Chemical Rate Constants Research Articles

Generation of response maps of gas mixtures

Large area field effect structures with thin catalytic metal gates can be used to generate two dimensional images of the response of the metal to gas mixtures. This is done by using a scanning light pulse technique to determine polarization changes occurring in the thin metal film due to chemical reactions on the metal. Such images appear to be a new concept in chemical sensing. The present contribution is a first attempt to predict the shape of these images. We show that the occurrence of maxima in the response at certain points on the surface is most likely due to temperature dependent chemical rate constants and to the consumption of molecules on the catalytic metal surface. Experimental results of the detection of methanol, ethanol, and hydrogen on palladium and platinum, with a temperature gradient along the metals, are used to support the theoretical arguments.

Digital simulation of steady state and non-steady state voltammetric responses for electrochemical reactions occurring at an inlaid microdisk electrode: Application to EC irr, EC' and CE first-order reactions

A general algorithm based on the Hopscotch method and a conformal map is used to treat electrochemical reactions with coupled homogeneous chemical reactions occurring both at conventionally sized electrodes and at ultramicroelectrodes. A change of the dimensionless parameter p = a(nFv/RTD) 1 2 , where a is the radius of the electrode, v the potential sweep rate and D the diffusion coefficient, allows us to describe properly the planar and the convergent mass transfer to an inlaid disk-shaped electrode. The dimensionless parameter λ′ = ka 2/ D, which is a function of the sum of the chemical rate constants ( k) and of the electrode radius, describes the kinetics and may be used instead of the conventional parameter λ = k(RT/nFv). A suitable choice of the space-time grid gives accurate results, even for kinetic problems affected by stiffness difficulties. The adequacy of the implementation is established by comparison with known solutions relative to the EC irr' EC' and CE mechanisms for two limiting cases, i.e. planar and radial mass transport conditions.

Time-resolved detection of reaction products in the infrared laser chemistry of sulfoxides: C 2H 4SO, (CH 3) 2SO, (CD 3) 2SO

The first observations of the infrared laser chemical reaction of organic sulfoxides after IR multiphoton excitation of the SO infrared chromophore (with large band strength G=2.0 pm 2 in (CH 3) 2SO) with pulsed CO 2 laser radiation are reported. The collisionless IR photochemical primary products are shown to be C 2H 4 and SO ( 3Σ −) for C 2 H 4SO, and CH 3 and ( 3Σ −) SO (via CH 3SO) for (CH 3) 2SO by means of time-resolved laser spectroscopic observation of C 2H 4, SO, and CD 3. Effective laser chemical rate constants k I(st)=1.2 cm 2 J −1 for C 2H 4SO (9R32) and 0.06 cm 2 J −1 for (CH 3) 2SO (9R32) are obtained from static yield measurements as well as unimolecular decay constants k≈10 7 to 10 8 s −1 (for C 2H 4SO) after excitation above threshold and laser probing of C 2H 4 and SO. A nonlinear intensity dependence of k(st) is reported for C 2H 4SO and nanosecond intramolecular relaxation for (CH 3) 2SO.

Evaluation of electrochemical parameters for an EC mechanism from a global analysis of current-potential-time data: application to reductive cleavage of methylcobalamin.

Simultaneous evaluation of electron-transfer rate constant, k degree, following chemical reaction rate constant, kf, electron-transfer coefficient, alpha, and standard potential, E degree', for electron transfer coupled to a following chemical reaction (EC mechanism) is described. A mathematical model for the current response to a potential step is developed by incorporating the appropriate concentration terms into the Butler-Volmer equation. Experimental current-potential-time (i-E-t) surfaces are fit to this model to evaluate the parameters. Fitting individual i-t or i-E curves did not yield unique parameter values whereas an i-E-t surface constituted by several i-t or i-E curves could be fitted to obtain unique values. A generalized kinetic zone diagram for the EC reaction is drawn by examining the limiting forms of the expression for current. Theoretical limits of measurable rate constants are estimated from the zone diagram. The three-dimensional electro-chemistry described above was used to study the reductive cleavage of methylcobalamin in dimethyl sulfoxide (DMSO) solvent and 0.1 M tetrabutyl-ammonium perchlorate supporting electrolyte. The parameters estimated are as follows: alpha = 0.552 +/- 0.004; k degree = 0.011 +/- 0.0015 cm s-1; kf = 1500 +/- 140 s-1; E degree' = -1.54 +/- 0.01 V. The rate constant for the following reaction, kf, in DMSO solvent is approximately 4000-fold faster than the similar process in aqueous medium. It is suggested that this enhancement is relevant to methyl group transfer in enzymatic reactions, e.g., methionine synthase, if the enzyme mechanism involves a reductive cleavage which produces a methyl radical.

