Jander Equation Research Articles

Reaction of molten sodium carbonate with aluminum oxide

The rate of reaction of alumina with sodium carbonate has been studied over the temperature range 820 to 1100/sup 0/C, and as a function of alumina particle size from 1 to 300..mu..m. Alumina reacts with sodium carbonate to form sodium aluminate (NaAlO/sub 2/) which is insoluble in molten sodium carbonate. During the course of the reaction, the sodium aluminate forms a protective film on the surface of the alumina particles limiting the rate of reaction to the rate of diffusion of the reactants (and/or products) through that layer. Experimental data were analyzed according to the Jander equation and a modified Ginstling-Brounshtein equation, and the results compared. The modified Ginstling-Brounshtein equation provides the best representation of the data. The Arrhenius activation energy for the diffusion process was determined to be 62 +- 3 kcal/mol.

Kinetics and Mechanism of the Reaction of Powdered Chromium with Gaseous Phosphorus

The phosphidation kinetics of powdered chromium has been studied under gaseous phosphorus atmosphere of 100-760 mmHg in a closed vessel at 600-700°C. As a sinter of phosphides formed, a-alumina powder was previously added to the chromium sample as a diluent at a weight ratio (Cr/Al2O3) of 2.The reaction products were CrP and Cr3P as a result of X-ray diffraction analysis, and CrP2, a higher phosphide, was not found. In an earlier stage of the phosphidation the reaction proceeded linearly with time and, subsequently, parabolically. In an earlier stage, the ratedetermining step seemed to be a surface reaction; therefore the study was made by applying the Langmuir adsorption isotherm. As its result, it could be presumed that the phosphidation proceeded under the adsorption-dissociation of gaseous P4, molecule into four phosphorus atoms. On the other hand, in an advanced stage of the phosphidation, the data showing the relation between the fractional phosphidation and time fitted approximately Jander's equation under the present reaction condition. Hence, the rate-determining step seemed to be a diffusion process.It could be concluded that the rate-determining step of the phosphidation of chromium transferred from the surface reaction to the diffusion process.

Reaction Kinetics in the Silicothermic Magnesium Process

AbstractThis paper is a contribution to the theory and quantitative understanding of the processes for the production of magnesium metal by the reaction Experimental data from earlier investigations are analyzed using powder reaction2CaO(s) + 2MgO(a) + Si(s) → 2Mg(g) + Ca2SiO4(s) models and the failure of these models to adequately describe reaction kinetics is shown. A two-component model is then developed, where the chemical reaction rate is described by the Jander equation and the latter is coupled with a slow heat transfer step. It is shown that this model offers good potential to predict experimental rates and to account for the observed dependence of rate on reactant particle size, briquette size and calcined dolomite properties. Resume Ce travail a pour but de contribuer a la comprehension theorique et a l'evaluation quantitative du procede de production de magnesium metallique par la reaction2CaO(s) + 2MgO(a) + Si(s) → 2Mg(g) + Ca2SiO4(s) Les donnees experimentales des travaux anterieurs sont norm...

Sintering of PbTiO3 doped with PbO-TiO2-Al2O3-SiO2 Glass

The formation and sintering of PbTiO3 containing a small amount of PbO-TiO2-Al2O3-SiO2 glass were investigated by means of X-ray diffraction, thermal analysis, electron microscopy, dilatometry and the measurement of isothermal shrinkage.The rate of formation of PbTiO3 from PbO and TiO2 containing 0.01 wt % glass was determined. Reaction isotherms were best described by the Jander's equation. The apparent activation energy of the reaction was about 50 kcal/mol.The PbTiO3 powder was mixed with 0.005 or 0.01 wt % glass powder, pressed into pellets at 1 ton/ cm2, and heated at 1100-1200°C for 1-2 hr in various atmospheres. All the sintered specimens had grain size of 0.5-2μ and a bulk density of 7.23-7.63g/cm3. The density of 7.63 g/cm3 was obtained by heating at 1120°C for 1 hr in the oxygen atmosphere. The order of the sinterability in various atmospheres of PbTiO3 contained the glass was O2>PbO>air>N2. This fact suggests that the sintering of PbTiO3 is affected by partial pressure of oxygen.The mechanism of initial sintering in PbTiO3 contained 0.01 wt % the glass was studied by isothermal shrinkage at temperatures ranging from 900°to 1050°C in air and oxygen. Time dependence of the shrinkage was consistent with the mechanism based on grain boundary diffusion in air and volume diffusion in oxygen, and the activation energies for sintering processes were about 46 kcal/mol and 76 kcal/ mol, respectively. Comparison our data with others suggests that the diffusion of Pb2+ in air and Ti4+ in oxygen control the initial sintering.

