Linear Rate Law Research Articles

Reactions Between Silica and Graphite

Reactions between silica and graphite were studied in vacuum from 1445° to 1765°C by continuously measuring the amount of carbon monoxide formed. At low temperatures and/or short times, the reaction followed a linear rate law with an apparent activation energy of 117 kcal. At higher temperatures and/or longer times, the reaction showed a more complex behavior, indicative of a nucleation-growth process with an apparent activation energy of 122 kcal. It is shown that the reaction could proceed via the gas phase by dissociation of silica into oxygen and silicon monoxide and subsequent reaction with graphite. The onset of the nucleation-growth-controlled process could be correlated with the transformation of quartz to cristobalite.

The Effect of Nitrogen on the Oxidation of Tantalum at High Temperatures

The effect of nitrogen on the oxidation of tantalum has been studied at 600°, 820°, and 925°C. In all cases, the oxygen partial pressure was close to 360 Torr; nitrogen partial pressures in the range 0 to 250 Torr were investigated. At all three temperatures, nitrogen reduces the rate of oxidation, the effect increasing with temperature. Although the oxidation in pure oxygen follows a linear rate law, with nitrogen present the reaction ceases to be linear. The interpretation of the results in terms of the existing kinetic models is discussed. It is suggested that the pressure drop associated with the flow of the gas through the porous outer scale cannot be neglected.

Kinetics of High-Temperature Hydrolysis of Magnesium Fluoride: I, Evaluation of Reaction Mechanism

The rates of hydrolysis of polycrystalline magnesium fluoride slabs were investigated by a gravimetric method as functions of temperature from 745° to 835°C and water-vapor pressure from 1 to 20 mm Hg. A linear rate law was found, and it was concluded that the rate-determining process was chemical reaction at the MgF2-MgO interface. A three-step reaction mechanism is proposed: (1) the chemisorption of water vapor. (2) formation of a hydroxyfluoride complex. and (3) decomposition of the hydroxyfluoride complex to form products. Assuming that the chemisorption step was in equilibrium and that the HF pressure was negligible, an expression was developed showing that the rate was proportional to the concentration of chemisorbed water vapor. The rate dependence on water-vapor pressure was expressed in terms of the Langmuir adsorption isotherm equation. Values of –16.9 kcal/mole and–4.2 eu were obtained for the enthalpy and entropy of chemisorption. The activation enthalpy and frequency factor for the decomposition of the chemisorbed intermediate, MgF2.H2O(chem), were 46.0 ± 0.5 kcal/mole and 1.75 × 1O10 sec−1.

The Oxidation Mechanism of Pure Uranium in Carbon Dioxide Between 350° and 650°C

Weight gain/time curves obtained on a thermobalance are related to metallographic observations of the oxide. It is found that the oxide is initially protective, but as a result of nonuniform oxidation and cracking the oxidation rate accelerates until finally a linear rate law is obeyed. In the early stages of oxidation a separate layer of oxide grows at the oxide‐gas interface, but soon attains a limiting thickness of a few thousand Angstroms and does not influence the over‐all oxidation behavior. Carbon monoxide formed from the reaction between uranium and carbon dioxide reacts further in the cracks in the oxide.

Mass transfer in reacting systems near equilibrium: Use of the affinity function

Three problems involving reacting systems near chemical equilibrium are discussed: (1) evaluation of the phenomenological coefficient in the linear rate law for a diffusion limited catalytic reaction, (2) the augmentation of mass transfer resulting from reaction in the absence of convection and (3) extension of the augmentation theory to convective systems. In each case the affinity function is employed as the primary dependent variable to simplify the analysis.