Hollow fiber solvent extraction removal of toxic heavy metals from aqueous waste streams

This study is concerned with the applications of the immobilized interface-based techniques to reversible chemical complexation-based solvent extraction of toxic heavy metals from industrial wastewaters using microporous hydrophobic hollow fiber (MHF) modules. Toxic heavy metals studied were copper and chromium(VI). Each metal was individually removed in separate once-through experiments from a synthetic wastewater by organic extractants flowing in the shell-side countercurrent to wastewater flowing in the fiber bore. The organic extractant used for copper extraction was 5-20 % v/v LIX 84 diluted in n-heptane, and that for chromium extraction was 30 % v/v TOA (tri-n-octylamine) diluted in xylene. A mathematical model was developed to predict the extent of copper extraction from the aqueous synthetic wastewater by the MHF module. The equilibrium constant for copper was determined to be 1.7 from experimental partitioning data. The experimental data on copper extraction in the MHF module are described well by the model if the forward interfacial chemical reaction rate constant is 9.0 X 10[sup [minus]6] cm/s.

The kinetics of manganese (II) extraction in the acidic sulphate-D2EHPA-n-hexane system using the rotating diffusion cell technique

The kinetics of the extraction of manganese (II) from acidic sulphate solutions by di-2-ethylhexyl-phosphoric acid (D2EHPA, HR) dissolved in n-hexane have been studied over a wide range of manganese concentrations, extractant concentrations, pH and temperature conditions using the Rotating Diffusion Cell (RDC) technique. The generalised mass transfer with chemical reaction model (MTWCR) of Hughes and Rod has been used to fit the experimental data. A ΔpH term has been introduced to calculate the interfacial pH, which yields better fitting of the experimental data, together with a constant value of the kinetic parameter Φ 1 where Φ 1 = k R· D HR/ P HR 2· K HR. Here k R is the chemical rate constant, HR and P HR are the acid dissociation and the partition coefficient of the monomeric reagent, and D HR is the diffusivity of the reagent in the reaction zone. The variation of fluxes of metals with pH is not due to the variation of P HR in the kinetic parametr, Φ 1, but is mainly due to the variation of interfacial pH with the small variation in the mass transfer coefficients, particularly the aqueous mass transfer coefficient. The log-log plots of flux, F, versus experimental variables suggest that the formation of a 1:1 complex in the aqueous film is the rate-determining chemical reaction step. The low activation energy of around 20 kJ mol −1 suggests that the extraction mechanism is mixed chemical with mass transfer control.

Solution of the Boltzmann equation for a reacting gas mixture

A spatially homogeneous gas mixture consisting of structureless molecules of kind A, B, C, D is considered in which the reversible bimolecular reaction A+B ^ C+D occurs. The Boltzmann equation describing this model gas is solved numerically by using the multigroup method. The collision cross sections correspond to the reactive hard sphere model. Parameters are the heat of reaction, the activation energy and the steric factor. Emphasis in the presentation of the results is laid on highly exothermic reactions with large activation energy, in which case the gas undergoes a thermal explosion. It is found that the corrections of the chemical rate constants due to translational non-equilibrium effects are noticeable. The result is a shortening of the reaction period by up to 25%.

Kinetics of Gaseous Reduction of Iron Ore Fines.

Unsintered beds of blue dust of varying thicknesses were subjected to reduction in flowing reducing gases. The temperature range was 898 to 1123 K for hydrogen reduction and 1073 to 1373 K for reduction by carbon monoxide. Reduction by CO was carried out in two-stages, and only the data of second stage (wustite→iron) were analysed further. Several approaches to data analysis were attempted. The most satisfactory one was to take the slope of the initial linear region of fractional reduction vs. time curve as a measure of rate constant (k). Extrapolation of k vs. bed depth data to hypothetical zero bed depth for H2-reduction and to 0.4 mm depth for CO-reduction allowed determination of chemical rate constants (kc). In kc vs. 1/T plots were not straight lines. This and other anomalous behaviours were attributed to structural changes in the bed during reduction.

