Ratio Of Rate Constants Research Articles

Deeply self-reconstructing CoFe(H3O)(PO4)2 to low-crystalline Fe0.5Co0.5OOH with Fe3+–O–Fe3+ motifs for oxygen evolution reaction

In this study, phosphate FeCo(H3O)(PO4)2 nanosheet arrays (NAs) were synthesized using an electrochemical strategy. FeCo(H3O)(PO4)2 NAs as precatalyst could undergo significant self-reconstruction, including leaching of phosphate anions and electro-oxidation of Co2+ during anodizing at the potential range of oxygen evolution reaction (OER) in 1 M KOH solution, eventually resulting in the formation of Fe0.5Co0.5OOH NAs with low crystallinity. The high content of Fe in Fe0.5Co0.5OOH NAs promoted the formation of active Fe3+–O–Fe3+ motifs that increased OER occurrence. Additionally, Fe incorporation increased the ratio of the reaction rate constants of oxygen evolution to Co3+/Co4+ (kOER/kM,ox) and enhanced the reaction order on the hydroxyl ion. These factors significantly contributed to the outstanding OER catalytic performances of Fe0.5Co0.5OOH NAs.

Rate constant ratios in the consecutive chlorination of liquid‐phase p ‐xylene with Cl 2 and an iron(III) chloride catalyst

AbstractGiven that p‐xylene is an important chemical feedstock for many final products in the market from pesticides, pharmaceuticals, peroxides to dyes, its chlorinated derivatives are of interest in the chemical industry. In this paper, the rate constant ratios of the consecutive chlorination of p‐xylene at 70°C in a gas–liquid semibatch reactor using molecular chlorine and iron(III) chloride as a catalyst was investigated up to the fourth successive reaction (tetrachloro‐p‐xylene production). The ratios were determined with both mathematical expressions and a graphical method proposed recently in the literature by use of the maxima of the successive products. The ratios found for monochloro‐p‐xylene (2‐chloro‐p‐xylene), dichloro‐p‐xylene (the sum of 2,3‐dichloro‐p‐xylene and 2,5‐dichloro‐p‐xylene), trichloro‐p‐xylene (2,3,5‐trichloro‐p‐xylene), and tetrachloro‐p‐xylene (2,3,5,6‐tetrachloro‐p‐xylene) are k2/k1 = 0.295, k3/k1 = 0.0826, and k4/k1 = 0.00383. The ratio of the dichlo‐isomers produced was also determined as 2.12 in favor of 2,5‐dichloro‐p‐xylene, which is reasonable since 2,3‐dichloro‐p‐xylene is highly hindered by the adjacent groups on the aromatic nucleus. The existing knowledge found in the literature on the rate constant ratios of consecutive reactions was also extended in this paper with a new mathematical expression for the determination of the third stage product peak concentration. The standard uncertainties of the rate constant ratios, the standard deviation of the means, as well as the expanded uncertainties of the means, were calculated. Finally, the propagation of uncertainties for the trichloro‐p‐xylene was estimated using the partial derivatives of this product for each of the rate constants.

Large Isotope Effects in Organometallic Chemistry.

The kinetic isotope effect (KIE) is key to understanding reaction mechanisms in many areas of chemistry and chemical biology, including organometallic chemistry. This ratio of rate constants, kH /kD , typically falls between 1-7. However, KIEs up to 105 have been reported, and can even be so large that reactivity with deuterium is unobserved. We collect here examples of large KIEs across organometallic chemistry, in catalytic and stoichiometric reactions, along with their mechanistic interpretations. Large KIEs occur in proton transfer reactions such as protonation of organometallic complexes and clusters, protonolysis of metal-carbon bonds, and dihydrogen reactivity. C-H activation reactions with large KIEs occur with late and early transition metals, photogenerated intermediates, and abstraction by metal-oxo complexes. We categorize the mechanistic interpretations of large KIEs into the following three types: (a) proton tunneling, (b) compound effects from multiple steps, and (c) semi-classical effects on a single step. This comprehensive collection of large KIEs in organometallics provides context for future mechanistic interpretation.