Reactivity of η‐, γ‐, and α‐Al2O3 for ZnAl2O4 Formation

AbstractThe rate of ZnAl2O4 formation was measured for η‐, γ‐; and α‐ Al2O3 in order to distinguish the reactivity of them. The reactivity decreased as follows: η‐ > γ‐ > α‐Al2O3. The reaction rate fitted to Jander's equation and the activation energies calculated were 33, 47 and 113 Kcal/mol for η‐, γ‐ and α‐Al2O3 systems, respectively. These differences are explained by an assumption that η‐ and γ‐Al2O3 resulted in a ZnAl2O4 with imperfect spinel structure, but α‐Al2O3 gave the perfect spinel structure. This assumption is based on the theoretical consideration of the activation energy needed for the diffusion‐controlled reaction and date of lattice constant of each ZnAl2O4 obtained from three aluminas. The fact that η‐Al2O3 shows very high reactivity compared with that of γ‐Al2O3 was found to be explained on the basis of Jander's equation, a comparison of specific surface area and the defect structures of the aluminas.

Effects of Ball Milling on the Kinetics and Mechanism of Solid State Reaction between BaCO3 and Sio2

Effects of ball-milling en the reaction of equimolar mixtures of BaCOs and SiO2 have been studied in the temperature range between 800 and 900C by means of isothermal thermogravimetry, electron microscopy, X-ray diffraction analysis and DTA.The main part of the reaction, which corresponds to the formation of Ba2SiOi, was best expressed by Jander's equation and the activation energywas.determined as 53 kcal/mol irrespective of the ball-milling tirne. The reaction was found to proceed in three stages:BaCOs+SiO2= BaSiOs+CO, (1)BaCO3 +BaSiO3 = Ba2SiO4 + CO2 (2)Ba2SiO+SiO2=2BaSiO3 (3)The reaction (1) was independent of CO2 partial pressure, whereas the reaction (2) was checked by CO2.The increase in the reactivity as caused by ball-milling was detected by an endothermic peak at about 7500C in DTA. This peak was found to be associated with theformation of BaSiO3 (reaction(1)).The effect of ball-milling is possibly interpreted in terms of the decrease in particle size of BaCOs in early stage of ball-milling, and of the improvement of SiO2 dispersion in later stage, respectively.

Kinetic Studies of Fluorination of Graphite in Diffusion Controlled Region

Our previous work revealed that the curve of the weight increase vs.time in the fluorination of graphite by fluorine gas consisted of four parts. The mechanism of the final part was studied in this paper by means of the thermobalance specially designed for fluorine gas. The flaky graphites from Madagnscar ores with the 800 μ of mean diameter were used for the sample. Experiments have been carried out under the fluorine pressure of 50, 100 and 200 mmHg in the temperature range from 500 to 600 C.The relationship between the degree of transformation, x, and reaction time, t, was expressed by a modified Jander's equation, [1-(1-x)1/2]2=kt. The reaction rate, k, was proportional to square root of fluorine pressure. The apparent activation energy was found to be 26 ± 1kcal/mol. The reaction rate was depressed when the fluorination of graphite crystal proceeded about 6 μ from edge plane. The time required for the formation of final compound (C:F=1:1) depended upon the diameter of graphite particle. The experimental results indicated that the rate-determining point of the reaction lay in the transfer step of fluorine molecules through the fluorinated layer of the graphite.