Seasonal and latitudinal variations of gravity wave‐driven fluctuations in OH nightglow

The seasonal and latitudinal variations of the gravity wave‐driven fluctuations in the OH nightglow are investigated theoretically using a model that accounts for emission from an extended OH layer and includes the effects of eddy diffusivities in the gravity wave dynamics. The mean (unperturbed) state is obtained from a two‐dimensional, nighttime model so that mean‐state number densities, temperatures and eddy diffusivities are all self‐consistent. Seasonal and latitudinal variations in the background OH nightglow emission and in the propagation and dissipation characteristics of the gravity waves influence how the OH nightglow modulations due to gravity waves depend on season and latitude. At intermediate gravity wave periods (i.e., periods between 0.5 and 3 hours for λx = 100 km; between 3 and 10 hours for λx = 500 km; and greater than about 4 hours for λx = 1000 km) possible trends in the behavior of <η> (equal to , where I is the airglow intensity, T is intensity‐weighted temperature, an overbar denotes the mean state, a prime denotes a perturbation about that mean state and the brackets indicate vertical integration over all emission levels) with latitude and season could be masked by interference effects. At long periods (i.e., periods greater than 3 hours and 10 hours for λx = 100 and 500 km, respectively) trends are complicated by the competing effects of eddy diffusivities, which directly modify both local values of and the altitudes of maximum wave amplitude, and the vertical distributions of the minor species. Only at periods of a few hours or less (depending on horizontal wavelength) are any seasonal trends seen in <η>, and these are more noticeable in the magnitude of <η> than in its phase. These seasonal variations in <η> are primarily due to seasonal variations in the undisturbed temperature which affect the temperature‐dependent chemical rate constants involved in the OH nightglow. A specific case showing latitudinal trends is presented, but the result is not representative of all of our results obtained involving latitudinal variations.

Activation process model: application for diffusivity in covalent crystals

In this paper we try to produce an activation process model. The physical essence of the model is different from the Boltzmann-Arrhenius model. The proposed model is based on two assumptions: (1) in elementary activation interaction act, the potential energy of moving atoms changes discretely or in quanta: elementary activation act appears to be a series of quantum subsystems occurring in sequence (these subsystems may also be defined as identical quantum oscillators); (2) in statistical equilibrium with thermal radiation an energy exchange between IR radiation and interacting atoms results in discrete translational motion changes of those atoms which absorb and subsequently emit an oscillation energy quantum series. In accordance with the model proposed, a formula describing the average energy of the translationally moving atoms participating in an elementary activation act has been derived from first principles. As an application of the model, the formulae of solid state atomic diffusivity plus first-order chemical reaction rate constants have been obtained. The method of calculation of diffusivity in covalent crystals has been elaborated on the basis of the model proposed. The diffusivities of silicon, oxygen and their singly charged ions in monosilicon have been calculated. For this purpose the MO LCAO method in the CNDO/2 valence approximation has been used. Analysis of the calculation results obtained indicates the quality of the model proposed when applied to the diffusion process.

Optimized calculations of reaction paths and reaction-path functions for chemical reactions

In this paper we optimize several algorithms for the computation of reaction rates based on information calculated along minimum energy reaction paths and we evaluate the efficiencies of the optimized algorithms. The investigations are based on the calculation of chemical reaction rate constants using variational transition state theory and multidimensional semiclassical transmission coefficients including reaction path curvature. Several methods are evaluated and compared by a systematic set of applications to test cases involving the hydrogen-atom transfer reactions CH3+H2→CH4+H and OH+H2→H2O+H. For each method we present general recommendations for all algorithmic choices other than gradient step size so that future calculations may be carried out reasonably efficiently by varying only one parameter. In the process of these optimizations we have found that the accuracy of the Euler stabilization method can be significantly increased by choosing the auxiliary parameters differently than in previous work; the optimized algorithm is called ES1*. Our final recommendations for future work are (i) when the Hessian/gradient computational cost ratio is low (≲3): the Page–McIver algorithm with the Hessian recalculated at every step, with a cubic starting step, and with curvature calculated from the derivative of the gradient, and (ii) when the Hessian/gradient computational cost ratio is moderate or large: the ES1* algorithm with a Hessian step size three times larger than the gradient step size, with a quadratic starting step, and with curvature calculated from the derivative of the gradient.

Rates of Nitrogen and Carbon Removal from Liquid Iron in Low Content Region under Reduced Pressures.

