale desulfurization of the hot coal gas.

Hydrogen effect modeling on Ziegler-Natta catalyst and final product properties in propylene polymerization

Abstract
 
 Hydrogen, as chain transfer agent, effects on kinetic of propylene polymerization; consequently variation of hydrogen concentration leads to change final product properties and also activates site of used catalyst. This phenomenon is one of the most important process variables is to adjust the final product properties and optimize the operating conditions. This work has attempted to present a mathematical model that cable to calculate the most important indices of end used product, such as melt flow index, number and weight average molecular weight and poly dispersity index. The model can predict profile polymerization rates determining important kinetic parameters such as the activation energy, lumped deactivation reaction initial reaction rate and deactivation constant. The mathematical model was implemented in Matlab/Simulink environment for slurry polymerization in laboratory scale. The modeling approach is based on polymer moment balance method in the slurry semi-batch reactor. In addition, in this work have provided a model that calculating fraction activated sites catalyst via hydrogen concentration. The model was validated by experimental data from lab scale, reactor. The experimental and model outputs were compared; consequently, the errors were within acceptable range.
 KEY WORDS: Mathematical modeling, Propylene polymerization, Kinetics study, Hydrogen response, population balance
 Bull. Chem. Soc. Ethiop. 2018, 32(2), 371-386.
 DOI:https://dx.doi.org/10.4314/bcse.v32i2.15

Modelling the influence of storage temperature and time after cutting on respiration rate of diced red onions (Allium cepa L. cv. Vermelha da Póvoa)

Ready-to-use diced onions are very convenient to final consumers and food service companies due to unpleasant pungency and lacrimation effects during bulb cutting. Nevertheless maintaining freshness and functional quality of diced onions is a challenge in the food industry. Thus it is important to know and model the influence of external factors on the product respiration phenomena in order to better control product deterioration. The respiration rate (RR) of diced red onions (Allium cepa L., cv. Vermelha da Póvoa) was studied over a period of storage time after dicing at different temperatures (4, 8, 12, 16 and 20 °C) under a normal atmosphere.At each of the tested temperatures, RR for both O2 and CO2 showed an exponential increase over time. This effect was enhanced with temperature. It was further observed that both the initial RR and reaction rate constants changed with temperature according to an Arrhenius-type equation with identical activation energy. This effect was incorporated in the primary model and the fit of the global model to experimental data was good (R2 = 0.94), with normal distribution of the residuals and correlation coefficients between the model constants below 0.85. Results helped establish a global mathematical model describing RR dependency on temperature over a period of storage time after dicing onions that will allow for a proper package design of this product.

Online Measurement of Oxygen-Dependent Enzyme Reaction Kinetics.

As the application of biocatalysis to complement conventional chemical and catalytic approaches continues to expand, an increasing number of reactions involve poorly water-soluble substrates. At required industrial concentrations necessary for industrial implementation, this frequently leads to heterogeneous reaction mixtures composed of multiple phases. Such systems are challenging to sample, and therefore, it is problematic to measure representative component concentrations. Herein, an online method for following the progress of oxygen-dependent reactions through accurate measurement of the oxygen mass balance in the gas phase of a reactor is demonstrated and validated. The method was successfully validated and demonstrated by using two model reactions: firstly, the oxidation of glucose by glucose oxidase and, secondly, the Baeyer-Villiger oxidation of macrocyclic ketones to lactones. Initial reaction rate constants and time-course progressions calculated from the oxygen mass balance were validated against conventional online methods of dissolved oxygen tension and pH titration measurements. A feasible operating window and the sensitivity to dynamic changes of reaction rates were established by controlling oxygen transfer through the operating parameters of the reactor. Such kinetic data forms the basis for reaction characterisation, from which bottlenecks may be made evident and directed improvement strategies can be identified and implemented.

