Formal Reaction Order Research Articles

Kinetics of the Decomposition of Hydrogen Sulfide in a Dielectric Barrier Discharge Reactor

AbstractKinetics of hydrogen sulfide (H2S) decomposition to hydrogen and sulfur was investigated in a nonthermal plasma dielectric barrier discharge (NTP‐DBD) reactor operated under ambient conditions. The reactions were carried out with a fixed flow rate and varying inlet concentration. The results indicated that the dissociation of H2S into H2 and S may be initiated by excitation of the carrier gas argon. A reaction rate model based on a Langmuir Hinshelwood/Michaelis‐Menten model was proposed. The formal reaction order approaches zero at high H2S concentrations. The parameters of the kinetic model were found to be dependent on the power input.

Reaction orders of radiation-induced dechlorinations of some aliphatic chlorinated hydrocarbons in aqueous solutions

Previously obtained data regarding radiation-induced dechlorination of some aliphatic chlorinated hydrocarbons tetrachloroethene (PCE), trichloroethene (TCE), chloroform (CHCl 3) and tetrachloromethane (CCl 4) in aqueous solutions were used for determination of formal reaction order of dechlorination. The influence of various factors on this process was investigated. It was found that the formal reaction order changes in the course of reaction and may depend on the initial concentration of chlorinated hydrocarbons.

CO2 Gasification of Biomass Chars: A Kinetic Study

The CO2 gasification of pine and birch charcoals was studied by thermogravimetric analysis (TGA) at CO2 partial pressures of 51 and 101 kPa. Linear and stepwise heating programs were employed to increase the information content of the experimental data sets. Low sample masses were used because of the high enthalpy change. Seven experiments with different experimental conditions were evaluated simultaneously for each sample. The method of least-squares was employed. Three reactions appeared in the temperature domain evaluated (600−1000 °C). The first and second reactions were due to the devolatilization and did not show a significant dependence upon the CO2 concentration. They were approximated by first-order kinetics. The third reaction corresponded to the gasification. Its modeling was based on an empirical approximation of the change of the reaction surface during the gasification and by a formal reaction order with respect to the CO2 concentration. Very close results were obtained for the two charcoals...

Experimental evaluation of a kinetic method for the study of non-catalysed heterogeneous reactions in solid-liquid systems: leaching of apatite by dilute nitric acid

A method for evaluating the formal reaction order n of a chemical reaction is proposed, based on a kinetic equation describing chemical dissolution of solid particles in a batch reactor. The evaluation is based on the fact that the function expressing the dependence of the conversion, X B , on the term C A0 n t has the same course for different initial concentrations of the liquid reactant, C A0 (t denotes time), at constant temperature and ratio of reactants. The measured dependences of the conversion on the time give a function, f s (X B ), characterizing changes of the solid surface area during the reaction. Minimization of deviations of this function permits the influence of mass transfer between the bulk of the liquid and the solid surface on the measured formal reaction order to be corrected. Knowledge of the value of n and the function f s (X B ) enables the derived kinetic equation to be integrated numerically and the dependence of the conversion on time to be calculated. A set of experimental data measured during dissolution of natural apatite in dilute nitric acid (0.1-1.5 mol/dm 3 ) at 20°C was used for demonstration of the proposed method.

Vapour-phase trimerization of formaldehyde to trioxane catalysed by 1-vanado-11-molybdophosphoric acid

The kinetics of the trimerization of anhydrous formaldehyde vapour were examined in a tube reactor in the temperature range from 102.5°C to 110°C and in the pressure range from 0.7 to 1.15 bar. 1-Vanado-11-molybdophosphoric acid on a silicon carbide support was used as catalyst. Evaluation of the data obtained shows a steady increase of the reaction rate with growing partial pressure of formaldehyde. A description of the rate by a power-law leads to a formal reaction order of six. This high formal order could not be explained satisfactorily. Investigations in a Berty-type recycle-reactor showed that the reaction rate increased stepwise with growing partial pressure of formaldehyde. Intracrystalline diffusion within the pseudo-liquid phase of the heteropolyacid particles obviously is the rate-determining step of the reaction. The temperature dependence of the reaction rate was found to be inverse and extremely strong. Differences in the shapes of tube reactor and recycle reactor kinetic curves can be explained by the levelling effect of temperature gradients in the catalyst bed of the tube reactor.

Propene polymerization using homogeneous MAO‐activated metallocene catalysts: Me2Si(Benz[e]Indenyl)2ZrCl2/MAO vs. Me2Si(2‐Me‐Benz[e]Indenyl)2ZrCl2/MAO

AbstractPropene was polymerized at 40°C and 2‐bar propene in toluene using methylalumoxane (MAO) activated rac‐Me2Si(Benz[e]Indenyl)2ZrCl2 (BI) and rac‐Me2Si(2‐Me‐Benz[e]Indenyl)2ZrCl2 (MBI). Catalyst BI/MAO polymerizes propene with high activity to afford low molecular weight polypropylene, whereas MBI/MAO is less active and produces high molecular weight polypropylene. Variation of reaction conditions such as propene concentration, temperature, concentration of catalyst components, and addition of hydrogen reveals that the lower molecular weight polypropylene produced with BI/MAO results from chain transfer to propene monomer following a 2,1‐insertion. A large fraction of both metallocene catalyst systems is deactivated upon 2,1‐insertion. Such dormant sites can be reactivated by H2‐addition, which affords active metallocene hydrides. This effect of H2‐addition is reflected by a decreasing content of head‐to‐head enchainment and the formation of polypropylene with n‐butyl end groups. Both catalysts show a strong dependence of activity on propene concentration that indicates a formal reaction order of 1.7 with respect to propene. MBI/MAO shows a much higher dependence of the activity on temperature than BI/MAO. At elevated temperatures, MBI/MAO polymerizes propene faster than BI/MAO. © 1995 John Wiley & Sons, Inc.