Non-protective and protective scaling of a commercial 1¾% silicon-iron alloy in the range 800°C-1000°C

During an investigation, by a thermobalance technique, of the oxidation of a commercial silicon-iron alloy containing 1·74% Si and 0·3% Al in the range 800–1000°C it was found that the mode of scaling was dependent on the atmosphere used. In dry air the initial scale formed is protective and inhibits further increase in weight. In CO 2 the scale formed is not protective and oxidation proceeds according to a linear rate law. On substituting CO 2 for air as the oxidizing atmosphere the protective scale breaks down and oxidation then follows a linear law, but on substituting air for CO 2 the linear rate of scaling is replaced by a much slower rate which decreases with time. If a sequence CO 2-air-CO 2 is used the appropriate change in scaling behaviour is observed at each of the two changes in atmosphere. Metallographic and X-ray investigations showed that in air the initial scale formed consists of hematite and silica and that in CO 2 the oxidation products are magnetite, wüstite and fayalite. The apparent reversibility of the mode of scaling is explained in terms of the breakdown of the protective scale at a number of isolated points. This breakdown, which occurs readily in CO 2 but not in air, is discussed in terms of the thermodynamic instability of the higher oxides of iron in CO 2 and of the phase-boundary reaction at the scale/gas interface.

Spectrum-Line-Reversal Temperature Measurements Through Unsteady Rarefaction Waves in Vibrationally Relaxing Oxygen

Abstract : Pressure and spectrum-line-reversal temperature measurements were made of the structure of an unsteady expansion wave initiated in a vibrationally-excited gas in a shock tube by the rupture of a second diaphragm. With oxygen initially at about 2500 deg K and 0.75 atmospheres pressure the vibrational temperature was observed to fall from its initial (fully-frozen) value at the tail of the wave to a minimum before rising again to the original equilibrium value at the head of the wave. This agrees broadly with Appleton's calculations based on a linear rate law and Landau-Teller theory for Tau sub v, although the temperature minimum was slightly higher and occurred later than he predicted; it was also predicted qualitatively by Stulov. More detailed studies with, for example, nitrogen would be desirable for seeking a full explanation of the small differences with theory revealed by these preliminary tests.

Clay‐catalyzed reactions of olefins. III. Kinetics of polymerization of styrene

AbstractThe polymerization of styrene in the presence of acid clay catalysts has been reported previously. The kinetics were studied in solution at 0°C. by a dilatometric method relating monomer concentration to volume and heat of reaction. An approximately linear rate law was derived which fit the data over a 100‐fold range of concentration. The integrated rate equation is: The equilibrium constant KM for monomer absorption was found to be 863 ± 70 cc./mole and the propagation constant kp was found to be 191 ± 14 cc./mole/sec. An Arrhenius plot is in accord with the equation k′p = Ae−7.7/RT with an activation energy 7.7 ± 1.5 kcal. and an Arrhenius factor of 3.39 × 108 cc./mole/sec. The effect of added inhibitor I was interpreted qualitatively on the basis of an exact rate equation which in differential form is: The factor KI[I]/[I0] was estimated from the equation: and found to be negligible at 0.1M monomer concentration and consistent with experiment. An explanation for low values of kp in the presence of added inhibitor was proposed based upon the exact rate law.

Longitudinal Impact on Viscoplastic Rods—Linear Stress-Strain Rate Law

Hohenemser and Prager [1] proposed a constitutive law for a solid of Bingham type We use a form of this law to study some cases of longitudinal impact on a bar causing large plastic strains. The results are intended to be of use in the design of impact tests on structural metals and in the interpretation of data from them, as well as helpful in guiding similar studies on materials with more complex plastic strain rate behavior.

Reactions Between Refractory Oxides and Graphite

Reactions between alumina, magnesia, spinel, beryllia, and graphite have been studied in vacuum by measuring the amount of carbon monoxide formed. Two types of reactions were observed: a diffusion‐controlled reaction with alumina, beryllia, and thoria, and a phase boundary‐controlled reaction with magnesia, beryllia, spinel, and titania. The following activation energies were obtained: 316 kcal for , 40 kcal for below 1700°C (parabolic rate law), 61.3 kcal for above 1700°C (linear rate law), 59.8 kcal for , 59.5 kcal for spinel, and 59 kcal for . The relative reactivities of these oxides with graphite increase in the following order: , spinel, , , , . For the reactions following a linear rate law a mechanism is proposed. It was concluded that the reaction proceeds over the gas phase by dissociation of the oxide into atomic oxygen and that the desorption of carbon monoxide from the graphite surface is the rate‐determining step.

