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Characterization of variation of experimental results is achieved by repeating experiments. Frequently, results are averaged before data are analysed but that may not be the best practice because valuable information is then lost. Three other ways to analyze repetitions are: (1) each experiment is analyzed on its own (no pooling of data), (2) all experiments are analyzed together in one go (complete pooling), (3) data are analyzed together while allowing for similarities as well as differences in the result (partial pooling). Multilevel modeling uses partial pooling by partitioning variance over more than one level. Level 1 consists of the measurements themselves; higher levels consist of groups or clusters of measurements (repetitions, experiments at various temperatures, at various pH values, etc.) and parameters are analyzed both at the population and at the group/cluster level. The approach is applied to a case study in which heat-induced isothermal degradation of ascorbic acid was studied with 15 repetitions in an aqueous solution, making it a two-level study. The data were analyzed using averaging and complete pooling, complete pooling without averaging, no-pooling at all, and partial pooling. The kinetic model was established by letting the data decide about the order of the reaction, while this was compared to a model where the order was fixed at 1 (first-order model). Results show that both averaging with complete pooling, as well as complete pooling without averaging, strongly underestimate variation. The no-pooling technique overestimates variation, while partial pooling partitions variation over the levels and thus gives a better impression of the variation involved. The kinetics of ascorbic acid appear to be subject to strong variation when each experiment is considered separately because it is a compound that is very sensitive to all kinds of experimental conditions. With multilevel modeling it appeared to be possible to characterize the uncertainties involved much better than with single level modeling. A Bayesian analysis was performed, in which parameters are allowed to be variable, which is useful because multilevel modeling leads to characterization of variation of parameters. The Bayesian method allows to visualize the posterior distribution of parameters, thereby giving more insight in their behaviour. Also, a Bayesian analysis focuses more strongly on predictive accuracy of models, including multilevel models. The predictive accuracy of 4 models describing the same ascorbic acid data was compared and the multilevel model with reaction order estimated from the data performed by far the best in this regard. The pros and cons of multilevel modeling are discussed and it is concluded that multilevel modeling is to be preferred whenever the data allow to perform such an analysis.

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The kinetics of reactions of dehydrogenation of polycyclic naphthenes (cyclohexane, decalin, bicyclohexyl, ortho-, meta-, and para-isomers of perhydroterphenyl) is modeled on the basis of a formal comparison of kinetic equations of the 1st and 2nd orders based on real experimental data. It is shown that the reaction of the 1st order is predominating in the series of cyclohexane-bicyclohexyl-perhydroparatherphenyl. For all other substrates, the probability of describing the reaction in accordance with the equation of the 2nd order increases markedly, and for trans-decalin it becomes the predominant form of describing the kinetics of the reaction.

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Common peroxidase action and haloperoxidase action are quantifiable as light emission from dioxygenation of luminol (5-amino-2,3-dihydrophthalazine-1,4-dione). The velocity of enzyme action is dependent on the concentration of reactants. Thus, the reaction order of each participant reactant in luminol luminescence was determined. Horseradish peroxidase (HRP)-catalyzed luminol luminescence is first order for hydrogen peroxide (H2O2), but myeloperoxidase (MPO) and eosinophil peroxidase (EPO) are second order for H2O2. For MPO, reaction is first order for chloride (Cl-) or bromide (Br-). For EPO, reaction is first order for Br-. HRP action has no halide requirement. For MPO and EPO, reaction is first order for luminol, but for HRP, reaction is greater than first order for luminol. Haloperoxidase-catalyzed luminol luminescence requires acidity, but HRP action requires alkalinity. Unlike the radical mechanism of common peroxidase, haloperoxidases (XPO) catalyze non-radical oxidation of halide to hypohalite. That reaction is second order for H2O2 is consistent with the non-enzymatic reaction of hypohalite with a second H2O2 to produce singlet molecular oxygen (1O2*) for luminol dioxygenation. Alternatively, luminol dehydrogenation by hypohalite followed by reaction with H2O2 yields dioxygenation consistent with the same reaction order. Haloperoxidase action, Cl-, and Br- are specifically quantifiable as luminol luminescence in an acidic milieu.