A kinetic study of the chlorination of MO 3 by CCl 4

The surface and morphological properties of molybdenum trioxide were characterized using microcalorimetric and SEM methods. The number of acidic and basic sites were measured by NH 3 and SO 2 adsorption, respectively. According to the microcalorimetric data, strong dissociative adsorption of NH 3 takes place on the surface, while there is no interaction between the MO 3 lattice and SO 2 gas. The chlorination kinetics of MO 3 with gaseous CCl 4 were studied by thermogravimetry. The values of the apparent activation energy and the formal reaction order were calculated from the temperature and partial pressure dependence of the initial rate, respectively. From the results obtained, the combined control of pore diffusion and chemical reaction, as well as the dissociative adsorption of CCl 4, were deduced. Due to the very low porosity of the solid particles, in addition to the reaction occurring in a zone near the pore tunnels, chlorination at the external surface cannot be neglected. Thus, to describe the conversion versus time curves, a kinetic model was proposed based on the different linear rates of the interfacial chemical reaction at the external surface of the particles and that in the reaction zone controlled by pore-diffusion processes. Using this model, a fairly good correspondence between the measured and calculated kinetic curves was obtained.

Functionalization of PMMA by a functional “iniferter”: Kinetics of polymerization of MMA using N,N′‐diethyl‐N,N′‐bis(2‐hydroxyethyl) thiuram disulfide

Abstractα,ω‐Dihydroxy‐terminated‐PMMA was synthesized by the bulk polymerization of methyl methacrylate in the presence of a functional “iniferter,” viz., N,N′‐diethyl‐N,N′‐bis(2‐hydroxyethyl)thiuram disulfide (DHTD). The kinetics of the polymerization were studied by determining the polymerization rate as a function of the “iniferter” concentration at 60, 70, 85, and 95°C. Evaluation of the data by a computerized multiple regression analysis led to calculation of the various kinetic parameters and the activation energies of the related phenomena. The maximum observed in the Rp–initiator concentration curve was found to shift to lower initiator concentration as the temperature increased. The formal reaction order with respect to the concentration of the initiator decreased with increasing temperature and concentration of DHTD. The chain transfer constants of DHTD with MMA were calculated from the molecular weights of the resulting polymers. The functionalities of the oligomers were calculated from the elemental analysis of the chain end groups. Thermogravimetric analysis revealed that the polymer chain ends were devoid of unsaturated groups and that the polymer underwent degradation only by random scission.

Some aspects of mathematical statistics as applied to non-isothermal kinetics

As a numerical characteristic of the sensitivity of the kinetic parameter calculation method to the form of the kinetic function in non-isothermal kinetics, the value of the curvature of the line plotting residual dispersionvs. formal reaction order at the minimum point is suggested. The efficiency of this characteristic is exemplified.

On the kinetic.evaluation of the thermogravimetric curves

The information content of the non-isothermal TG- curves is discussed. At simple surface reactions, three formal characteristics of the measured curves (the width, the asynraetry and the position on the temperature axis) define uniquely three kinetic parameters: the activation energy, the formal reaction order and the preexponential factor.The actual determination of these kinetic parameters should be based on the least squares fitting of the solution of the kinetic differential eouation to the experimental data. To illustrate it, the dehydratation of calcium oxalate monohydrate is treated.

Computer-aided thermogravimetric determination of kimetic parameters of calcination of BeSO4 · 4 H2O

The multistage thermal decomposition of BeSO4· 4 H2O is investigated by computer-aided simultaneous thermal analysis (TG, DTG, DTA) in dependence on the gas atmosphere, using the thermogravimetric data the kinetic parameters activation energy, pre-exponential factor, and formal reaction order of some decomposition stages are calculated by different methods.

The effects of imperfect temperature programming on the kinetic evaluation of thermoanalytical curves. Part 3. Error bounds for the activation energy and the formal reaction order

The difference between the actual and the measured temperature of the sample examined distorts the estimated values of the kinetic parameters. This distortion has been analysed in the instances of simple parameter estimation methods. The results obtained can help to judge the correctness of the kinetic evaluation of the non-isothermal measurements.

The effects of imperfect temperature programming on the kinetic evaluation of thermoanalytical curves. Part 1. A simple mathematical example

In thermal analysis, the actual temperature inside the sample usually differs from the prescribed temperature. This fact may influence the evaluation of the kinetic parameters. In this paper the effects of slightly curved actual temperature-time functions are studied. It is shown that an alteration of about 5 K from the prescribed linear temperature program and its neglect in the kinetic evaluation can change the formal reaction order and the apparent activation energy by about 20%.

Kinetics and mechanism of ethane hydrogenolysis on silica-supported platinum and platinum-iron catalysts

A kinetic analysis of ethane hydrogenolysis has been carried out on Pt SiO 2 and PtFe SiO 2 catalysts with a wide range of concentration of the components, and with an excess of ethane. With the help of the theory of stationary reactions on heterogeneous surfaces, kinetic equations were obtained describing the reaction rate both in excess hydrogen and excess ethane which are in full agreement with the experimental observations. On platinum in excess hydrogen the rate of hydrogenolysis is determined by the CC bond rupture of ethane adsorbed in a mildly dissociated C 2H x form, while in excess hydrocarbon it is determined by the CC bond rupture of ethane adsorbed in the deeply dissociated form of C 2H 2. The reaction rate passes through a maximum vs ethane pressure at constant hydrogen pressure and vice versa. The formal reaction order in hydrogen and hydrocarbon can be either positive or negative depending on the conditions; the formal power-rate equations may be considered as approximations of the more complicated equations presented in this work.