Fractional Reaction Order Research Articles

Kinetics of pyrite oxidation in sodium carbonate solutions

The kinetics of pyrite oxidation in sodium carbonate solutions were investigated in a stirred vessel, under temperatures ranging from 50 °C to 85 °C, oxygen partial pressures from 0 to 1 atm, particle size fractions from −150 + 106 to −38 + 10 µm (−100 + 150 Mesh to −400 Mesh + 10 µm) and pH values of up to 12.5. The rate of the oxidation reaction is described by the following expression:−dN/dt = SbkpO 2 0.5 [OH−]0.1 whereN represents moles of pyrite,S is the surface area of the solid particles,b is a stoichiometric factor,k is an apparent rate constant, pO```2`` is the oxygen partial pressure, and [OH−] is the hydroxyl ion concentration. The experimental data were fitted by a stochastic model for chemically controlled reactions, represented by the following fractional conversion(X) vs time (t) equation: (1−X)−2/3−1 =k STt The assumption behind this model,i.e., surface heterogeneity leading to preferential dissolution, is supported by the micrographs of reacted pyrite particles, showing pits created by localized dissolution beneath an oxide layer. In addition to the surface texture, the magnitude of the activation energy (60.9 kJ/mol or 14.6 ± 2.7 kcal/mol), the independence of rate on the stirring speed, the inverse relationship between the rate constant and the initial particle diameter, and the fractional reaction orders are also in agreement with a mechanism controlled by chemical reaction.

Lewis Base Complexation, Aggregation, and Reactivity of .sigma.-Organolithiums. Significance of Fractional Reaction Orders in RLi

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTLewis Base Complexation, Aggregation, and Reactivity of .sigma.-Organolithiums. Significance of Fractional Reaction Orders in RLiH. Luitjes, F. J. J. de Kanter, M. Schakel, R. F. Schmitz, and G. W. KlumppCite this: J. Am. Chem. Soc. 1995, 117, 14, 4179–4180Publication Date (Print):April 1, 1995Publication History Published online1 May 2002Published inissue 1 April 1995https://doi.org/10.1021/ja00119a038RIGHTS & PERMISSIONSArticle Views137Altmetric-Citations22LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (2 MB) Get e-AlertsSupporting Info (2)»Supporting Information Supporting Information Get e-Alerts

Removal of lead from polluted water using decaying leaves

Abstract Decaying leaves have been proven capable of partially removing lead from polluted water. Several factors affecting the removal process have been studied. These include the concentration of lead ions, concentration of leaves, drying leaves, degree of crushing of leaves, leaf extracts, pH, agitation and presence of competing and of complexing agents. The relative capability of some common types of leaves for the removal of lead from water has been studied. The release of lead from leaves saturated with lead ions has been studied under the effect of varying pH, addition of competing ions and the addition of complexing agents. The results of the present work indicate that the interaction between lead ions and leaves is mainly an adsorption process and fit the Freundlich adsorption isotherm whose parameters have also been calculated. A fractional order of reaction (0.7) has been determined for the reaction between lead ions and leaves using two methods of evaluation. A mechanism in which film diffusion being the most probable limiting step has been suggested.

On the Kinetics and Mechanism of Oxygen Reduction at Oxide Film‐Covered Pt Electrodes in Acid Solutions: II . Electron Transfer Through the Oxide Film and Mechanism of the Reduction