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The identity of the rate-determining step (RDS) in the electrochemical CO reduction reaction (CORR) on Cu catalysts remains unresolved because: 1) the presence of mass transport limitation of CO; and 2) the absence of quantitative correlation between CO partial pressure (pCO ) and surface CO coverage. In this work, we determined CO adsorption isotherms on Cu in a broad pH range of 7.2-12.9. Together with electrokinetic data, we demonstrate that the reaction orders of adsorbed CO at pCO <0.4 and >0.6 atm are 1st and 0th , respectively, for multi-carbon (C2+ ) products on three Cu catalysts. These results indicate that the C-C coupling is unlikely to be the RDS in the formation of C2+ products in the CORR. We propose that the hydrogenation of CO with adsorbed water is the RDS, and the site competition between CO and water leads to the observed transition of the CO reaction order.

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A denitrification process with simultaneous suspended solids separation and denitrification was studied in pilot-scale filters. Denitrification rates for the total, upper, middle, and lower layer of the filter bed were 21.3, 79.0, 27.8, and 21.9 g (NO3+NO2)-N m-3 filter bed h-1 (g NOx-N m-3 h-1), respectively. The biofilm on the grains showed denitrification rates for not backwashed grains and grains backwashed once of 8.8 and 7.8 g NOx-N m-3 h-1, respectively, indicating a robust biofilm. Construction and operation strategies of full-scale filters were done based on the pilot-scale study results. For further optimization of the denitrification process, 1 of 60 filters in operation was chosen for a full-scale study. The denitrification rates for the total layer, upper layer, middle layers, and lower layer of the filter bed were 12.7, 15.6, 27.3, 27.9, 27.8, and 14.0 g NOx-N m-3 h-1, respectively. The rate of 27.8 g NOx-N m-3 h-1 was obtained for a middle layer in both filters. The amount of nitrogen possible to reduce in the full-scale filters was calculated to 8.8 mg N L-1 or 2403 kg N d-1. This paper presents results of denitrification rates, reaction orders, rate constants, and suspended solids separation.

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The bulk chlorine decay rate in drinking water supply systems depend on many factors, including temperature. In this document, the method to determine the order of reaction of chlorine with water is reported, as well as the method to estimate Kb (Bulk reaction rate constant). Experiments were carried out to determine the bulk chlorine decay, for which a set of water samples to determine the free residual chlorine every hour were analyzed. Chlorine concentrations were graphed against time and adjusted appropriately to the developed model. The experimental results showed that the average value of the mass decomposition rate was 0.15 h-1. It was shown that temperature affects the variation of the reaction rate of chlorine with water, Kb increases as temperature increases. In this manuscript it is reported:•The method that allows determining the reaction kinetic order of chlorine with drinking water.•The method that can help residual chlorine modelers in the correct definition of the bulk reaction rate constant.•The effectiveness of the method for evaluating the decomposition of residual chlorine in drinking water distribution networks as a function of temperature.

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Photo-thermo catalysis, which integrates photocatalysis on semiconductors with thermocatalysis on supported nonplasmonic metals, has emerged as an attractive approach to improve catalytic performance. However, an understanding of the mechanisms in operation is missing from both the thermo- and photocatalytic perspectives. Deep insights into photo-thermo catalysis are achieved via the catalytic oxidation of propane (C3 H8 ) over a Pt/TiO2 -WO3 catalyst that severely suffers from oxygen poisoning at high O2 /C3 H8 ratios. After introducing UV/Vis light, the reaction temperature required to achieve 70 % conversion of C3 H8 lowers to a record-breaking 90 °C from 324 °C and the apparent activation energy drops from 130 kJ mol-1 to 11 kJ mol-1 . Furthermore, the reaction order of O2 is -1.4 in dark but reverses to 0.1 under light, thereby suppressing oxygen poisoning of the Pt catalyst. An underlying mechanism is proposed based on direct evidence of the in-situ-captured reaction intermediates.

