Empirical Rate Law Research Articles

Concerted C−N and C−H Bond Formation in a Magnesium-Catalyzed Hydroamination

Coordinatively saturated To(M)MgMe (1; To(M) = tris(4,4-dimethyl-2-oxazolinyl)phenylborate) is an active precatalyst for intramolecular hydroamination/cyclization at 50 °C. The empirical rate law of -d[substrate]/dt = k'(obs)[Mg](1)[substrate](1) and Michaelis-Menten-type kinetics are consistent with a mechanism involving reversible catalyst-substrate association prior to cyclization. The resting state of the catalyst, To(M)MgNHCH(2)CR(2)CH(2)CH═CH(2) [R = Ph, Me, -(CH(2))(5)-], is isolable, but isolated magnesium amidoalkene does not undergo unimolecular cyclization at 50 °C. However, addition of trace amounts of substrate allows cyclization to occur. Therefore, we propose a two-substrate, six-center transition state involving concerted C-N bond formation and N-H bond cleavage as the turnover-limiting step of the catalytic cycle.

Kinetic Analysis of Chalcone Epoxidation in a Biphasic System

The kinetics of chalcone epoxidation in a biphasic water/heptane medium system consisting of chalcone as the substrate, hydrogen peroxide as the oxidant, sodium hydroxide as the base, and dodecyltrimethylammonium bromide (DTAB) as the surfactant was investigated. The empirical rate law was established to be described as follows: rate = k[chalcone]0.74[DTAB]0.50[NaOH]0.87[H2O2]1.53. As a preliminary study, the apparent activation energy of the reaction was determined to be 25.9 kJ/mol.

Mechanistic Investigation of Organolanthanide-Mediated Hydroamination of Conjugated Aminodienes: A Comprehensive Computational Assessment of Various Routes for Diene Activation

The present computational mechanistic study comprehensively explores alternative scenarios for activation of the amine-linked diene C=C linkage toward C-N ring closure in intramolecular hydroamination of a prototypical aminodiene by a well-characterised lanthanocene-amido catalyst. Firstly, the non-insertive mechanism by Scott featuring ring closure with concomitant amino proton delivery onto the diene unit has been explored and key features have been defined. This scenario has been compared with the classical stepwise insertion mechanism that involves rapid substrate association/dissociation equilibria for the 3t-S1 resting state and also for azacycle intermediates 4s, 4a, facile and reversible exocyclic migratory diene insertion into the La-N(amido) σ-bond, linked to turnover-limiting La-C azacycle aminolysis. The Ln-N σ-bond insertive mechanism prevails for the examined intramolecular hydroamination of (4E,6)-heptadienylamine 1t by [Cp*(2)La-CH(TMS)(2)] starting material 2.The following aspects are in support of this mechanism: 1) the derived rate law is consistent with the observed empirical rate law; 2) the assessed effective barrier for turnover-limiting aminolysis does agree remarkably well with empirically determined Eyring parameters; 3) the ring-ether double-bond selectivity is consistently elucidated. This study reveals that the non-insertive mechanism is not achievable for the particular lanthanocene-amido catalyst and furthermore cannot account for the observed product spectrum. Notwithstanding of these findings, the non-insertive mechanism cannot be discarded a priori for intramolecular aminodiene hydroamination. Spatial demands around the lanthanide centre influence the two mechanisms differently. The Ln-N σ-bond insertive mechanism critically relies on a sufficiently accessible lanthanide and enhanced encumbrance renders cyclisation and aminolysis steps less accessible kinetically. It contrasts with the non-insertive mechanism, where greater lanthanide protection has a rather modest influence. The present study indicates that the non-insertive mechanism would prevail if the lanthanide centre were to be protected effectively against C=C bond approach. Notably, a different product spectrum would be expected for aminodiene hydroamination following the insertive or non-insertive route.