Highly efficient degradation of bisphenol A with persulfate activated by vacuum-ultraviolet/ultraviolet light (VUV/UV): Experiments and theoretical calculations

Enhanced degradation and mineralization of bisphenol A (BPA) known as a typical endocrine disrupting chemical (EDC) in VUV/UV-activated persulfate process (VUV/UV/PS) were investigated. The pseudo-first-order reaction rate constant and total organic carbon (TOC) removal ratio of BPA in this process were 1.75 and 1.70 times of those in UV-activated PS process (UV/PS), respectively. The excitation-emission matrix (EEM) fluorescence spectroscopy of reaction solution at different time clearly indicated the change of BPA and its intermediates during the reaction process. The significant interactive effects of three important operating parameters including the initial concentration of BPA, the initial concentration of PS and the initial pH of solution on BPA degradation efficiency were evaluated and optimized by using central composite design (CCD) of response surface methodology (RSM). At the optimum experimental conditions (i.e., 30 mg/L BPA, 1.25 mM PS and at pH 9), the maximum degradation efficiency of BPA at 2 min was up to 92.2%. Sulfate radicals (SO4•-) were the dominant reaction activate species for BPA degradation. Based on the analysis of liquid chromatograph-mass spectrometry (LC/MS), gas chromatograph-mass spectrometry (GC/MS) and Fourier transform infrared spectroscopy (FTIR) of the reaction mixture and density function theory (DFT) calculation, it was proposed that BPA degradation was mainly caused by SO4•--induced hydroxylation reaction, HO• addition and β-scission of C–C bond. Moreover, the electrical energy consumption of BPA degradation in VUV/UV/PS process was less. Additionally, BPA in real water samples could also be effectively degraded at lower treatment costs in this process. Hence, the present study demonstrates that VUV/UV activation of PS is a highly efficient and economical alternative to remove BPA in real water matrices..

Effect of a Cocatalyst on a Photoanode in Water Splitting: A Study of Scanning Electrochemical Microscopy.

With a proper band gap of ∼2.4 eV for solar light absorption and suitable valence band edge position for oxygen evolution, scheelite-monoclinic bismuth vanadate (BiVO4) has become one of the most attractive photocatalysts for efficient visible-light-driven photoelectrochemical (PEC) water splitting. Several studies have indicated that surface modification of BiVO4 with a cocatalyst such as NiFe layered double hydroxide (LDH) can significantly increase the PEC water splitting performance of the catalyst. Herein, we experimentally investigated the charge transfer dynamics and charge carrier recombination processes by scanning electrochemical microscopy (SECM) with the feedback mode on the surface of BiVO4 and BiVO4/NiFe-LDH as model samples. The ratio of rate constants for photogenerated hole (kh+0) to electron (ke-0) via the photocatalyst of BiVO4/NiFe-LDH reacting with the redox couple is found to be five times larger than that of BiVO4 under illumination. In this case, the ratio of the rate constants kh+0/ke-0 stands for the interfacial charge recombination process. This implies the cocatalyst NiFe-LDH suppresses the electron back transfer greatly and finally reduces the surface recombination. Control experiments with cocatalysts CoPi and RuOx onto BiVO4 further verify this conclusion. Therefore, the SECM characterization allows us to make an overall analysis on the function of cocatalysts in the PEC water splitting system.

Intrinsic Nucleophilicity of Inverting and Retaining Glycoside Hydrolases Revealed Using Carbasugar Glyco-Tools