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The surface functional group plays an important role in H2S catalytic oxidization. However, the specific effect of each group species has seldom been investigated. For the first time, we revealed by experimental and theoretical methods that the pyrone group was the most valuable group. An increase in the pyrone-group amount obviously decreased the kinetic reaction order of H2S catalytic oxidization. The catalyst with the largest amount of pyrone group (0.1321 mmol·g-1) showed the lowest reaction order (0.5896) and activation energy (16.25 kJ·mol-1). By comparison, a catalyst with 0.0008 mmol·g-1 of pyrone group had a reaction order of just 1.1852 and an activation energy of 81.22 kJ·mol-1. The contribution of pyrone content to the kinetic reaction order had a negative correlation coefficient of -8.0665, which was three and five times larger than that of the quinone (-2.5568) and acidic groups (-1.7454), respectively. Moreover, density functional theory calculations showed that the pyrone group had the lowest energy gap (0.156 eV), far less than that (1.921 eV) of the carboxyl group. After H2S was adsorbed, the pyrone group had a Mulliken atomic charge of 0.510, which was larger than that (0.236) of the carboxyl group. In other words, the pyrone group showed the best ability to facilitate electron transfer. As a result, the catalyst with 0.1321 mmol·g-1 of the pyrone group removed 100% of the H2S (450 ppm). This amount was 42% higher than a catalyst with 0.0008 mmol·g-1 of the pyrone group. The main results of this work help to explain the mechanism of carbon material in various types of catalysis.

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In this paper, the theoretical analysis of the critical autoignition conditions for exothermically reacting systems at any value of the reaction order was conducted. The calculated and approximate analytical dependencies for the relationship between the parameters at the ignition limit were obtained. On the basis of the obtained diagrams of critical parameters, the conditions of thermal explosion (TE) degeneration for reactions of arbitrary order were determined. It was established that the existing theory of TE gives the correct estimates of ignition temperatures for a given condition of exothermic reaction realization (heat transfer coefficient, specific surface area, initial concentration). However, the theory gives unsatisfactory predictions for the mentioned critical TE conditions at a given ambient temperature. Moreover, the classical theory cannot be applied in the intermediate case when the effect of reactant consumption is already significant but the reaction still proceeds with all the signs of a TE.

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Understanding how normally soluble peptides and proteins aggregate to form amyloid fibrils is central to many areas of modern biomolecular science, ranging from the development of functional biomaterials to the design of rational therapeutic strategies against increasingly prevalent medical conditions such as Alzheimer's and Parkinson's diseases. As such, there is a great need to develop models to mechanistically describe how amyloid fibrils are formed from precursor peptides and proteins. Here we review and discuss how ideas and concepts from chemical reaction kinetics can help to achieve this objective. In particular, we show how a combination of theory, experiments, and computer simulations, based on chemical kinetics, provides a general formalism for uncovering, at the molecular level, the mechanistic steps that underlie the phenomenon of amyloid fibril formation.

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The prion protein forms ß-rich soluble oligomers in vitro at pH4 in the presence of physiological concentrations of salt. In the absence of salt, oligomerization and misfolding do not take place in an experimentally tractable timescale. While it is well established that a lowering of pH facilitates misfolding and oligomerization of this protein, the role of salt remains poorly understood. Here, solution-state NMR was used to probe perturbations in the monomeric mouse prion protein structure immediately upon salt addition, prior to the commencement of the oligomerization reaction. The weak binding of salt at multiple sites dispersed all over the monomeric protein causes a weak and non-specific perturbation of structure throughout the protein. The only significant perturbation occurs in the loop between helix 2 and 3 in and around the partially buried K193-E195 salt bridge. The disruption of this key electrostatic interaction is the earliest detectable change in the monomer before any major conformational change occurs and appears to constitute the trigger for the commencement of misfolding and oligomerization. Subsequently, the kinetics of monomer loss, due to oligomerization, was monitored at the individual residue level. The oligomerization reaction was found to be rate-limited by association and not conformational change, with an average reaction order of 2.6 across residues. Not surprisingly, salt accelerated the oligomerization kinetics, in a non-specific manner, by electrostatic screening of the highly charged monomers at acidic pH. Together, these results allowed a demarcation of the specific and non-specific effects of salt on prion protein misfolding and oligomerization.