Charge-density-based analysis of the current–voltage response of polythiophene/fullerene photovoltaic devices

A key challenge for organic electronics research is to develop device models that correctly account for the structural and energetic disorder typically present in such materials. In this paper we report an approach to analyze the electrical performance of an organic electronic device based upon charge extraction measurements of charge densities and transient optoelectronic measurements of charge carrier dynamics. This approach is applied to a poly(3-hexyl thiophene) (P3HT)/6,6 phenyl C61 butyric acid methyl ester (PCBM) blend photovoltaic device. These measurements are employed to determine the empirical rate law for bimolecular recombination losses, with the energetic disorder present in the materials being accounted for by a charge-density-dependent recombination coefficient. This rate law is then employed to simulate the current/voltage curve. This simulation assumes the only mechanism for the loss of photogenerated charges is bimolecular recombination and employs no fitting parameters. Remarkably the simulation is in good agreement with the experimental current/voltage data over a wide range of operating conditions of the solar cell. We thus demonstrate that the primary determinant of both the open-circuit voltage and fill factor of P3HT:PCBM devices is bimolecular recombination. We go on to discuss the applicability of this analysis approach to other materials systems, and particularly to emphasize the effectiveness of this approach where the presence of disorder complicates the implementation of more conventional, voltage-based analyses such as the Shockley diode equation.

Fluorite dissolution at acidic pH: In situ AFM and ex situ VSI experiments and Monte Carlo simulations

Dissolution of the fluorite (1 1 1) cleavage surface was investigated by means of in situ atomic force microscopy (AFM) and ex situ vertical scanning interferometry (VSI) experiments at pH range 1–3 in HCl solutions. Surface retreat was quantified at different pH values, yielding dissolution rates that were used to derive an empirical rate law for fluorite dissolution: Rate fluorite ( mol m - 2 s - 1 ) = 2.0 ± 0.4 × 10 - 6 · ( a H + ) 0.38 ± 0.07 where a H + is the proton activity. The influence of Δ G on fluorite dissolution rate at pH 2 was investigated by means of AFM and VSI surface measurements and flow-through experiments with powdered fluorite. The fluorite dissolution rate decreases non-linearly with increasing Gibbs energy (Δ G) and a dissolution plateau is obtained at Δ G ⩽ −7 kcal mol −1. This Δ G effect can be expressed with a rate law of the form Rate fluorite mol m - 2 s - 1 = k · a H + n 1 - exp - 4.7 × 10 - 2 · | Δ G | RT 1.41 ± 0.24 An alternative form based on a formulation making use of a Temkin number is also possible Rate fluorite mol m - 2 s - 1 = k · a H + n 1 - exp Δ G 8 RT Dissolution proceeds by formation of equilateral triangular etch pits with trigonal pyramidal morphology and emanation of stepwaves that are responsible for the surface retreat. The results of Monte Carlo simulations are consistent with this reaction mechanism.

Inhibitory Effects of a Phage-Derived Peptide on Au Nanocrystal Nucleation and Growth

Peptides have been shown to mediate the reduction and clustering of inorganic ions during biomineralization processes to build nanomaterials with well-defined shape, size, and composition. This precise control has been linked to specific amino acid sequence; however, there is a lack of information about the role of peptides during mineralization. Here, we investigate the nucleation and growth behavior of Au nanocrystals that are mediated by the engineered peptide AYSSGAPPMPPF. Unlike other nanocrystal synthesis schemes, this peptide produces Au nanocrystals from Au(III) ions at very low relative peptide concentrations, at ambient temperature, and in water at neutral pH. Our data show that (i) the peptide AYSSGAPPMPPF actually inhibits nucleation and growth of nanocrystals, (ii) HEPES plays an active chemical role as the reducing agent, and (iii) HAuCl4 accelerates the kinetics of nanoparticle nucleation and growth. Herein, we propose empirical rate laws for nucleation and growth of Au nanocrystals and compare kinetic rate laws for this peptide, citrate, and various other polymer ligands. We find that the peptide belongs to a unique class of nonreducing inhibitor ligands regulating the surface-reaction-limited growth of nanocrystals.

Coral reefs may start dissolving when atmospheric CO2 doubles

Calcification rates in stony corals are expected to decline significantly in the near future due to ocean acidification. In this study we provide a global estimate of the decline in calcification of coral reefs as a result of increase in sea surface temperature and partial pressure of CO2. This estimate, unlike previously reported estimates, is based on an empirical rate law developed from field observations for gross community calcification as a function of aragonite degree of saturation (Ωarag), sea surface temperature and live coral cover. Calcification rates were calculated for more than 9,000 reef locations using model values of Ωarag and sea surface temperature at different levels of atmospheric CO2. The maps we produced show that by the time atmospheric partial pressure of CO2 will reach 560 ppm all coral reefs will cease to grow and start to dissolve.