Hydrolyses of cyclohexenyl-based carbasugars that mimic either α-d-glucose or α-d-galactose were explored with two Bacteroides thetaiotaomicron enzymes from glycoside hydrolase family 97: an inverting α-glucosidase (BtGH97a) and a retaining α-galactosidase (BtGH97b). Both enzymes yield nucleophilic substitutions at the pseudo-anomeric center of the carbasugar substrates, giving significantly different linear energy relationships for the catalytic rate constant as a function of the leaving group ability. Specifically, the kinetic data for the inverting α-glucosidase is consistent with the reaction giving a hydrolyzed inverted carbaglucose product by a mechanism that proceeds with little nucleophilic participation by the bound water molecule at the reaction transition state. In contrast, the reaction of carbagalactose substrates with the retaining GH97 enzyme involves a rate-limiting nonchemical step, likely a conformational change, followed by rapid substitution involving a nucleophilic amino acid residue to give a covalently bound intermediate. Considering the structural similarities between these two GH97 enzymes, the kinetic data nonetheless reveal a significant (>106) difference in the rates of nucleophilic attack between the unique enzymatic nucleophiles─with the less nucleophilic species being H2O in the inverting α-glucosidase and the better nucleophile being a carboxylate in the retaining α-galactosidase. The enzymatic rate constant ratio for the phenyl carbasugars contrasts with the corresponding kinetic data obtained using natural substrate phenyl glycopyranosides. Last, for the galactocarbasugar with a phenol leaving group, the second-order rate constant for alkylation of the GH97 α-galactosidase is only ∼10-fold lower than that for glycosylation of this enzyme by the parent carbohydrate phenyl α-d-galactopyranoside. This modest difference in rate constants underscores our conclusion that retaining glycoside hydrolases may not have optimized the nucleophilicity of their active site nucleophiles with the result that the transition state free energies for formation and hydrolysis of the covalent enzyme intermediate are matched.

State-to-state Rate Constants for the H + LiH(v 0 = 0, j 0 = 0) Reaction: An Accurate Nonadiabatic Dynamical Study

Abstract The state-to-state rate constants for hydrogen abstraction, nonadiabatic hydrogen abstraction, and exchange channels of the H + LiH reaction have been studied in the temperature range from 10 to 5000 K by using the nonadiabatic time-dependent wave packet method. The total and vibrational state-resolved rate constants of the H + LiH (v 0 = 0, j 0 = 0) → Li(22S) + H2 reaction are calculated and compared with previous adiabatic values. The results indicated that adiabatic values always overestimate the rate constant due to the nonadiabatic effect not being considered. In addition, the ratio of adiabatic vibrational state-resolved rate constants versus that of nonadiabatic ones is calculated for the hydrogen abstraction channel. This reflects that the nonadiabatic effect is mainly focused on the low-lying vibrational states. Moreover, the rovibrational state-resolved rate constants show that the largest population of product is located at (v′ = 2, j′ = 11), (v′ = 0, j′ = 5), and (v′ = 0, j′ = 6) for the hydrogen abstraction, nonadiabatic hydrogen abstraction and exchange channels, respectively. The total and vibrational state-resolved rate constants of the Li(22P) → Li(22S) quenching process are also calculated in the temperature range up to 5000 K. The results show that when the temperature is lower than 200 K, the quenching efficiency increases rapidly, but with the further increase of temperature, the quenching efficiency hardly changes.

Double diffusion in stretched flow over a stretching cylinder with activation energy and entropy generation

Present study accords exploration of double diffusion in an axisymmetric flow of chemically reacting viscous fluid which impulsively starts flowing over a cylinder due to stretched surface. Non-Fourier law is employed to explain the heat flow whereas non-Fick's law of mass flux is employed to delve into the diffusion of mass. Activation energy is also taken into account. Transformed governing equations are solved using efficient mathematical technique called Homotopy Analysis Method (HAM). For the validity of the solution technique convergence table and h curves are plotted. Numerical solution has also been computed by using Shooting method for comparison with HAM. Entropy generation of the system has been investigated. Significant impact of pertinent flow parameters on thermal profile, concentration and velocity distribution are examined graphically. Velocity and thickness of momentum boundary layer increase by increasing curvature. Thermal profile is inversely related with Prandtl number and thermal relaxation time. Concentration profile trickles down by an increase in Schmidt number, mass relaxation parameter, Fitted rate constant and temperature ratio parameter. Most of the studies available in the literature focused on the double diffusion using generalized Fourier and Fick's laws neglecting activation energy and entropy generation which is an inevitable aspect in practical problems now a days. These features have been considered in the present article and it is the novelty of the present research.

An Approximate Analytical Solution Of Nonlinear Equations In N-Aminopiperidine Synthesis: New Approach Of Homotopy Perturbation Method)

the synthesis of N-aminopiperidine (NAPP) using hydroxylamine-O-sulfonic acid (HOSA) is based on system of nonlinear rate equations. The new approach to homotopy perturbation method is applied to solve the nonlinear equations. A simple analytical expression for concentrations of hydroxylamine-O-sulfonique acid (HOSA), piperidine (PP), N-aminopiperidine (NAPP), sodium hydroxide (NaOH) and diazene (N2H2) along with NAPP yield is obtained and is compared with numerical result. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation. The obtained analytical result of NAPP yield is compared with the experimental results. The influence of reagents ratio p and rate constants ratio r on yield has been discussed.