The kinetics and mechanism of oxygen reduction at oxide film‐covered Pt electrodes in acid solution is analyzed. Two linear regions are observed when it is ensured that the thickness of the oxide film for each point is the same. The kinetics in the high current density (cd) region is characterized by the Tafel slope of −120 mV. In the low cd region, the slope is −60 mV. The reaction order with respect to is and 1 in the high‐ and the low‐cd region, respectively. Because of the observed fractional reaction order in the high‐cd region, the kinetics in either cd region cannot be explained in terms of any classical, commonly used procedure in mechanistic analysis with a simple model of electrified interfaces. Currents at a constant potential in the cd region with the −120 mV slopes decrease exponentially with the thickness of the oxide film. In contrast, currents in the region with the −60 mV slope are invariant with thickness. Three models are used in mechanism analysis to account for the observed pH dependencies. The model of splitting the interfacial potential difference into two components, and the acid‐base equilibria model can explain the observed pH dependencies. However, they do not account for the observed kinetic behavior with respect to the thickness of the oxide film. The model of the distribution of the unoccupied electron energy levels in solution and electron tunneling through the oxide film accounts both for the observed pH dependencies and for the dependence of the rates on oxide film thickness. With this model it is shown that the electron energy level in the ground state of the reacting complex increases 60 meV as pH increases one unit. This dependence of the electron energy levels on pH provides physical significance for the observed pH dependence and fractional reaction order with respect to .

The electrochemistry of chromium in acidic chloride solutions: Anodic dissolution and passivation

The electrodissolution and passivation of pure chromium in acidic chloride solutions was studied using potentiodynamic techniques and rotating disc electrodes. The anodic dissolution is pH dependent with a negative fractional reaction order with respect to [H +]. No dependence on the Cl − concentration was found in pH 1 solutions. A model is proposed where the anodic dissolution proceeds via the formation of adsorbed Cr(OH) 2 as the rate determining step, followed by chemical dissolution to Cr 2+ (aq). The passivation reaction is the oxidation of divalent adsorbed hydroxide to trivalent oxide-hydroxide. Chloride ions may react with the divalent hydroxide in a competitive substitution reaction, extending the potential region for anodic dissolution. The oxidation of Cl −-containing divalent intermediates, renders the ligands inert and yields a chloride containing passive film.

Oxidative coupling of methane on alkali metal-promoted nickel titanate: II. Kinetic studies

The activity, stability, and kinetics of methane oxidative coupling over Li- and Na-promoted nickel-titanate catalysts have been studied. It was found that under the conditions used the C 2+ yield reached a maximum at 9.7% Li loading and 22% Na loading. Time-on-stream experiments showed that a 1.6% Na-promoted catalyst did not deactivated significantly in 50 h time-on-stream. The 9.7% Li-promoted catalyst and the 22% Na-promoted catalysts lose 15 and 40% yield, respectively, during the same period on stream. Kinetics results obtained under differential conditions resulted in fractional reaction orders and apparent activation energies for methane conversion of 40.9 and 50.5 kcal/mol for the 9.7% Li/NiTiO 3 and the 1.6% Na/NiTiO 3 catalyst, respectively. The kinetic results are interpreted via a reaction model consisting of a Rideal-redox mechanism for the 9.7% Li-promoted catalyst, and an Eley-Rideal mechanism for the 1.6% Na-promoted catalyst. The reaction pathway proposed agrees well with previous transient measurements of the effect of lattice and adsorbed oxygen on the reaction.

Metal electrodes bonded on solid polymer electrolyte membrane(SPE)—VI. Methanol oxidation on molybdenum modified Pt-SPE electrode

The methanol gas phase oxidation on Pt-SPE electrode is enhanced by molybdenum modification. The Tafel plot is divided into three regions: region I with an extremely low polarization, around ca 0.1 V (25°C); region II around 0.2–0.25 V (25°C), ca 0.15 V lower than that on the unmodified Pt-SPE electrode; and region III with a polarization above ca 0.4 V (25°C) where the modification effect disappeared. The catalytic effect of the molybdenum species is enhanced further at higher temperatures, > 10 2 times larger current in region II at 80°C than at 25°C. The modification conditions were examined in detail. The methanol pressure dependence with a fractional reaction order of 0.3 and the different activation energy between modified and unmodified Pt-SPE electrode, 12 and 24 kcal mol −1, are briefly discussed. The oxidation products are CO 2 and HCOOCH 3. The water supply affects both the oxidation current and the product distribution.