Kinetics and Mechanism of Columbium Alloy Corrosion In Superheated Steam

Abstract Screening tests of numerous binary, ternary, and quaternary columbium alloys in superheated steam, up to 704 C, showed that Nb-V binary alloys had the greatest corrosion resistance.1 The binary alloys were studied in detail and were observed to follow initially low power rate laws varying from quartic to parabolic behavior. A rate transition occurred after longer exposures to a linear rate law which was associated with spalling and cracks in the oxide films. The corrosion product was shown to be different than that formed in air or oxygen for Nb-3.5V and was a complex unknown phase. An increase in vanadium content to 10 atomic percent (a/o) enabled beta-Nb2O5 to form with the unknown phase, and Nb02 also formed as a third phase on Nb-15V. A change in oxide morphology was noted as the vanadium increased from 3.5 to 8.9 a/o, the latter forming oxide “fingers” which grew into the substrate. The activation energy for corrosion, 13 kcal/mol, was the same for binary Nb-V alloys which formed either the unknown oxide phase or NbO2 at temperatures below 482 C, and was considerably less than that for oxygen diffusion in Nb2O5 containing 1 mol percent V2O5. The apparent diffusion-controlled process, according to the kinetics, and low corrosion activation energy strongly suggest oxide grain boundary diffusion as a rate-limiting step during the pretransition period. Oxygen contamination of the substrate occurred readily, the tolerance for oxygen decreasing with increasing vanadium. Cracks which formed in the oxide due to volume mismatch at the oxide-metal interface were observed to have propagated through the embrittled substrate. Spoiling and contamination characteristics appear to be limiting properties for corrosion limetime.

Oxidation of uranium monocarbide

Compacts of uranium monocarbide with a density of 11.7–12.7 g/cm 3 have been oxidized in I atm of CO 2, O 2, N 2 and CO at temperatures in the range 350–1000°C and all the reactions found to obey a linear rate law. The linear rate constants increased as the temperature increased and the density decreased, and for dense compacts were normally similar to or less than the corresponding values for uranium metal, the notable exception being for CO 2 at 500–700°C.

Oxidation Studies on 304 Stainless Steel

The kinetics of oxidation of 304 stainless steel are studied between 500° and 1150°C at 0.1 atm for reaction times up to 6 hr. At 500°C about 2.3 µg/cm2 of oxide are formed in a time period of 6 hr. The rate of increase after 6 hr is 0.1 µg/cm2/hr. At 800°C a transition is observed in the rate of oxidation with the kinetics changing from the parabolic rate law to the linear rate law. This transition occurred for a weight gain of 9 Mg/cm2. At 900 °C and for weight gains above 90 µg/cm2 the parabolic rate law again was found to hold. A second transition is found in the kinetics of oxidation at 1150°C. This transition we relate to the vapor pressure of iron and chromium which acts to speed up the transfer of metal atoms through the oxide scale. A comparison of the kinetics of oxidation is made with the heat‐resistant Kanthal alloys and with pure chromium.

Reaction-Rate Studies of Thorium-Uranium Dicarbides in Moist Air

A number of arc-melted or sintered thorium or uranium carbides were reacted in moist air at 30° and 50° C. The initial reactions appeared to follow a simple linear rate law, the thorium-containing carbides being about ten times more reactive than UC2. Initial rate constants at 50° C based on bulk particle surface area were 0.25 μg per cm2per second for UC2 and 2.78 pg per cm2per second for ThC2. Rate constants for mixed, thorium and uranium carbides fell between these values. The reaction produced both gaseous and solid products. Solid reaction products consisted of thorium or uranium oxides and condensed hydrocarbons; the oxides could be hydrated. The gaseous products were principally aliphatic hydrocarbons and hydrogen.