Dissolution of mechanically activated sphalerite in the wet and dry milling conditions

The aim of this work has been to examine the effect of intensive ball milling of sphalerite in the wet and dry modes on the microstructural changes and the subsequent effect on its dissolution rate. Sample characterization showed that the BET surface area and the amorphization degree were obtained to 18.2 m2/g and 78.92% in the wet mode and 7.72 m2/g and 90.35% in the dry mode milling after 180 min, respectively. The maximum extraction of Zn obtained 23.7, 67.12 and 85% in the unmilled, wet and dry milled samples, respectively. The ratio of kinetic rate constant has been increased by 37 and 67 times, respectively. Also, the activation energy was decreased with increasing of milling time. Selectivity of sphalerite leaching versus surface area was obtained higher than that of the wet milling. Leaching experiments indicated that structural disordering had a drastic effect on the reactivity of mechanically activated sphalerite.

Molecular Weight Distribution in Ring‐Opening Polymerization of Propylene Oxide Catalyzed by Double Metal Complex: A Model Simulation

AbstractIn the present work, method of moments is used to model the molecular weight distribution (MWD) of polypropylene glycol (PPG) produced with ring‐opening polymerization of propylene oxide catalyzed by double metal complex (DMC), and an explicit expression about the polydispersity index (PDI) of PPG is obtained. The simulated results indicate that decreasing the initial concentration ratio of monomer to total chains (K1) or increasing the rate constant ratio of chain transfer to propagation (K2) leads to smaller PDI. Reducing the concentration of DMC can induce larger PDI. When the PPG's initial PDI (i.e., PDI of initiator) increases, PDI of the final PPG grows up linearly. However, with the increase of monomer conversion, PDI increases first and then decreases, that is, there is a critical conversion. The possible lack of chain transfer at the beginning of polymerization and the insufficient chain transfer caused by increased K1, decreased concentration of catalyst, and decreased K2 will cause larger PDI, namely, broad MWD.

Separation of homogeneous palladium catalysts from pharmaceutical industry wastewater by using synergistic recovery phase via HFSLM system

Separation of homogeneous palladium catalysts from pharmaceutical industry wastewater by using synergistic recovery phase via hollow fiber supported liquid membrane (HFSLM) system is presented. HFSLM impregnated with N-methyl-N,N,N-trioctylammonium chloride (Aliquat 336) as the extractant dissolved in cyclohexane. The influence of various chemical parameters, including the concentration of extractant and recovery phases as well as recovery selector concentration in recovery phase, were also studied. A mixture of hydrochloric acid and thiourea was used as synergistic recovery phase. The highest percentage of extraction and recovery was 99.95% and 88.12%, respectively. Furthermore, the kinetics of recovery reaction was studied to provide reaction order, reaction rate constant, equilibrium constant and distribution ratio.

Quantitative E. coli Enzyme Detection in Reporter Hydrogel-Coated Paper Using a Smartphone Camera.

There is a growing demand for rapid and sensitive detection approaches for pathogenic bacteria that can be applied by non-specialists in non-laboratory field settings. Here, the detection of the typical E. coli enzyme β-glucuronidase using a chitosan-based sensing hydrogel-coated paper sensor and the detailed analysis of the reaction kinetics, as detected by a smartphone camera, is reported. The chromogenic reporter unit affords an intense blue color in a two-step reaction, which was analyzed using a modified Michaelis–Menten approach. This generalizable approach can be used to determine the limit of detection and comprises an invaluable tool to characterize the performance of lab-in-a-phone type approaches. For the particular system analyzed, the ratio of reaction rate and equilibrium constants of the enzyme–substrate complex are 0.3 and 0.9 pM−1h−1 for β-glucuronidase in phosphate buffered saline and lysogeny broth, respectively. The minimal degree of substrate conversion for detection of the indigo pigment formed during the reaction is 0.15, while the minimal time required for detection in this particular system is ~2 h at an enzyme concentration of 100 nM. Therefore, this approach is applicable for quantitative lab-in-a-phone based point of care detection systems that are based on enzymatic substrate conversion via bacterial enzymes.

