Showing papers on "Rate equation published in 1972"

On the theory of void formation during irradiation

Abstract: A simple theory of the swelling of materials subjected to high energy particle irradiation is developed. Chemical reaction rate equations are used as a basis. Point defects, interstitials and vacancies, are assumed to be produced randomly throughout the solid. They move by random walk through the material until they cease to exist either by recombination with the opposite type of defect or by incorporation into the crystal at sinks such as dislocations, grain boundaries and voids. The rate equations for interstitials and for vacancies, which are coupled via the recombination term, are solved for steady state conditions under irradiation. Defect concentrations, supersaturations, recombination and total sink annihilation rates are obtained in terms of the production rate, sink annihilation probabilities, jump frequencies and thermal equilibrium concentrations of defects. The swelling rate is derived using sink annihilation probabilities at three principally different types of sinks, i.e. voids, sin...

Carbon Monoxide Oxidation on a Pt(110) Single Crystal Surface

Abstract: The catalytic reaction between CO and O2 on a Pt (110) surface is investigated by residual gas analysis for different partial pressures of CO and O2 and various temperatures. The surface cleanliness of the Pt crystal is monitored by Auger electron spectroscopy. The results of the reaction study are generally in agreement with previous studies for polycrystalline Pt catalysts. The temperature dependence of the formation rate of CO2 exhibits a maximum whose position depends on the composition of the gas phase. At T=215°C two different rate laws are valid. For PO2>PCO the rate of CO2 formation is proportional to PO21.1PCO−0.6, while for PO2>PCO it is proportional to PO20.25 PCO0.75. These observations support the idea that the reaction obeys an Eley-Rideal mechanism in the pressure and temperature range investigated, and the results are evaluated accordingly. The influence of segregated Si on the CO oxidation reaction is investigated and found to be small.

On the Mechanism of Low‐Temperature Oxidation (23°–450°C) of Polycrystalline Nickel

Abstract: The oxidation of "clean" nickel has been investigated from 24° to 450°C at oxygen pressures of . Ultra‐high vacuum techniques made it possible to start oxidation on specimens free of oxide and surface impurities such as C, Si, and S. Oxygen uptake was measured manometrically with a capacitance gauge of submonolayer sensitivity. Initial rapid oxygen adsorption (and place exchange) on nickel was followed by slower oxidation obeying a logarithmic rate law over the thickness range 8–30Aa. Growth of thicker films was in accord with a parabolic rate law, transport through the oxide occurring predominantly via easy diffusion paths. The value of 41 kcal·mole−1 calculated from an Arrhenius plot of the parabolic rate constants from 300° to 450°C is an approximate measure of the activation energy for growth via leakage paths. A p1/6 dependence of the parabolic growth rate on oxygen pressure was found at 450°C.

Effect of homogeneous and heterogeneous reactions on the dispersion of a solute in the laminar flow between two plates

Abstract: The paper presents an analytical solution for the dispersion of a solute in a liquid flowing between two parallel plates in the presence of an irreversible first-order chemical reaction. The effects of both homogeneous and heterogeneous reactions on the dispersion are studied under isothermal conditions. It is found that for homogeneous reaction in the bulk of the liquid, the effective Taylor diffusion coefficient decreases with increase in the reaction rate constant. Further for heterogeneous reaction at the catalytic walls, Taylor diffusion coefficient is also found to decrease with increase in the wall catalytic parameter for fixed reaction rate constant corresponding to the bulk reaction.

Biological Sciences: The So-called Thermodynamic Compensation Law and Thermal Death

Abstract: IT has frequently been reported that, for a structurally related series of compounds undergoing a defined chemical reaction, the activation parameters, ΔH‡ and ΔS‡, are linearly related: This is sometimes called a thermodynamic compensation law because the form of the rate equation derived from transition state theory (equation (2)) is such that parallel changes in the activation parameters have opposite effects on the value of the rate coefficient, k, As Leffler1 pointed out, however, the relationship can arise as a computational artefact from experimental errors in the rate coefficients from which the activation parameters are calculated. Exner2,3 further showed that the form of the equations used in the calculation tended, in any case, to generate the relationship. Hammett4, from statistical mechanical considerations, has produced a set of formal conditions which must be satisfied if the relationship is to be observed but these seem to have no simple physical interpretation. Behaviour which appears to be consistent with the compensation law makes a comparison of rate constants of doubtful value since, at a temperature T=1/a, all the rate coefficients are the same. Above this so-called isokinetic temperature the order of rate coefficients is the reverse of that observed below it (see ref. 5).

Effect of VV Transfer on the Rate of Diatomic Dissociation

Abstract: The effect of VV transfer processes on the rate of thermal dissociation of diatomic molecules is considered within the steady‐state approximation for a single‐quantum step master equation. An accurate rate law is obtained for the truncated harmonic oscillator through replacement of the agents for VV transfer by the vibrational energy. Approximate numerical solutions for a Morse oscillator model of the representative species O2, H2, and HCl are in quite satisfactory agreement with the measured rates and provide at least qualitative explanations for nearly all the unusual features of the measurements. The rate enhancement effect of VV transfer is found to be slight; the primary, and quite general consequence of VV transfer is rather a depression of the rate, especially at high temperatures, which then appears as a considerable reduction in activation energy. This effect is shown to arise from a violation of detailed balance for the VV processes whenever the vibrational energy is depleted by rapid dissociation.