Kinetics of the thermal decomposition of aqueous manganese(II) nitrate solution

Isothermal weight studies were performed upon aqueous solutions of manganese(II) nitrate. The loss of water followed a first order rate law with activation energies varying from 6 to 10 kcal/mole depending upon the atmosphere. The resulting anhydrous nitrate decomposed to form manganese(II) oxynitrate in accordance with the Erofeev equation with n = 4. The activation energies are 20–25 kcal/mole and show little variation with atmosphere. The resulting oxynitrate decomposed to form manganese(IV) oxide. The rate fits several expressions satisfactorily but a contracting area form is chosen as generally best. The activation energy is about 12 kcal/mole lower in the presence of moisture but this effect upon the rate is partially offset by a substantial decrease in the preexponential term. The manganese(IV) oxide loses oxygen to form manganese(III) oxide. The best rate law is the Jander equation and activation energies are in the range of 47–57 kcal/mole.

Urea Adduct Formation in a Solid Phase Reaction. II.

The reactive rate of adduct formation in solid phase reaction has been examined with reference to its length of fatty acid chain. Quantitative analysis of the amount of urea adduct is made by using X-ray, in which two reflection i.e. (100) reflection (7.14Å) of adduct and (003) reflection (9.113.3Å) of fatty acid are used for its calibration curve. As a result, it has been disclosed that the shorter the length of the fatty acid chain is, the greater the reactive rate of adduct formation becomes.Followed this the reactive rate of urea adduct formation has been investigated under various conditions and it has been recognized all the reaction are explained well by Jander's rate equation. The apparent activation energy obtained by Arrhenius's equation are as follows; C-12 : 31.1, C-14 : 26.1, C-16 : 22.0, C-13 : 22.9, C-15 : 19.2, C-17 : 15.6kcal/mol, which shows that the activation energy is decreased with the increase of the carbon number of the guest molecule fatty acid and there exists zigzag relation between even and odd membered fatty acids.

Kinetic study of the oxidation of the carbides of iron

A kinetic study has been made of the rate of evolution of carbon dioxide in the reaction of three different preparations of carbides of iron with gaseous oxygen. All three reactants contained “free” carbon; cementite B contained a considerable amount. Both carbidic and free carbon were oxidized to carbon dioxide and, simultaneously, iron was oxidized initially to Fe3O4, though later significant Fe2O3 formation occurred. Carbon dioxide evolution was strongly deceleratory and results fitted the Jander equation over the first part (∼50 %) of the reaction. Values of the activation energies were : cementite A(Fe3C, low surface area) 105±12 kJ mol–1(405-500° C); cementite B(Fe3C, high surface area) 102±12 kJ mol–1(240-340°C); Hagg carbide (Fe5C2, low surface area) 100±16 kJ mol–1(300-400°C). From quantitative comparisons between these results and the published data for the reaction of iron with oxygen, it is concluded that, in each of the reactants studied here, carbon was oxidized at a metallic phase (carbide)/oxide interface which progressively moved through the reactant particles. On such a model, the rate-controlling process in the oxidation of iron, and of carbon in the iron carbides, is the diffusion of the same species through the adherent barrier layer of product oxide.

Kinetics and mechanism of formation of zinc ferrite

The kinetics of the formation of zinc ferrite from zinc oxide and iron(III) oxide powders have been studied. Below about 1000°C Jander's equation is obeyed. Vaporization of the more mobile reactant (ZnO) occurs to form a coating on the particles of the other reactant with subsequent diffusion into it. An activation free energy of 72 ± 10 kcal/mole has been obtained in this temperature region. The general features of this reaction are similar to other spinel-producing reactions; and the mechanistic treatment proposed covers much of the previously reported work.

