Fractional Reaction Order Research Articles

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.

Reaction intermediates as a controlling factor in the kinetics and mechanism of oxygen reduction at platinum electrodes

A rotating platinum disk electrode was used to study oxygen reduction over the entire pH range and to compare the kinetics in acid and alkaline solutions. In both solutions two Tafel regions are confirmed. At low cd's ∂ V/∂ln i = − RT/F and at high cd's it is −2 RT/F. In the low cd region, the reaction order with respect to H 3O + is 3 2 in acid, and 1 2 in alkaline solutions. For the high cd region the reaction orders are 1 and 0 in acid and alkaline solutions, respectively. Transition of the kinetics from the low to the high cd region, as well as the fractional reaction orders at low cd's, are interpreted in terms of the first charge transfer step as rate determining in both cd regions but under Temkin adsorption conditions in the low, and Lagmuirian conditions in the high cd region. Coverages, θ, with oxygen intermediates are also determined as a function of potential and pH. At all pH's, substantial coverages are observed only at potentials in the low cd region. The usual Tafel slope of −120 mV for the first charge transfer step as rate determining is not observed at low cd's since it is modified by the dependence of activation energy on θ, and hence on V. At high cd, θ is low and ineffective and the usual slope for the first charge transfer step is observed. At all pH's the transition from low to high cd's occurs at potentials, V T , that decrease 60 mV as pH increases one unit. Dependence of V T and i T on pH is discussed. Fractional reaction orders at low cd's are also related to θ. Real reaction orders with respect to H 3O + are modified by the dependence of activation energy on θ, and hence on pH. The change of the kinetics from the acid to the alkaline region is discussed. The range of cd's accessible to measurements is limited at both high and low cd's. At high cd's it is limited by the supply of oxygen and/or H 3O + from the solutions. At low cd's, V—log i relationship extends only to a rest potential which decreases 60 mV as pH increases one unit. The limits of measurements and the nature of the rest potential are discussed.

Kinetics and mechanism of O 2 reduction at Pt IN alkaline solutions

A rotating disk electrode was used to examine the steady state kinetics of O 2 reduction at oxide free Pt in alkaline solutions of various pH's. Two linear V-log i regions are observed. At low current densities, the ∂V/∂ log i slope is close to −60 mV; at high cd's it is close to −120 mV. In the low cd region, the reaction order with respect to OH − is −1/2. In the high cd region, the reaction order is zero. In both regions the order with respect to O 2 is 1. The “unusual”, fractional reaction order of −1/2 cannot be accounted for in terms of simple electrode kinetics with Langmuirian conditions. It is suggested that in both regions the first electrochemical step is rate determining. In the low cd region, due to intermediate coverages with adsorbed oxygen species, Temkin conditions prevail and lead to the ∂ V/∂ log i slope of −60 mV and the “unusual” reaction order. At high cd's, the coverage is low and the “usual” kinetics with ∂ V/∂ log i = −120 mV and zero reaction order with respect to OH − follow.

Convective diffusion to a solid particle in the case of nonlinear kinetics of heterogeneous chemical reaction

An approximate solution is obtained for a stationary problem of mass transfer between a moving solid spherical particle and a laminar gas flow at low finite Peclet and Reynolds numbers. The case of a chemical surface reaction which depends arbitrarily on reagent concentration at the particle surface is considered. The results obtained may be used, in particular, to determine the rate of mass transfer between a particle and a flow for the integral- and fractional-order reactions. The solution of the problem has been found by the method of matching outer and inner asymptotic expansions in the Peclet number. The concentration field has been determined. The dependence of the total reagent flow at the particle surface on the reaction kinetics, rate constant and the Peclet number has been obtained.

Isothermal nth order reaction in catalytic pellets : Effect of external mass transfer resistance

The effectiveness factor for the isothermal power-law decomposition of a reactant within symmetrical catalytic pellets is obtained from the solution of a single first order differential equation. The effects of external mass transfer are taken into account, as well as the effect of simple types of non-uniform distribution of the catalyst within the particle. For fractional and negative reaction orders there are solutions with zero concentration in a central region of the particle. For negative reaction orders intervals of multiplicity of solutions are found.

Anodic Oxide Films as Barriers to Charge Transfer in O 2 Evolution at Pt in Acid Solutions

The kinetics of oxygen evolution reaction at platinum anodes in acid solutions with different pH's is examined, and possible reaction mechanisms are discussed. The activity of the reaction at initially prereduced electrodes brought to a constant potential, or kept at a constant current density, decreases with time. Only at the electrodes initially subjected for a given time either to a high potential, or to a high anodic current density, it is possible to observe in “run down,” or subsequent “run up” experiments a linear relationship for over several decades of current density with a slope close to 115 mV. The positions, but not the slopes of Tafel lines, are affected by time or conditions of pretreatments of electrodes (various or ). The decrease in the activity is attributed to the increase in average thickness of anodically formed surface oxide films. Only when it is assured that the film thickness remains practically unaltered during the measurements, meaningful kinetic parameters for the oxygen evolution reaction are obtained. The reaction order with respect to H+ is then found to be negative and fractional according to the over‐all rate equationA model is suggested according to which a surface oxide film forms a barrier to charge transfer in series with the double‐layer barrier. The fractional reaction order is accounted for with this model. A chemical step that follows a charge transfer step is rate determining. It is suggested that oxygen atoms in the surface oxide films participate in the oxygen evolution reaction.