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The recent technological evolution of reaction monitoring techniques has not been paralleled by the development of modern kinetic analyses. The analyses currently used disregard part of the data acquired, thus requiring an increased number of experiments to obtain sufficient kinetic information for a given chemical reaction. Herein, we present a simple graphical analysis method that takes advantage of the data-rich results provided by modern reaction monitoring tools. This analysis uses a variable normalization of the time scale to enable the visual comparison of entire concentration reaction profiles. As a result, the order in each component of the reaction, as well as kobs , is determined with just a few experiments using a simple and quick mathematical data treatment. This analysis facilitates the rapid extraction of relevant kinetic information and will be a valuable tool for the study of reaction mechanisms.

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The Group 14 enolates play an important part in many organic reactions. Herein, the reduction of an α-bromo ketone with germanium(II) salts cleanly afforded the corresponding germyl enolate as an isolatable species. This experimental reductive generation of a germyl enolate enabled us to characterize both C- and O-bound tautomers derived from an identical precursor and to unveil the tautomeric mechanisms, including the kinetic parameters and the relative stability of these tautomers, along with confirmation from DFT calculations. Moreover, the highly coordinated germyl enolates were isolated by a stabilization process induced by adding ligands. All products were characterized by NMR spectroscopy and X-ray crystallography.

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A medium-scale melting experiment rig was designed and constructed in this study. A detailed experimental study was conducted on the melting behavior and the chemical kinetic characteristics of three typical thermoplastic materials, including polypropylene (PP), polyethylene (PE) and polystyrene (PS). It is observed that the thermal decomposition of the thermoplastic materials mainly consists of three stages: the initial heating stage, the melting-dominated stage and the gasification-dominated stage. Melting of the materials examined takes place within a certain temperature range. The melting temperature of PS is the lowest, moreover, it takes the shortest time to be completely liquefied. To quantitatively represent the chemical kinetics, an nth-order reaction model was employed to interpret the thermal decomposition behavior of the materials. The calculated reaction order is largely in accordance with the small-scale thermal gravimetric analysis (TGA). The small difference between the results and TGA data suggests that there are some limitations in the small-scale experiments in simulating the behavior of thermoplastic materials in a thermal hazard. Therefore, investigating the thermal physical and chemical properties of the thermoplastic materials and their thermal hazard prevention in medium or large-scale experiments is necessary for the fire safety considerations of polymer materials.

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The widespread use of jarosite-type compounds to eliminate impurities in the hydrometallurgical industry is due to their capability to incorporate several elements into their structures. Some of these elements are of environmental importance (Pb(2+), Cr(6+), As(5+), Cd(2+), Hg(2+)). For the present paper, AsO4 (3-) was incorporated into the lattice of synthetic jarosite in order to carry out a reactivity study. Alkaline decomposition is characterized by removal of sulfate and potassium ions from the lattice and formation of a gel consisting of iron hydroxides with absorbed arsenate. Decomposition curves show an induction period followed by a conversion period. The induction period is independent of particle size and exponentially decreases with temperature. The conversion period is characterized by formation of a hydroxide halo that surrounds an unreacted jarosite core. During the conversion period in NaOH media for [OH(-)] > 8 × 10(-3) mol L(-1), the process showed a reaction order of 1.86, and an apparent activation energy of 60.3 kJ mol(-1) was obtained. On the other hand, during the conversion period in Ca(OH)2 media for [OH(-)] > 1.90 × 10(-2) mol L(-1), the reaction order was 1.15, and an apparent activation energy of 74.4 kJ mol(-1) was obtained. The results are consistent with the spherical particle model with decreasing core and chemical control.