Laser Induced Infrared Fluorescence: Thermal Heating, Mass Diffusion, and Collisional Relaxation in SF6

Abstract: Experimental results of the study of 10‐μ and 16‐μ laser induced fluorescence in SF6 and SF6‐rare gas mixtures are presented. The fluorescence at both wavelengths is found to exhibit a fast and a slow decay process. The major features of the experimental fluorescence decay curves are well described by a simple model with only two energy levels. The rate equations for this model system include terms which couple collisional relaxation with heat and mass transport. The fast fluorescence decay process at each wavelength is found to be characteristic of binary collisional deactivation. The rate of decay of the slow process, however, is controlled by transport of both heat and mass to the wall of the fluorescence cell with heat transport being the dominant effect. The experimental results and the analysis based on a two level model system are consistent with a two step vibrational deactivation mechanism. The first step is a rapid equilibration of the vibrational modes. The second step is a somewhat slower equi...

Closed-Form Solution to Rate Equations for an F + H 2 Laser Oscillator

Abstract: Chemical lasers pumped by the reaction of atomic fluorine with molecular hydrogen emit power from rotation–vibration transitions of excited HF with upper levels as high as v = 3. Collisional processes compete with stimulated emission for the energy of the excited HF. A simplified analysis is presented here for intensity, energy, and chemical efficiency of a class of such lasers. Results are obtained in closed form. A comparison with more exact computer solutions establishes the validity of the analysis despite its simplifications. A comprehensive parametric study examines the relative importance of initial conditions, optical cavity parameters, and rate coefficients for pumping and deactivation reactions.

Excitation processes and relaxation rates in the pulsed water vapor laser.

Abstract: This paper presents an experimental study of time-resolved gain in H(2)O, H(2)O-He, and H(2)O-H(2) mixtures as a function of gas composition and excitation current. Utilizing the fast rising (~70 nsec) pulse from H(2)O-He laser as a probe, the amplifier gain was measured with a time resolution of about 100 nsec. The gain was observed to follow the excitation current pulse rather closely indicating that population inversion was established in times less than 100 nsec. This suggested that excitation was most likely by means of rapid cascading from higher levels and/or by direct electron impact. The gain was found to be describable by a two-level rate equation model containing one dominant relaxation rate and assuming immediate excitation of the levels involved by inelastic collisions with electrons. With pure H(2)O, the relaxation rate was proportional to pressure to within 10%, indicating that the upper level was de-excited primarily by c llisions with other H(2)O molecules. At a pressure of 1 Torr the relaxation rate in pure H(2)O was 0.35 +/- 0.05 for the 28-microm transition. The addition of small amounts of foreign gases was observed to increase this relaxation rate, consistent with the measured decrease in the amplifier gain. By subsequently increasing the water vapor pressure it was found possible to optimize the gain at an enhanced level over the pure H(2)O case. The peak gain obtained in water vapor at 1000 A was 0.34 m(-1). Under foreign gas addition this increased to 0.68 m(-l) for the same peak current. In this case the relaxation rate, as a function of the foreign gas (He or H(2)) pressure, remained constant to within 10%, suggesting that these gases at higher concentrations may enhance the system gain by altering the discharge conditions without appreciably collisionally de-exciting the upper laser level.

Sorption in Flow Through Porous Media

Abstract: Publisher Summary This chapter discusses the sorption in flow through porous media. The three kinetic mechanisms are presented, these are: (1) chemical reaction kinetics; (2) liquid phase diffusion; and (3) solid phase diffusion. It is generally conceded that chemical reaction kinetics is not rate limiting. Either or both of the other two mechanisms may be rate limiting, however, depending on chemical and flow conditions; it is very difficult to discern the conditions controlling the respective kinetic mechanisms. Obtaining a practical rate law for either category of diffusion is also difficult. Fick's first law describes either solid or liquid phase diffusion, but is difficult to apply in its differential form. The approximations to Fick's first law (flux density = diffusion coefficient x grad. concentration) for both liquid and solid phase diffusion which, when combined with the mass action equilibrium equations, results in expressions for each mechanism having a form identical to the equation for second-order reaction kinetics for the sorption reaction. It is applied to the methods of Hiester and Vermeullen to predict breakthrough curves for fluidized beds; their experimental results agree well with predicted breakthrough curves.