General models for r-molecular reactions

In the present paper we consider the r-molecular reversible reaction rA⇌B from several viewpoints. The deterministic theory for integral reaction orders is considered first and is subsequently extended to cover the case of fractional order reactions. Stochastic models are then proposed, the analyses being carried through by spectral methods and, in the case of first order reactions, the first passage time problem is also examined. Finally, we use a diffusion theory approach to the problem to obtain results which are valid for a large number of molecules.

General models for r-molecular reactions

In the present paper we consider the r-molecular reversible reaction rA⇌B from several viewpoints. The deterministic theory for integral reaction orders is considered first and is subsequently extended to cover the case of fractional order reactions. Stochastic models are then proposed, the analyses being carried through by spectral methods and, in the case of first order reactions, the first passage time problem is also examined. Finally, we use a diffusion theory approach to the problem to obtain results which are valid for a large number of molecules.

Conversion and equilibration rates of hydrogen on nickel

The pH2 conversion rate has been compared with that for oD2 and H2+ D2→ 2HD on nickel wires rigorously cleaned in vacuo of 10–10 torr. The rates are significantly higher than on evaporated films, prepared under similar conditions but still possibly contaminated. The results at 1 torr fall into three temperature ranges (a) 330–400°K, a fractional order (ca. 0.6) reaction, activation energy 5–7.5 kcal mole–1. There is evidence for a zero order H2+ D2 reaction setting in as the pressure is lowered to 0.3 torr; (b) 200–300°K, a fractional order reaction, 0.05–0.40, with a lower activation energy, 1.5–2.7 Kcal mole–1. In (a) and (b), pH2, oD2 and H2+ D2 rates are very similar to each other. On decreasing the temperature to (c) 77–200°K, the activation energies for the pH2 and oD2 rates decrease to zero, so that at 77°K these two reactions go 103 times faster than H2+ D2. The mechanisms advanced are for (a) Bonhoeffer-Farkas, (b) Eley-Rideal, and (c) a paramagnetic conversion induced probably by unpaired d electrons in the Ni and proceeding through a Harrison-MacDowell mechanism.

Graphical Methods for Obtaining Steady State of Concentrations and Temperatures in Flow Reactors

In a preceding paper, the graphical solution of heat and material balance equations for the stirred tank flow reactor has been presented for simple reactions. This method is also useful for fractional-order reactions, reversible reactions, simultaneous reactions and consecutive reactions.The behavior of the stirred tank reactors in series may be estimated by repeated applications of this method. Assuming that a tubular reactor is approximately equivalent to n-stage tank reactor sequence, the temperature and concentration profiles in a tubular reactor may be calculated by the graphical method for the stirred tank reactors in series. Parametric sensitivity of tubular reactors is easily estimated by the same method. These methods are also applicable to the reactor system with the heat exchanger.

Studies on the Decomposition of Ammonia and Hydrazine by High Frequency Discharge

Abstract 1) The decomposition of both ammonia and hydrazine were carried out under high frequency discharge and the effects of frequency on the chemical reactions were investigated. The frequencies of electric current were 100 and 250 MC. 2) The effects of frequency appeared clearly on the decomposition of hydrazine: under 100 MC frequency discharge the decomposition was a 1st order reaction, while under 250 MC it was approximately zero order reaction, and the overall reaction was retarded moderately by the hydrogen produced in the course of the reaction. 3) As for the decomposition of ammonia, in any case, the reactions were retarded by hydrogen. Under 100 MC frequency discharge the reaction was 1st order, while under 250 MC it was a fractional order reaction.

Vulcanization of Elastomers XV. The Vulcanization of Natural and Synthetic Rubber with Sulfur in Presence of Organic Bases (I)

Abstract The results obtained from preliminary kinetic studies of the vulcanization of natural rubber (NR) with sulfur in the presence of organic bases may be summarized as follows. 1) The change of concentration of sulfur with time during reaction with NR for an initial sulfur concentration of 2.5 g per 100 g of mixture follows a fractional reaction order, n, of 0.6 at all temperatures. This result and the findings of other authors suggest that the reaction of sulfur with rubber is autocatalytic. From the temperature dependence of the rate constant the activation energy is found to be 35.3 kcal. 2) In the presence of zinc oxide and with a similar initial sulfur concentration, the reaction is first order and the activation energy, namely 35.6 kcal, is practically the same. 3) In the presence of diphenylguanidine (DPG) during cure sulfur decrease is a reaction of fractional order, n=0.75, and the activation energy is 29.8 kcal. 4) For a given initial concentration of sulfur and at constant temperature the rate of sulfur decrease during vulcanization increases with rising DPG content and reaches a limiting value; i.e., the rate constant depends on DPG concentration. Also, for various base (DPG is basic) concentrations sulfur decrease is of various fractional orders, n=0.5…0.7, etc. 5) The influence of base on the rate of sulfur decrease is interpreted broadly as a case of intermediate-catalysis (Zwischenstoff-Katalyse). 6) Vulcanization with sulfur is unaffected by tertiary amines and secondary amines have only a slight effect. 7) Primary amines, depending on basic strength, are strong accelerators of the rate of sulfur decrease. 8) In the presence of organic bases (aromatic amines) other than DPG, sulfur decrease is of fractional order where n varies between 0.5 and 0.7.