Comparative study of the kinetics and mechanisms of dissolution of carbonate minerals

The influence of pH on the rate of dissolution of various carbonates (calcite, aragonite, witherite, magnesite and dolomite) has been investigated at 25°C using a continuous fluidized bed reactor. The general rate dependence on pH observed for the simple carbonates is very similar and is in agreement with the results observed for calcite and aragonite by L.N. Plummer and coworkers. However, the rate of dissolution of magnesite is approximately four orders of magnitude lower than calcite. For simple carbonates, the elementary steps involved in the dissolution reaction are: ▪ where M represents the metal ion which can be Ca, Mg and Ba. According to the stoichiometry of the three reaction steps and the thermodynamic constraints, the total forward and backward rates can be expressed as: R f=k 1a H+k 2a H 2CO 3 ∗ +K 3 r b=k -1 aM 2+ aHCO 3 -+k -2 aHCO 3 - +k -3 aM 2+ aCO 3 2- The rate constants ( k 1, k 2, k 3 and k −3) determined with our experimental results for calcite, aragonite and witherite show that the dissolution rates are similar for these three minerals and that the nature of the cations does not play a significant role. The good agreement between the K sp calculated from the measured k 3 k −3 ratio and the theromodynamic value suggests that our dissolution mechanism is coherent. The rate dependence on pH of the dissolution of dolomite obeys a fractional order at low pH's and confirms previously published observations therein. However, the two-step reaction mechanism proposed does not explain the fractional reaction order observed, which is likely due to a more complex surface reaction.

Palladium Electrode in Oxygen‐Saturated Aqueous Solutions: Potential Dependent Adsorption of Oxygen Containing Species and Their Effect on Oxygen Reduction

Adsorption of oxygen species at palladium electrodes at various potentials, , was determined by a programmed potentiodynamic method in solutions of different pH. In all solutions examined, a linear relationship between and coverage,θ, with oxygen species was established in the range . An equation is obtained relating θ to and pH. This linear relationship extends from about vs. RHE to about 0.95V vs. RHE. This is the same potentials region in which the Tafel slope of −60 mV/dec has been reported for oxygen reduction at Pd electrodes. In view of the intermediated coverages, it is suggested that the first charge transfer under Temkin adsorption condition is the rate determining step for oxygen reduction. Fractional reaction orders with respect to H+, previously reported for the reduction in the Tafel region of −60 mV/dec, are now accounted for by the adsorption of oxygen species under Temkin conditions.

On the Kinetics and Mechanism of O 2 Reduction at Oxide Film Covered Pt Electrodes: I . Effect of Oxide Film Thickness on Kinetics

Oxygen reduction reaction is examined at oxide‐covered Pt electrodes in acid solutions. In the high current density region characterized by the Tafel slope of −120 mV, the reaction is affected by the thickness of the oxide film. As the film thickness increases, current at the same potential decreases. In the low current density region characterized by the Tafel slope of −60 mV, the rate of reduction is unaffected by film thickness. In both current density regions, the potential at a given current decreases 60 mV as pH increases one unit. This leads to the fractional reaction order of with respect to in the high current density region. In the low current density region, the order is 1. Possible mechanisms compatible with the observed kinetic parameters are discussed.

Kinetics of the transesterification of dimethyl terephthalate with 1,4-butanediol

The kinetics of transesterification of dimethyl terephthalate with 1,4-butanediol have been studied in a semibatch reactor under non-isothermal conditions. Also, the kinetics of tetrahydrofuran production by side reactions were studied. Models were fitted by using an algorithm of parameter estimation in differential equations based on the Gauss-Newton method. It was found that the transesterification reaction had an overall order of three, with one order each for dimethyl terephthalate (DMT), 1,4-butanediol (BD) and catalyst concentration, whereas the formation of tetrahydrofuran (THF) involved reactions with fractional reaction order.