The investigation of triethylammonium carboxylates influence on the kinetics of urethane formation processing during waterborne polyurethane synthesis

Kinetic features of the catalytic reaction of isophorone diisocyanate with triethylammonium salt of 2,2‐bis(hydroxymethyl)propionic acid, a hydrophilic agent for obtaining waterborne polyurethane, also with the model 1,1‐bis(hydroxymethyl)ethane and with physical mixture 1,1‐bis(hydroxymethyl)ethane‐triethylamine were studied using IR spectroscopy. The observed rate constant ratios of isophorone diisocyanate aliphatic and cycloaliphatic isocyanate groups interaction with the studied compounds were established, and the catalysis efficiency was evaluated. It was shown that a synergic effect is observed in catalytic systems based on dibutyltin dilaurate and triethylammonium carboxylates with regard to the reactivity of isophorone diisocyanate aliphatic group alone in the urethane formation reaction.

The Role of Charge and Recombination‐Enhanced Defect Reaction Effects in the Dissociation of FeB Pairs in p‐Type Silicon under Carrier Injection

The dissociation of FeB pairs in p‐type silicon under injection is often explained by the charge state change of interstitial Fe (Fei) from positive to neutral. It is also sometimes interpreted as a recombination‐enhanced defect reaction (REDR) mechanism. The charge effect and the REDR have fundamentally different impacts on the dissociation/association reactions: the former changes the concentration of Fei+, whereas the latter changes the reaction rate constants. Herein, the two effects are investigated and compared through measuring and analyzing the dynamics of the reactions. The results confirm that the dissociation of FeB under carrier injection cannot be purely attributed to the change of charge states. The extracted dissociation/association rate constant ratio shows an approximately linear dependence on the recombination rate on each FeB pair, indicating the REDR effect. The results allow the two effects to be directly compared, highlighting the dominant role of the REDR effect in dissociating the pairs.

Correlations for catalyst deactivation during valorization of biomass-derived acetone and butanol

Recently we reported valorization of biomass-derived acetone and butanol in which acetone hydrogenation and butylation exhibited systematic trends for catalyst life as a function of total reaction pressure. These works did not address kinetics of catalyst deactivation behaviour. The present, relatively short, communication attempts to determine rate constants for main and deactivation reactions are calculated for different pressures. Variation of rate constants with pressure has scantily been reported unlike with temperature. Values of both constants decreased with increasing pressure; however, main reaction rate constant declined slowly resulting in much higher values of their ratios. This particular aspect led to higher conversions at higher pressures which were simultaneously accompanied by reduced coking. Knowledge of rates of catalyst deactivation helps select reactor configuration, i.e., fixed and fluidised beds or moving bed reactors. Thus this study assists selection of reactor, catalysts, and operating conditions to impart value addition to biomass-derived chemicals. A parameter accounting for pressure effect on rate constants too has been determined. The same parameter for deactivation reaction has been correlated with ratio of rate constants for main and deactivation reactions.

Theoretical studies on the initial reaction kinetics and mechanisms of p-, m- and o-nitrotoluene

The potential energy surfaces (PESs) of three nitrotoluene isomers, such as p-nitrotoluene, m-nitrotoluene, and o-nitrotoluene, have been theoretically built at the CCSD(T)/CBS level. The geometries of reactants, transition states (TSs) and products are optimized at the B3LYP/6-311++G(d,p) level. Results show that reactions of -NO2 isomerizing to ONO, and C-NO2 bond dissociation play important roles among all of the initial channels for p-nitrotoluene and m-nitrotoluene, and that the H atom migration and C-NO2 bond dissociation are dominant reactions for o-nitrotoluene. In addition, there exist pathways for three isomer conversions, but with high energy barriers. Rate constant calculations and branching ratio analyses further demonstrate that the isomerization reactions of O transfer are prominent at low to intermediate temperatures, whereas the direct C-NO2 bond dissociation reactions prevail at high temperatures for p-nitrotoluene and m-nitrotoluene, and that H atom migration is a predominant reaction for o-nitrotoluene, while C-NO2 bond dissociation becomes important by increasing the temperature.