Electroless Nickel Phosphorus Plating on AZ31

One of the major drawbacks to using magnesium parts in automotive applications is poor corrosion resistance, which can be improved with a nickel-boron coating placed on a nickel-phosphorus coating, which, in turn, is placed on a phosphate-permanganate conversion-coating layer produced on the magnesium alloy AZ31. This work reports on the determination of the optimum kinetic parameters for producing a coherent nickel-phosphorus coating using an electroless-procedure phosphate-permanganate conversion-coating layer and for studying the effects of the experimental variables of the electroless plating process on the phosphorus content, surface morphology, and structure of the electroless nickel-phosphorus (EN-P) coatings produced. Measurements of the plating rate as a function of experimental variables such as the compositions of the plating bath constituents, temperature, and pH were implemented using the weight-gain method; the phosphorus content of the EN-P coatings was measured using energy-dispersive spectroscopy (EDS) analysis. The surface morphology of the coating was examined using a scanning electron microscope (SEM); X-ray diffraction (XRD) was used to characterize the structure of each coating. An empirical rate law was determined for EN-P plating on a phosphate-permanganate conversion coating. It is found that the deposition rate of the EN-P coating increases by increasing the deposition temperature, the concentration of free nickel ions, and the concentration of hypophosphite ions in the plating bath. In addition, the deposition rate decreases by increasing both the plating bath pH and the concentration of citric acid in the plating bath.

Initial Degradation Rate of p-Nitrophenol in Aqueous Solution by Fenton Reaction

Because of environmental concern, wastewater containing nitrophenols must be treated before it is allowed to discharge. In addition to traditional treatment methods, advanced oxidation processes (AOPs) using a powerful hydroxyl radical to decompose organic pollutants in wastewater receive great attraction. Among the many AOPs to degrade nitrophenols, the Fenton reaction was proven to be the most effective and the least expensive method, and the resultant solutions treated by the Fenton reagent were not toxic. However, owing to the complicated mechanism involved in the Fenton reaction, an oversimplified first-order rate equation or empirical rate laws were usually used to model the Fenton reaction. Such oversimplified or empirical kinetics cannot be used confidently in the design and operation of large-scale Fenton processes. A series of experiments were carried out to determine the initial decomposition rates of p-nitrophenol (PNP) at varying initial ferrous ion, hydrogen peroxide, and PNP concentrations. The PNP decomposition rate equations for two proposed mechanisms were derived by the general rate methodology. The rate equation resulting from the reaction mechanism involving the PNP reaction with both hydroxyl and hydroperoxy radicals fits the experimental data well.

Influence of Size on Reductive Dissolution of Six-Line Ferrihydrite

This work investigates size dependence of the kinetics of reductive dissolution of six-line ferrihydrite, ranging in average length from 3.4 to 5.9 nm. Empirical rate laws, activation energies, and pre-exponential factors were determined for freshly prepared aqueous suspensions and dried powders of each ferrihydrite sample. Mass-normalized initial rates of reductive dissolution are substantially faster for the freshly prepared suspensions than for reactions using the dried powders, which is consistent with a drop in reactive surface area upon drying. In addition, results demonstrate substantial differences between the empirical rate laws for the freshly prepared and the dried six-line ferrihydrite. Comparing surface-area-normalized rates of reductive dissolution reveals a small dependence on size for the freshly prepared ferrihydrite, no dependence on size for the dried ferrihydrite nanoparticles, and no statistically significant change in the activation energy for reaction in either case. In addition, X-...