CO2 SORPTION USING NA2CO3/AL2O3 SORBENT WITH VARIOUS FLOW PATTERNS OF FIXED/FLUIDIZED BED REACTORS

In this study, the carbon dioxide sorption using solid sorbent (sodium carbonate supported on alumina) in fixed and fluidized bed reactors was investigated. The key objective was to examine the carbon dioxide concentration profile or breakthrough curve (as well as capture capacity) and carbon dioxide sorption kinetic parameters with various flow regimes/flow patterns. The basic information for the sorption kinetic parameter computation was the breakthrough curve under different flow operating conditions. From the results, all the breakthrough curves were constant at the beginning stage then it decreased with the sorption time. The fixed bed gave longest sorption time. All the carbon dioxide gas was not captured in the fast fluidization flow regime. The turbulent fluidization flow regime exhibited highest carbon dioxide capture capacity. In addition, the employed deactivation kinetic model fitted well with the obtained experimental information. The initial sorption and deactivation reaction rate constants were the highest at the turbulent fluidization flow regime.

Kinetics investigation on the hydrogenation of acrylonitrile-butadiene rubber latex by using new catalytic reaction system

The kinetics of hydrogenation of acrylonitrile-butadiene rubber latex with hydrazine hydrate/hydrogen peroxide/selenium catalytic reaction system was investigated by calculating the initial reaction rate constants. The reaction rate constants of the reaction system were obtained by initial reaction measurements of different reactant dosages, such as selenium, hydrazine hydrate, and hydrogen peroxide. Hydrogenation rate constants and reaction order corresponding to the various factors were obtained from the hydrogenation kinetic data. The kinetic equation of this reaction system between 50–70°C and the reaction activation energy was derived.

Role of CO2 in Mass Transfer, Reaction Kinetics, and Interphase Partitioning for the Transesterification of Triolein in an Expanded Methanol System with Heterogeneous Acid Catalyst

Fatty acid methyl ester (FAME) production via transesterification of triglycerides (TGs) over a heterogeneous acid catalyst is mediated by carbon dioxide in an expanded methanol system. A representative TG, triolein, is used to determine the mechanisms and interactions responsible for the improved yields over Nafion-NR50 in these system conditions. Namely, the system mass transfer limitations, reaction kinetics, and interphase partitioning behavior are explored by varying mixing conditions and catalyst characteristics over a time series of 4 h. It is found that CO2 enhances mass transfer leading to improved reaction yields and product profiles due to increased substrate transport to and from the catalyst surface. CO2 also contributes to catalyst expansion, leading to greater exposure of active sites and faster reaction kinetics. Initial reaction rate constants using methanol-soaked Nafion reflect pseudo-first-order kinetics. Finally, the substrate-reagent mediating properties of CO2 are discussed in refer...

Quantum Dynamics of Li+HF/DF Reaction Investigated by a State-to-State Time-dependent Wave Packet Approach

Using the reactant coordinate based time-dependent wave packet method, on the APW potential energy surface, the differential and integral cross sections of the Li+DF/HF(v=0, j=0, 1) reactions were calculated over the collision energy range from the threshold to 0.25 eV. The initial state-specified reaction rate constants of the title reaction were also calculated. The results indicate that, compared with the Li+DF reaction, the product LiF of Li+HF reaction is a little more rotationally excited but essentially similar. The initial rotational excitation from j=0 to 1 has little effect on the Li+DF reaction. However, the rotational excitation of DF does result in a little more rotationally excited product LiF. The different cross section of both reactions is forward biased in the studied collision energy range, especially at relatively high collision energy. The resonances in the Li+HF reaction may be identifiable as the oscillations in the product ro-vibrational state-resolved integral cross sections and backward scattering as a function of collusion energy. For the Li+HF reaction, the rate constant is not sensitive to the temperature and almost has no change in the temperature range considered. For the Li+DF reaction, the rate constant increase by a factor of about 10 in the temperature range of 100–300 K. Brief comparison for the total reaction probabilities and integral cross section of the Li+HF reaction has been carried out between ours and the values reported previously. The agreement is good, and the difference should come from the better convergence of our present calculations.

Model for photodegradation of polybrominated diphenyl ethers.

Polybrominated diphenyl ethers (PBDE) were, and in some countries still are, used as flame retardants for plastic materials. When released from plastics, PDBE cause harm to the environment. This creates the incentive for further investigation of the PBDE degradation. This work focused on a formulation of a PBDE photodegradation model based on the PBDE properties obtained by the quantum chemical calculations. The proposed model predicted degradation routes of arbitrary PBDE congener. The routes of selected congeners were validated by the two independently published data sets and showed the high fitting degree. The model can be easily modified for any reactor system if the initial reaction rate constant of one congener is available for the given system.