The kinetics of nitrogen and carbon removal from a liquid iron surface in low content regions by blowing Ar gas mixture under reduced pressures have been studied using the same vacuum induction furnace at 1 600°C, respectively. The results obtained are as follows:(1) The nitrogen removal reaction is described as a second order reaction with respect to nitrogen content. The overall reaction rate constant, kovN, decreases with the increase of total pressure, and oxygen and sulfur content.Assuming that the nitrogen removal reaction progresses by a mixed control and that the chemical reaction for nitrogen gas formation is caused by adsorbed nitrogen atoms, the chemical reaction rate constant, krN, and the adsorption coefficient of oxygen, κO, and of sulfur, κS, are estimated as follows:N+N=N2+_??_krN(=k[N]/fN2) cm/mass%/sec = 15/(1+κO·aO+κS·aS)2, κO=161, κS=63.4In the Fe-20mass%Cr-0.2Mass%C-S system also, the value of krN can be expressed by the same equation. It is thus concluded that, macroscopically, the mechanism of nitrogen removal is the same irrespective of whether or not the melt contains chromium.(2) In the carbon content range below 200 ppm, the overall carbon removal reaction rate constant, kovC, exhibits a maximum value against oxygen content, and decreases with the increase of sulfur content.Assuming that the chemical reaction for CO gas formation caused by the adsorbed carbon and the adsorbed oxygen atoms as a following equation, the dependence of the chemical reaction rate constant on oxygen and sulfur content is explained by the values of the adsorption coefficients κO and κS, respectively.C+O=CO+_??_The value of κO is equal to about 100-300 and that of κS is equal to about 40-65.These values are in general accord with those determined from the nitrogen desorption reaction.

Effect of Slag Composition on the Kinetics of the Reduction of Iron Oxide in Molten Slag by Graphite.

A kinetic study has been made on the reduction of iron oxide in molten slag with graphite. The composition of the primary slag was changed so that SiO2 concentration varied between 0.33 and 0.50 mole fraction, and slag basicity between 1 and 2. The experimental temperature was 1300°C. The reaction rate is significantly affected by the slag composition. From values of the mass transfer coefficient, calculated by using penetration theory, it is presumed that for the slags with basicity of 2, the reaction rate is controlled by mass transfer in the slag phase, but chemical reaction resistance is predominant in slags with lower basicities. By applying a mixed-control model to the latter case, the apparent chemical reaction rate constant was calculated. The rate constant decreases largely with increasing the silica activity. The reaction rate also decreases with the presence of phosphorus in the slag. These behaviors indicate that the reaction rate is very sensitive to the interfacial chemisorption of the surface active agents.

Modelling of Laminar Phenomena of Chemical Heat Treating Processes.

A general equation of the concentration distribution under laminar conditions was proposed. On the basis of this equation an integral method was derived. This method is based on setting a balance of flux gradients of the transfer phenomena that occur. It was shown that the flux gradient is identical to the characteristic quantity N which defines the state at the cross-section perpendicular to the surface, the definition of which enables the formulation of the proposed general equation.The general approximative integral method was applied to the phenomena on the metal surface, mass transfer during a heterogeneous chemical reaction in the laminar boundary layer over a flat plate–measuring foil. A model of the mass transfer coefficient was presented as a function of the limiting heterogeneous chemical reaction rate constant, characteristic time relation and surface function of the appropriate gas atmosphere.The proposed model is a theoretical basis for the development of a measuring device of non-equilibrium gas carburizing processes.

Equatorial electrojet parameters and the relevance of Electromagnetic Drifts (EMD) over Thumba

The thermal imbalance in theE-region heights is inescapable and an undisputed fact. The equatorial electrojet parameters are being evaluated for an Indian Equatorial station of Thumba, making use of the observed electron density, electron temperature, and current density profiles for two rocket flights on 3 March, 1973 and 7 April, 1972 around local noon, corresponding to low and medium solar active conditions. The computed Joule heating due to Equatorial Electrojet Current (EEC) does not account for the observed difference between the electron and neutral gas temperatures. The discrepancy of about 6 km in the peaks of the observed and computed current density profiles may be attributed to the presence of the Electromagnetic Drifts (EMD). In order to see whether or not EMD plays an important role, the photoionization balance between production and loss rates have been computed by making use of the latest available solar flux and cross sections and chemical reaction rate constants for the appropriate solar epoch conditions including the transport term due to EMD. There is an excellent agreement between the observed and computed electron density profiles indicating its relevance.