Oxalate-promoted forsterite dissolution at low pH

We ran a series of 124 semi-batch reactor experiments to measure the dissolution rate of forsterite in solutions of nitric and oxalic acid solutions over a pH range of 0–7 and total oxalate concentrations between 0 and 0.35 m at 25 °C. We found that the empirical rate law for the dissolution of forsterite in these solutions is r = 10 - 7.03 a H + 0.46 + 10 - 5.44 m ox 2 - 0.40 a H + 0.47 where a H + is the activity of hydrogen ions, m ox is the concentration of oxalate in molal, and the rate is given in (mol/m 2 s). The first term of the rate law expresses the dissolution rate for solutions with no oxalate and the second term expresses the additional rate produced by the presence of oxalate ions. Our experiments show that oxalate-promoted dissolution rates depend upon both oxalate concentration and pH. Based on this, we propose a reaction mechanism in which a hydrogen ion and an oxalate ion are simultaneously present in the activated complex for the reaction that releases H 4SiO 4 into solution. By analogy, we propose that water acts as a ligand in the absence of oxalate, so the first term of our rate law has a H 2 O m (=1) as a hidden term. Thus, our results suggest that both a proton and a ligand (either an anion or a water molecule) must be present in the activated complex for forsterite dissolution, suggesting that proton-promoted and ligand-promoted dissolution are simply two aspects of the same process, and that the distinction between the two is artificial. The increased dissolution rate of forsterite produced by oxalate ions at a concentration of 0.001 m, a concentration comparable to the amount of organic acids in typical soils, translates into an approximately a 6-fold increase in forsterite dissolution rates at pH > 4.2. This suggests that organic acids have a measurable, but not profound, effect on chemical weathering.

Modeling Microbially Induced Carbon Degradation in Redox-Stratified Subsurface Environments: Concepts and Open Questions

The degradation of organic matter, including organic contaminants, in subsurface environments is controlled by the abundances and functional capabilities of the resident microorganisms. As a consequence, modeling approaches simulating the fate of organics and related changes in redox conditions have to account for the effects of microbial activity on the degradation kinetics, as well as for the spatial and temporal distributions of the chemical species (e.g., terminal electron acceptors, nutrients or toxic substances) that control microbial activity. The present paper reviews the principal modeling approaches that are used to simulate the degradation of organic matter in water-saturated porous media. Special attention is devoted to modeling the bioavailability of chemical substrates of microbial reactions, and the sequential occurrence of terminal electron accepting pathways. While the various model approaches found in the literature are capable of reproducing field data sets from various environmental settings, they are rarely compared in terms of performance and predictive ability. Most approaches incorporate simplifications or empirical rate laws, which limit their range of application. Thus, there remains a need for further development of more general, process-based modeling concepts to represent microbially mediated reactive processes.

Kinetics of Zinc Oxide Sulfidation for Packed-Bed Desulfurizer Modeling

The sulfidation process of porous zinc oxide sorbent with hydrogen sulfide can be described in five steps after external mass transfer and pore diffusion. They are surface adsorption of hydrogen sulfide gas on zinc oxide sorbent and dissociation of the gas molecule on the sorbent surface, followed by reversible surface reactions, sulfide ion migration under the surface, and sulfidation penetration into the solid crystallite. On the basis of the understanding of this chemistry, an empirical rate law for the intrinsic kinetics of the sulfidation process was derived in this study. Kinetics modeling results using this reversible, adsorption, and ion-migration (RAIM) model were found, consistent with selected experiments of single-particle sulfidation. Modeling results were also comparable with several well-defined sulfidation models in the literature. The intrinsic kinetics of a porous ZnO sorbent G-72E were measured in a microflow packed column and calculated using the RAIM model, using a finite difference approach. The effective pore diffusivity of gaseous hydrogen sulfide in the porous zinc oxide pellet was calculated using the general process modeling system (gPROMS). Finally, design calculation for a full-scale packed desulfurizer was performed using the gPROMS distributed reactor model. Case studies were presented for hydrogen sulfide removal from natural gas in a simulated fuel-processing train for syngas production.

Kinetic Isotope Effect and Extended pH-Dependent Studies of the Oxidation of Hydroxylamine by Hexachloroiridate(IV): ET and PCET