The Kinetics of Oxidation of Uranium between 125° and 250°C

Rates of oxidation of uranium have been measured volumetrically at constant pressure in the temperature range 125°–250°C and at oxygen pressures from 20 to 800 mm. The oxidation is best described by two linear rate laws, a marked increase in rate occurring after an average of 50 µg O2/cm2 has been consumed. The first stage rate in µg/cm2‐min is given by the expression where , is oxygen pressure in millimeters of mercury, and varies with temperature. The reaction is believed to be controlled by process occurring at the gas‐oxide surface. The increase in rate leading to the second stage is not treated quantitatively, but is attributed to a net increase in surface area.

The Kinetics of Oxidation and Nitridation of Lithium, Calcium, Strontium, and Barium

Reaction rates for lithium, calcium, strontium, and barium during 50–120 min of exposure to O2 or N2 were measured as a function of temperature and pressure by a manometric method. Many of the reaction rates were found to be exponential functions of time, but in some cases a linear rate law was found.

Kinetics of Absorption by Metals of Hydrogen From Water and Aqueous Solutions

Abstract The kinetics of absorption of hydrogen in corrosion is treated on the basis of a mechanism previously proposed for the absorption of hydrogen from H2 gas. Rate formulae are derived and compared with experimental data. On certain simple assumptions, a parabolic or a cubic rate law is derived for an initial period, during which absorption of hydrogen occurs. This rate law is succeeded by a linear rate law when the metal is saturated with hydrogen. The rate in acid solutions is proportional to the square root or the cube root of the acid concentration. The rate in water vapor is proportional to the square root of the water vapor pressure or independent of the water vapor pressure. 3.8.4

Kinetics of the oxidation of uranium by carbon dioxide

The rates of oxidation of uranium by carbon dioxide have been determined over the range 500–1000°C. The rate increases with temperature from 500 to 780°C with a sudden marked increase when the metal is near or at the β−γ transition (772°C). At higher temperatures up to 1000°C the rate decreases with increasing temperature. The reaction obeys a linear rate law for the range 500–800°C, although self-heating sometimes results in a non-linear weight increase-time graph. In the range 500–725°C the activation energy is 26 ± 10 kcal/mole which is consistent with oxygen ion diffusion being the rate controlling mechanism.

Kinetics of the Uranium‐Steam Reaction

Reaction rates of unalloyed uranium with super heated steam at 160°–1400°C and 1 atm pressure have been determined by a thermogravimetric method. Up to 880°C the reaction follows a linear rate law with maximum rates at approximately 300° and 750°C. Above 880°C a parabolic rate law applies for the first 60–120 min, after which corrosion is linear; the oxide formed in the initial period gives protection to the underlying metal, and the subsequent linear rate is as low as that at about 200°C. X‐ray diffraction of the reaction product indicated that uranium dioxide was formed over almost the whole temperature range.

ジルコニウムの空気酸化の研究

The reaction kinetics of the Kroll-processed reactorgrade zirconium under 1 atm. of air was studied over the temperature range of 650 to 900 deg C. An analysis of the rate data showed that the cubic rate law was applicable in the initial stage of oxidation. However, a breakdown of the oxide film was observed at 800 and 850 C, and then the oxidation proceeded in accordance with the linear rate law. A plot of the logarithms of the cubic rate law constants against the reciprocal of absolute temperature gave a straight line, and the activation energy of 48,400 cal/mol was calculated. Chemical analysis was used for the determination of the amount of nitrogen absorbed during oxidation of zirconium in air. The contents of absorbed nitrogen in the oxide layer increased with oxidation time and temperature, but no existence of a ZrN phase was found by x-ray analysis. The experimental formula of absorption of nitrogen during the oxidation of zirconium in air, W /sup 3/2 = kt (where W: weight of absorbed nitrogen, k: constant, t: time), is suggested. And the activation energy of 82,400 cal/mole was calculated for absorption of nitrogen during the reaction of zirconium with air, over themore » temperature range of 700 to 850 deg C. It is concluded that the rate-controlling step of the oxidation of zirconium is the process of diffusion of oxygen ion in the oxide film. (auth)« less