Temperature dependence of the rate constant for dissociation of absorbed molecules

An equation obtained by the Fokker-Planck formalism governing the temperature dependence of the chemical reaction rate constant is discussed. This equation is applied for the reaction of dissociation of a diatomic molecule adsorbed on a solid surface. It is shown that the denominator in the exponential term of the rate constant (which is kT in the classical Arrhenius equation) increases for this process as a consequence of the influence of surface phonons.

Muscle 31P-NMR in humans: estimate of bias and qualitative assessment of ATPase activity

A mathematical model is developed whereby the longitudinal magnetization of phosphocreatine (PC), ATP, Pi, and total phosphate (PT) can be calculated on the basis of assumed chemical rate constants (kappa i) and spin lattice relaxation times of the muscle PC in equilibrium ATP in equilibrium Pi exchange system. By means of this model, some unexplained 31P nuclear magnetic resonance (NMR) spectroscopy results from the literature (e.g., a decrease of PT in a closed system) could be explained simply on the basis of the physiological variability of kappa i. Moreover, appropriate model simulations indicate that 1) 31P-NMR spectra obtained with short relaxation delays may be influenced to various extents by the metabolic and physicochemical status of the muscle; 2) the assessment of kappa i by standard NMR spectroscopy techniques may be extremely critical; 3) delta PC/delta Pi, as obtained from conventional 31P-NMR spectra, may represent a sensible index of kappa 2 (the pseudo first-order chemical exchange rate constant of the adenosinetriphosphatase reaction); 4) delta PC/delta Pi changes as detected from sequential (short relaxation delays) 31P-NMR spectra obtained in humans during metabolic transients (e.g., during transition from rest to work and vice versa) may represent an index of transient changes of kappa 2.

Scanning electrochemical microscopy. 9. Theory and application of the feedback mode to the measurement of following chemical reaction rates in electrode processes

The use of the scanning electrochemical microscope (SECM), in both the steady-state and chronoamperometric feedback modes, is proposed as a new method for measuring the kinetics of following chemical reactions in electrode processes. Particular attention is given to the E,Ci mechanistic case (first-order irreversible chemical step following reversible electron transfer). Theory for the problem, relating the SECM feedback current to the tip-substrate distance, tip electrode radius, and rate constant for the chemical step, is developed numerically by using the alternating-direction implicit finite-difference scheme. The theoretical results demonstrate that both the chronoamperometric and steady-state feedback modes are sensitive techniques for accurate kinetic determinations, and that homogeneous chemical rate constants in excess of 2 X 104 s-' should be accessible to measurement with current SECM technology. The theoretical predictions are verified experimentally with the measurement of the rate of deamination, in aqueous basic solution (pH 10.2-1 2.4), of oxidized N,N-dimethyl-p-phenylenediamine, produced at a platinum electrode.

On stability and uniqueness of stationary one-dimensional patterns in the Belousov-Zhabotinsky reaction

In this paper, a numerical solution technique is presented for obtaining time-independent spatial patterns of chemical concentration in the Belousov-Zhabotinsky reaction. The Oregonator model of the reaction is assumed, and the concentrations of each of the three principal intermediate species are expressed as Fourier series in the spatial variable, and the coefficients are then obtained by a straightforward Galerkin technique. Results of extensive numerical calculation are discussed, and it is demonstrated that, in many instances, the spatial pattern obtained is not unique, in the sense that at least two different patterns could be produced at the same values of the chemical rate constants and diffusion coefficients. The problem of whether the steady patterns are stable in time to small perturbations is discussed in detail. A criterion for stability of patterns of infinitesimal amplitude is established, and it is shown that, when all the diffusion coefficients are equal, there can be no stable small-amplitude solutions. However in the non-linear case, large-amplitude “quasi-stable” patterns have been discovered and these are discussed.

Pulse radiolysis with conductometric detection: Two approaches to absolute dosimetry

In pulse radiolysis, the knowledge of the pulse dose is indispensable if chemical rate constants are to be extracted from kinetics other than first order. Two methods are introduced which by conductivity measurements in pulse radiolysis allow the pulse dose to be determined. One of them is based on the formation of methylsulfinic acid upon radiolysis of dimethyl sulfoxide in water, and the other on the neutralization reaction in water at pH 7.