The oxidation of hydroxylamine by [IrCl6]2- has been studied spectrophotometrically in deoxygenated aqueous solutions in the range of pH 4-9 at 25 degrees C. The reaction is catalyzed by Cu2+, Fe2+, and impurities of aquochloroiridium complexes. Oxalate is a very effective inhibitor of catalysis by copper and iron ions. With excess hydroxylamine, the reaction follows pseudo-first-order kinetics, and the stoichiometric ratio (DeltanIr(IV)/Deltanhydroxylamine) is 1.05 at pH 5.9. Over the pH range 4.2-8.8, the empirical rate law is -d[IrCl(6)2-]/dt=k[IrCl6(2-)][NH2OH]tot, with k=k1Ka1/([H+]+Ka1)+k'Ka1/([H+]([H+]+Ka1)), where Ka1 is the dissociation constant of NH3OH+. Least-squares fitting yields k1=(17.05+/-0.47) M-1 s(-1) and k'=(2.59+/-0.09)x10(-6) s(-1) at ionic strength of 0.1 M (adjusted by NaClO4) and 25 degrees C. The kinetic isotope effects (KIE) (kH/kD) for k1 and k' are 4.4 and 9.8, correspondingly. A mechanism is inferred in which k1 corresponds to concerted proton-coupled electron transfer (PCET) and k' corresponds to electron transfer from NH2O-. In this mechanism, the large KIE for k' is due almost entirely to the equilibrium isotope effect for the pKa of NH2OH.

Simulation of the Electron Transfer between the Tetraheme Subunit and the Special Pair of the Photosynthetic Reaction Center Using a Microstate Description

Charge transfer through biological macromolecules is essential for many biological processes such as, for instance, photosynthesis and respiration. Protons or electrons are transferred between titratable residues or redox-active cofactors, respectively. Transfer rates between these sites depend on the current charge configuration of neighboring sites. Here, we formulate the kinetics of charge-transfer systems in a microstate formalism. A unique transfer rate constant can be assigned to the interconversion of microstates. Mutual interactions between sites participating in the transfer reactions are naturally taken into account. The formalism is applied to the kinetics of electron transfer in the tetraheme subunit and the special pair of the reaction center of Blastochloris viridis. It is shown that continuum electrostatic calculations can be used in combination with an existing empirical rate law to obtain electron-transfer rate constants. The re-reduction kinetics of the photo-oxidized special pair simulated in a microstate formalism is shown to be in good agreement with experimental data. A flux analysis is used to follow the individual electron-transfer steps.

Kinetic analysis of the carbonation reactions for the capture of CO2 from air via the Ca(OH)2–CaCO3–CaO solar thermochemical cycle

Abstract A thermogravimetric analysis of the carbonation of CaO and Ca(OH)2 with 500 ppm CO2 in air at 200–450 °C is performed as part of a three-step thermochemical cycle to capture CO2 from air using concentrating solar energy. The rate of CaO-carbonation is fitted to an unreacted core kinetic model that encompasses intrinsic chemical reaction followed by intra-particle diffusion. In contrast, the Ca(OH)2-carbonation is less hindered by diffusion while catalyzed by water formation, and its rate is fitted to a chemically-controlled kinetic model at the solid interface not covered by CaCO3. The rates of both carbonation reactions increase with temperature, peak at 400–450 °C, and decrease above 450 °C as a result of the thermodynamically favored reverse CaCO3-decomposition. Avrami's empirical rate law is applied to describe the CO2 uptake from the continuous air flow by CaO and Ca(OH)2, with and without added water. The addition of water vapor significantly enhances the reaction kinetics to the extent that, in the first 20 min, the reaction proceeds at a rate that is 22 and nine times faster than that observed for the dry carbonation of CaO and Ca(OH)2, respectively.

Mechanism and exo‐Regioselectivity of Organolanthanide‐Mediated Intramolecular Hydroamination/Cyclization of 1,3‐Disubstituted Aminoallenes: A Computational Study

The complete catalytic reaction course for the organolanthanide-assisted intramolecular hydroamination/cyclization (IHC) of 4,5-heptadien-1-ylamine by a prototypical [(eta(5)-Me5C5)2LuCH(SiMe3)2] precatalyst has been critically scrutinized by employing a reliable DFT method. A computationally verified mechanistic scenario for the IHC of 1,3-disubstituted aminoallene substrates has been proposed that is consistent with the empirical rate law determined by experiment and accounts for crucial experimental observations. It involves kinetically rapid substrate association and dissociation equilibria, facile and reversible intramolecular allenic C=C insertion into the Ln-N bond, and turnover-limiting protonation of the azacycle's tether functionality, with the amine-amidoallene-Ln adduct complex representing the catalyst's resting state. This mechanistic scenario bears resemblance to the mechanism that has been recently proposed in a computational exploration of aminodiene IHC. The unique features of the IHC of the two substrate classes are discussed. Furthermore, the thermodynamic and kinetic factors that control the regio- and stereoselectivity of aminoallene IHC have been elucidated. These achievements have provided a deeper insight into the catalytic structure-reactivity relationships in organolanthanide-assisted cyclohydroamination of unsaturated C-C functionalities.