Kinetics of oxygen reduction at iridium electrodes in aqueous solutions

Oxygen reduction at Ir electrodes in acid and alkaline solutions is characterized by two linear Tafel regions. At high current densities (cds), the Tafel slope is close to −120 mV/decade. At low cds, it is close to −60 mV/decade. The reaction order with respect to molecular oxygen is one in both cd regions. Also, in both cd regions, the potentials taken at a constant cd decrease by 60 mV as the pH increases one unit. For the high cd regions, this is an uncommon pH dependence which leads to a fractional reaction order of 1 2 with respect to H 3O +. Such a fractional reaction order cannot be explained according to classical approaches in electrode kinetics.

Oxygen Evolution at Platinum Electrodes in Alkaline Solutions: I . Dependence on Solution pH and Oxide Film Thickness

The oxygen evolution reaction (OER) at platinum electrodes in alkaline solutions of various pH's is reexamined. The existence of two linear regions is confirmed, each having a different dependence on Pt oxide film thickness and the OH− concentration. At low current densities (c.d.) , and, at high c.d., it is 120 mV/decade. While the rate of the OER is independent of the oxide film thickness at the electrodes at low c.d., it is strongly dependent on the film thickness at high c.d., as shown by the large decrease of the rates at a given potential with increasing film thickness. At low c.d., the reaction order with respect to OH− is two, while, at high c.d., the order is . The fractional reaction order at high c.d., is unusual and cannot be accounted for by any standard mechanism proposed in the literature for the OER. These results show that the mechanism of the OER at platinum in alkaline solutions is complex and still not thoroughly understood.

Palladium Electrode in Oxygen‐Saturated Aqueous Solutions: Reduction of Oxygen in the Activation‐Controlled Region

Kinetics of electrochemical reduction of oxygen at oxide‐free palladium is studied using steady‐state galvanostatic technique. Measurements are taken in aqueous acid and alkaline solutions over a wide pH range and different oxygen partial pressures. relationships are characterized by two current density (c.d.) regions with distinctly different Tafel slopes. At low c.d.'s, the Tafel slope is close to −60 mV/decade, and, at high c.d.'s, to −120 mV/decade. The reaction order with respect to molecular oxygen is one in both c.d. regions in acid and alkaline solutions. In the high c.d. region, the reaction order with respect to is 1 in acid and 0 in alkaline solutions. In the low c.d. region, however, the reaction order with respect to is in acid and in alkaline solutions. These fractional reaction orders at Pd electrodes, reported here for the first time, are different than those reported in the literature. Possible causes for the difference are discussed. Mechanism of the reaction is suggested.

Oxygen Evolution at Platinum Electrodes in Alkaline Solutions: II . Mechanism of the Reaction

Kinetic data of the oxygen evolution reaction at Pt electrodes in alkaline solutions have shown two types of behavior, a Tafel slope of 60 mV/decade of current density at low applied current densities and a slope of 120 mV/decade at high current densities. At low current densities, and rate of the reaction was found to be independent of the thickness of the underlying Pt oxide film, while the electrode potential has a −120 mV dependence on solution pH. At high current densities, the rate is strongly dependent on film thickness and exhibits a −180 mV dependence on pH. A mechanism of the oxygen evolution reaction which is consistent with this data is presented. It involves a rate‐determining first electron transfer step at high current densities. At low current densities, the chemical step following the now rapid first electron transfer step is rate limiting. The −180 mV pH dependence observed at high current densities implies a fractional reaction order of with respect to the OH− ion. This has been explained in terms of a dual barrier model of the metal oxide film/solution interface. According to this model, the rates across each barrier are pH dependent. The fractional reaction order is due to the existence of these two dependences and is primarily related to the dependence of the potential difference across the outer Helmholtz layer on pH.

Extension of Darby's Model of a Hydrophylic Gas Fed Porous Electrode

A model presented previously by one of the authors (1,2) is reviewed and extended. Aspects of this model which were not previously available in the open literature are considered, and the model is extended to include previously neglected terms in the governing differential equations, fractional reaction orders in the current density‐overpotential expression, and mass‐transfer coefficients to account for mass‐transfer resistance of the reactants to the faces of the porous electrode. The model is used to predict quantities of interest for oxygen reduction in an acidic aqueous solution in a porous carbon electrode.