Experimental and theoretical studies on the reaction of H atom with C3H6

AbstractA comprehensive study on the reaction of H + C3H6 has been conducted in order to clarify the temperature and pressure dependence of product branching. Site‐specific rate of addition of a hydrogen atom to the center carbon is measured by a comparative method for the evolutions of H atoms behind reflected shock waves. The rate constant for the addition to the center carbon can be given by ln(k1‐2/cm3molecule–1s–1) = – (1.67 ± 0.65) × 103 T–1 – (24.18 ± 0.55) for H + C3H6 → n‐C3H7* → products (T = 1065‐1306 K) without pressure dependence for P = 1‐2 bar. Theoretical calculation was conducted to evaluate the pressure dependence of the product branching for the H + C3H6 reaction by using transition‐state theory and RRKM theory based on quantum‐chemical calculations of potential‐energy surfaces. The result indicates that transition of the main reaction channel from addition to the terminal carbon in the low temperature range to the central carbon at moderate pressures (0.001‐10 bar) and elevated temperatures causes S‐shaped non‐Arrhenius temperature dependence of the total reaction rate against T–1; at the transition temperature, a strong pressure dependence was predicted. Our experimental result of k1‐2 agrees very well with the predicted value and available experimental data. The predicted rate constant ratio for the terminal versus nonterminal additions at the high‐pressure limits agrees well with the temperature dependence reported by Manion and Awan for the analogous H + C4H8 reaction. Furthermore, the importance of H‐abstraction reactions at elevated temperatures from three different sites of C3H6 was predicted in this calculation. For kinetic modeling of combustion and pyrolysis of hydrocarbons, we have recommended the rate constants for the 3 abstraction reactions as well as for the production of i‐ and n‐C3H7 radicals by addition reactions at the high‐ and low‐pressure limits over the temperature range of 300‐2000 K.

Secondary organic aerosol formation from the ozonolysis and oh-photooxidation of 2,5-dimethylfuran

In this study, the O3 and OH radical oxidation of 2,5-dimethylfuran (2,5-DMF) were investigated in two different chambers at (296±1) K and atmospheric pressure to examine secondary organic aerosol (SOA) formation. Results for OH-photooxidation indicate that SOA yieldsdecrease (from 6.2 to 0.4) with the rise of 2,5-DMF concentration (from10 to 1000 ppb). In the absence of NOx and under high relative humidity (RH) conditions (60%), higher aerosol yields are favoured. SOA formation is dependent on the initial seed surface for two kinds of inorganic seed particles ((NH4)2SO4 and CaCl2), being the effect slightly greater for CaCl2. The ozonolysis only generates particles in the presence of SO2 and the increase of relative humidity from 0 to 15% lowers the particle number and particle mass concentrations. The water-to-SO2 rate constant ratio of the Criegee intermediate was derived from the SOA yield in experiments with different relative humidity values, with kH2O/kSO2 = (1.6±0.4)x10−5.

Kinetic study of reaction C2H5 + HO2 in a photolysis reactor with time-resolved Faraday rotation spectroscopy

The rate constant and branching ratios of ethyl reaction with hydroperoxyl radical, C2H5 + HO2 (1), a key radical-radical reaction for intermediate temperature combustion chemistry, were measured in situ for the first time in a photolysis Herriott cell by using mid-IR Faraday rotation spectroscopy (FRS) and UV-IR direct absorption spectroscopy (DAS). The microsecond time-resolved diagnostic technique in this work enabled the direct rate measurements of the target reaction at 40 and 80 mbar and reduced the experimental uncertainty considerably. C2H5 and HO2 radicals were generated by the photolysis of (COCl)2/C2H5I/CH3OH/O2/He mixture at 266 nm. By direct measurements of the transient profiles of C2H5, HO2 and OH concentrations, the overall rate constant for this reaction at 297 K was determined as k1(40 mbar) = (3.8 ± 0.8) × 10−11 cm3 molecule−1 s−1 and k1(80 mbar) = (4.1 ± 1.0) × 10−11 cm3 molecule−1 s−1. The direct observation of hydroxyl radical (OH) indicated that OH formation channel was the major channel with a branching ratio of 0.8 ± 0.1.