Precipitation of Silver Powders in the Presence of Ethylenediamine Tetraacetic Acid

Silver powders can be produced by the reduction of a silver salt in an aqueous solution. The manipulation of the rates of the reaction allows the control of the properties such as size and size distribution of the produced particles. In the present work, we studied the addition of ethylenediamine tetraacetic acid (EDTA) as a complexation agent to moderate the rate of the reduction of silver cations with hydrazine as the reducing agent. The experiments were carried out in a batch reactor at different concentrations of the reactants. In the absence of EDTA, the reaction between hydrazine and the silver cations is extremely fast. It was found that, in the absence of seeds, the reaction starts by the precipitation of the free silver ions followed by a period where any reduced elemental silver forms sub-micrometer particles by nucleation. The addition of seeds promotes the growth of particles and suppresses nucleation. When the concentration seeds are greater than 5.4 x 10 -1 mM, no nucleation is apparent. This allows the determination of the reaction rate between hydrazine and silver cations. At 20 °C, the empirical rate law for the reduction of silver was r Ag = 9.35 [Ag] 1.3 [N 2 H 4 ] 0.7 [EDTA] -1.1 in mmol of Ag/L-min.

Effect of ozone on ruthenium species in alkaline medium – Part II: Oxidation of pentahydroxo nitrosyl ruthenate(II) ion RuNO(OH)52-

SummaryOxidation of the nitrosyl ruthenium complex RuNO(OH)52-has been carried out in sodium hydroxide solutions in contact with a gas flow containing ozone. The RuNO(OH)52-complex is converted successively into ruthenate and perruthenate ions. An empirical kinetic rate law for the first step has been determined and was shown to depend on concentrations of (i) the ruthenium complex, (ii) the hydroxide ions and (iii) ozone concentration in the gas flow. The second step of the reaction, corresponding to the perruthenate ion formation, shows a complex mechanism and four competing reactions have been proposed to represent it. The influences on the second step kinetics of several parameters such as ozone or hydroxide concentrations or the conditions of the gas-liquid exchange area are also qualitatively discussed.

Organolanthanide‐Mediated Intermolecular Hydroamination of 1,3‐Dienes: Mechanistic Insights from a Computational Exploration of Diverse Mechanistic Pathways for the Stereoselective Hydroamination of 1,3‐Butadiene with a Primary Amine Supported by an ansa‐Neodymocene‐Based Catalyst

The complete catalytic reaction course for the organolanthanide-mediated intermolecular hydroamination of 1,3-butadiene and n-propylamine by an archetypical [Me2Si(eta5-Me4C5)2NdCH(SiMe3)2] precatalyst was critically scrutinized by employing a reliable gradient-corrected DFT method. A free-energy profile of the overall reaction is presented that is based on the thorough characterization of all crucial elementary steps for a tentative catalytic cycle. A computationally verified, revised mechanistic scenario is proposed which is consistent with the experimentally derived empirical rate law and accounts for crucial experimental observations. It involves kinetically mobile reactant association/dissociation equilibria and facile, reversible intermolecular diene insertion into the Nd-amido bond, linked to turnover-limiting protonolysis of the eta3-butenyl-Nd functionality. The computationally predicted effective kinetics (Delta(tot) = 11.3 kcal mol(-1), Delta(tot) = -35.7 e.u.) are in reasonably good agreement with experimental data for the thoroughly studied hydroamination of alkynes. The thermodynamic and kinetic factors that determine the almost complete regio- and stereoselectivity of the mechanistically diverse intermolecular 1,3-diene hydroamination have been unraveled. The present computational study complements experiments because it allows, first, a more detailed understanding and a consistent rationalization of the experimental results for the hydroamination of 1,3-dienes and primary amines and, second, enhances the insights into general mechanistic aspects of organolanthanide-mediated intermolecular hydroamination.