Optical absorption in thin films of highly unstable cuprous azide

The optical absorption spectrum of a thin film of highly unstable CuN3 has been studied by a special technique in which the film is prepared in situ by a solid-state reaction between CuI and alkali azide. The spectrum shows an absorption peak at 2670 Å followed by a sharp rise at 2500 Å which may be due to a direct band-to-band transition. The reaction product has been identified by X-ray diffraction. The kinetics of reaction was studied spectrophotometrically and was found to obey the Jander equation for diffusion-controlled reaction.

ハーシナイト (FeAl<SUB>2</SUB>O<SUB>4</SUB>) の生成と還元反応

The spinel hercynite (FeAl2O4) occurs as a reaction product with the deoxidation by aluminium of liquid steel, or when iron oxides come into contact with alumina refractories. The behaviors of hercynite in liquid iron and steel are of great interest, but until recently, few investigations of the rate of formation and reduction of hercynite have been carried out.In this work, the rate of formation of hercynite from mixture of ferrous oxide and alumina at temperatures from 850°C to 1200°C was measured. The rate of reduction by hydrogen stream at 700°C to 900°C was measured by the thermo-balance method. As the supplementary work, the products of reduction by hydrogen, solid carbon and soluble carbon in liquid iron were examined by X-ray diffraction.The results obtained are as follows:1) The rate of formation agrees with Jander's equation and the value of activation energy is 60kcal/mol, approximately. The relation between rate constant (k) and temperature (T°K) is represented by the equation:logk=-14410/T+7.692) The rate of reduction agrees with McKewan's equation and the relation between log k and T can be expressed by the following equation:logk=-8390/T+2.42From this equation, the activation energy is found to be approximately 39kcal/mol.3) It is found that FeAl2O4 is decomposed into Fe and materials of spinel type with H2 or carbon, in the first stage of reduction, and at high temperature the spinel materials finally become α-Al2O3.

Kinetics of Nickel Ferrite Formation

The rate of nickel ferrite formation is influenced by the milling technique and in the case of wet milling by the type of liquid media used. The reactivity of different types of α‐Fe2O3 of spherical shape decreases with an increase of the surface area ratio of α‐Fe2O3 to NiO. The particle shape of the iron oxides also affects their reactivity; cubical α‐Fe2O3 has the least reactivity in the formation of nickel ferrite. The validity of Jander's equation in ferrite formation is reviewed. Based on present findings the rate of ferrite formation is best represented by the equation dx/dt= (a‐x)/t, in which x is the percentage of ferrite formed, t the time, and a the kinetic isothermal reaction rate coefficient which is related to the surface area ratio of the reacting oxides. The application of the foregoing equation to the formation of magnesium ferrites from data found in the literature is also satisfactory.

Study on OP magnet (4th. Report)

OP magnet is industrially manufactured by nitric acid method. That is, the mixture of nitrate solutions of Fe and Co is prefired up to 850°C in air after evaporation and drying. The resulting powder is then pressed (compacted) to desired shape and fired above 1000°C in air of about 1mm Hg.The chief constituents of the prefired powder are CoFe2O4 and a-Fe2O3, while the fired magnet consists of a solid solution CoFe2O4-Fe2O4 of spinel structure, the composition being approximately CO0.75-Fe2.25O4. Hence, the main reaction during firing-reaction of magnet formation-was considered to be6 CoFe2O4+3 Fe2O3→8 Co0.75Fe2.25O4+1/2O2.Authors studied about the reaction by assuming that the reaction velocity is controlled mainly by the diffusion velocity of Fe and Co ions in the solid solution, and that evolution of oxygen has no great influence upon the reaction velocity, and found that the so-called Jander's equation holds good in this case. The activation energy of the reaction was calculated to be 41Kcal/mol.