A Study of the Anomalous pH Dependence of the Oxygen Evolution Reaction at Platinum Electrodes in Acid Solutions

Steady‐state relationships have been determined for the oxygen evolution reaction at platinum electrodes in acid solutions of various pH's. At all pH's, Tafel slopes close to have been obtained after initially cathodically pretreating the electrode, polarizing it at a high anodic current density for a particular length of time, and then measuring the relationships at current densities lower than that used in the initial anodic electrode pretreatment. The order of the reaction with respect to hydrogen ions is then found to be one‐half. In other experiments, a rotating Pt ring disk electrode was used in solutions of various pH's in order to separate the currents due to Pt oxide film growth and those due to the oxygen evolution reaction and to accurately determine the charge density utilized for film growth. From this, it could be seen that the potential, at any constant charge density and pH, increases 120 mV for a tenfold increase of the current density, and that at a given current density and charge density, the potential decreases 60 mV as the pH increases one unit. These results confirm that the unusual fractional reaction order with respect to hydrogen ions is still obtained when the thickness of the oxide film remains constant. Further, it is reported here that the dependence of the oxygen evolution rates on pH can be attributed entirely to the dependence on the pH of the potential difference across the outer Helmholtz layer at the oxide film/solution interface. This simultaneous study of oxide film growth and the oxygen evolution reaction has led to a model for the potential distribution across the metal/oxide film/IHL/OHL/solution interface during the oxygen evolution reaction and to the conclusion that a fast quasi‐equilibrium process exists across the outer Helmholtz layer.

Electron transfer and homogeneous redox catalysis on glassy carbon electrode—I. Linear sweep and cyclic voltammetric studies on Ti(IV) oxalate-NH 2 OH system in oxalic acid media

The electron transfer rate of titanic oxalate on glassy carbon is found to be slower when compared to the same on Hg electrode. The estimated rate constant using Nicholson's method was found to be 1.2 ± 0.1 × 10 −3 cm s −1. The effect of pH shows similarity with the reports on Hg electrode. Fractional reaction orders were obtained in the Tafel region. These observations may be due to the fact that the electrode surface under experimental conditions is partially covered. The estimated reduction rate of NH 2OH by the electrogenerated titanous oxalate agrees very well with the literature values at lower NH 2OH concentrations. However, deviations are noticed when higher concentrations of Ti (IV) oxalate as well as NH 2OH are employed. The possibility of existence of more complicated redox-catalytic mechanism is indicated.

ChemInform Abstract: REACTION INTERMEDIATES AS A CONTROLLING FACTOR IN THE KINETICS AND MECHANISM OF OXYGEN REDUCTION AT PLATINUM ELECTRODES

AbstractMit Hilfe einer rotierenden Pt‐Scheibenelektrode werden Kinetik und Mechanismus der O2‐Reduktion in sauren Medien in einem größeren pH‐Bereich als bei früheren Arbeiten erneut untersucht und die durch unterschiedliche öV/ölog i‐ und ölog i/ ö pH‐Abhängigkeiten charakterisierte Änderung der Kinetik beim Übergang ins Alkalische verfolgt.

Fractional reaction orders in oxygen evolution from acidic solutions at ruthenium oxide anodes

Oxygen evolution at RuO 2 anodes from acidic solutions exhibits a fractional reaction order with respect to H +. This is close to −1 for a set of “compact” film electrodes, and close to −2 for a set of “cracked” film electrodes. The difference in mechanism is related to the different defect structure of the surface. Possible reasons for the observed fractional reaction orders are discussed. It is suggested that the experimental observation may be explained in terms of the reaction proceeding with different mechanisms in parallel on different patches of the surface whose structure is governed by the acid-base properties of the oxide.