Solid Phase Reaction between Calcium Carbonate and Silica

In order to build up a background to the relative difficulty for burning the different raw materials in cement production the solid phase reactions between SiO2 and either CaCO3 or BaCO3 at the temperatures ranging 500°-800°C were studied by measuring the amount of CO2 liberated during the reaction. Then, applying the figures so obtained into the Jander's equation for solid phase reaction the authors have tried to work out the rate constants as well as the activation energies. However, it was found out that there were many examples which failed to fit in the equation, probably, due to the additional CO2 liberated by simple thermal dissociation of the carbonates.On the other hand, W. E. S. Turner et al. have suggested the acceleration of thermal dissociation of CaCO3 when it was mixed with the powder of silica or of pure gold. The same trend was confirmed to exist also in the case of BaCO3.Furthermore, the investigation of X-ray diffraction pattern has revealed that the reaction products of CaCO3 and SiO2 obtained by heating at 700°C in air for 242 hours was not wollastonite (βCaO⋅SiO2) but larnite (β2CaO⋅SiO2).

鉄鉱石Pelletの焼結機構(II)

In continuation to the previous research (Tetsu-to-Hagané, vol, 43, No. 5 1957, p. 619) the phenomena of sintering process of iron oxide pellet was investigated by use of new apparatus. And some kinetic considerátions were made on the sintering process and it was found that the W. Jander's equation on solid reaction, F=(1-3√1-x)(2)esactly had conformed to the experimental data.Deducting from these experiments and considerations, the authors distinguished the sintering process into two parts: i.e. the former was "film sintering" and the latter was "body sintering" at higher temperature, and much care should be paid to the former stage of practical pelletizing operations.

Dissolution of Quartz Grains in Feldspathic Fusions

The purpose of this paper is to study the behaviour of melting of coarse quartz gains in feldspathic fusions, one of the most important reactions occurring in porcelain bodies during firing. Small tablets consisting of 97% fine ground potash-or soda-feldspar and 3% definitely sized quartz graines (mean intersection diameter, 150.4 μ) were prepared. Some of them were fired at 1150°-1450°C with different rates of 60°, 120°, and 180°C per hr., and the others were maintained for 0.5 hr. -4hr. at 1300°, 1330°, 1350°, or 1400°C in anelectric furnace, and thence abruptly cooled in air. Intersection diameters of 100-300survived quartz grains scattered within glassy phases were measured through thin sections by polarization microscope, and, then, the mean values were calculated. Fromthe values obtained, melting behaviour of quartz grains in feldspathic fusions was inferred as follows:(1) The dissolution of quartz grains into feldspathic fusions was markedly slower than had been usually considered. In general, coarse quartz grains were more easily dissolved in potash-feldspathic fusions than in soda-feldspathic ones.(2) Jander's equation was applied approximately to the dissolution of quartz grains in feldspathic fusions, as treated in this paper.(3) It seems that Arrhenius' equation did not strictly hold for the dissolution of quartz grains into the feldspathic fusions.(4) The following relationship was obtained between firing temperatures and dissolution of quartz grains in the fusions:1-(1-x)1/3=Be-C/Twhere x: reaction ratio in volume, T: firing temperature, (°K), B and C: constants.(5) In the system soda-feldspar-quartz, it was found that the dissolution behaviour of quartz grains might show a marked change at some temperatures within 1250°-1300°CIt was also certified that the microscopical method was very advantageous and precise for the quantitative study on the dissolution of solid crystalline grains into fusion.

A Criticism on Jander's Equation of Reaction-Rate, Considering the Statistical Distribution of Particle Size of Reacting Substance

In 1927, Prof. W. Jander experimented the reaction rate of solid particle and derived the following theoretical equation;(1-3√1-w)2=kt, where w was the fractions of reacted part in sold particle, t the time and k the constant.The author pointed out that Jander's equation, based on the assumption of the equal particlesize, would not hold good of actual particle that had a irregularity of particle-radus.Considering on the statistical distribution of particle-size, the author derived a new theoretical equation and criticized Jander's resalts of experiment on this point of view.The equation is1-w=∫(r-q)3f(r)dr/∫r3f(r)dr, where r is the radius of particle, f(r) the distribution function of the radius and q the thickness of reacted layer in the solid particle.