Calculated efficiency of dye lasers as a function of pump parameters and triplet lifetime

Abstract: The rate equations governing pulsed laser operation in dyes have been solved numerically and the results discussed for a variety of material parameters and pump conditions, especially for pulses in excess of 1 μsec. The resulting laser parameters have been considered as a function of the triplet lifetime and the pump peak power. Calculated values of the efficiency in the conversion of pump light into laser light have been derived in general, and applied specifically to the case of Rhodamine 6G. The calculated efficiencies have been compared with known experimental results on Rhodamine 6G under laser and flashlamp excitation. The agreement is generally good. Since the predicted efficiencies for laser operation in excess of a few hundred nanoseconds depend critically on the values of the triplet lifetime τp in solution, especially for τp in the range 100–300 nsec, the results of the calculations can be reliably compared to experiment only when precise values of the triplet lifetimes become experimentally av...

Non-Steady-State Kinetics for a Double-Intermediate Enzyme Mechanism: The Case of High Enzyme Concentrations

Abstract: An equation has been derived for the non-steady-state kinetics arising from the mechanismin which the concentration of enzyme E is greatly in excess of that of the substrate A; EA and EA′ are two intermediates and X and Y the products. Solutions for the rate of formation of the first product X were given by Kasserra and Laidler. The present work is concerned with the rate of formation of Y. A general equation is derived for the rate of production of Y, and it is shown that under certain simplifying conditions, easily realized in practice, the rate law reduces to study of the rate of formation of Y therefore leads to a determination of k3.

Sorption of Nitrogen at Low Pressures by Titanium

Abstract: The sorption kinetics of nitrogen at pressures of 1×10−5 to 1×10−3 Torr on titanium foil was studied ill the range 600 °–800 °C, by using an ultrahigh vacuum microbalance. In the similar way to oxygen, the rate law of nitrogen sorption was separable into two types, i.e., the linear rate law in the initial period and the parabolic rate law in the latter period. The linear rate law was obeyed for shorter times as the nitrogen pressure and the reaction temperature increased. In the initial linear part, the sorption rate was proportional to the nitrogen pressure at each temperature, which showed the linear sorption to be controlled by the rate of arrival. The sticking probability and pumping speed per unit area (cm2) for nitrogen were constant with change of nitrogen pressure, e.g., at 800 °C, 0.0045 for sticking probability and 0.098 (liter sec−1) for pumping speed. The transtion in the sorption rate laws and critical pressure of nitrogen for the transition are discussed on the basis of a diffusion theory.

Effect of temperature on reaction rate

Abstract: ▼ Hydrochloric acid 2 mol dm –3 (Irritant). Teaching tips The method for this experiment is best understood when the teacher demonstrates it first. The end-point can be measured with a light sensor connected to a data-logger. A light sensor set up as a colorimeter can be used to monitor the precipitation on a computer – clamp a light sensor against a plastic cuvette filled with the reactants. The result, in the form of graphs on the computer, provides very useful material for analysis using data logging software. The software shows the change on a graph and this tends to yield more detail than the end-point approach used in this experiment. The rate of change can be measured from the graph slope or the time taken for a change to occur.

Gas‐Phase Reaction of NO2 and Ethylene at 25°C

Abstract: The thermal reaction of NO2 and C2H4 was studied in the gas phase at 25°C. The products of the reaction were CH3NO2, CH3ONO2, NO, N2O, CO2, C2H4O, and H2O. A mechanism is presented to explain the formation of these products, and some rate constants are derived from the mechanism, the rate of consumption of NO2, and the rate of formation of the products.

Chlorine abstraction reactions of fluorine. Part 2.—The kinetic determination of the bond dissociation energy D°0(CCl2F—Cl)

Abstract: The reaction of fluorine with CCl3F has been studied over the temperature range 491–586 K. The mechanism is identical to that found in Pyrex vessels except that the reaction is now a homogeneous gas phase one. The rate equation has the form: –d[CCl3F]/dt=k[F2]½[CCl3F]. The rate constants fitted the Arrhenius equation: log k(1.½ mol–½ s–1)=(11.95 ± 0.07)–(31490 ± 90)/2.303 RT where k=k2(Kc)½, k2 is the rate constant for the reaction F + CCl3F → ClF + CCl2F and kc is the equilibrium constant for the homogeneous gas phase dissociation of fluorine. This leads to D°0(CCl2F—Cl)= 72 ± 2 kcal mol–1 and ΔH°f0(CCl2F)=–24 ± 4 kcal mol–1. The temperature dependence of the ignition limits has been investigated, and treated by thermal explosion theory. The ignitions are shown to be the result of radical branching reactions brought about by the collisional deactivation of vibrationally excited CCl2F2 molecules. Induction periods were also observed and studied.

Stochastic Analysis of an Oscillating Chemical Reaction

Abstract: The rate equations of a model of certain autocatalytic chemical reaction which is extremely far from the thermodynamic equilibrium are represented by the non-linear differential equations of Volterra type. By using the stochastic model of this chemical reaction system, the sample processes of the reaction process are traced by computer simulation and the characteristic behaviour can be analyzed by the statistical analysis of the sample process without any difficulty resulting from non-linearity of the reaction system. That is, the behaviour of the reaction process near the stationary state shows the qualitative nature of the result from the linearized equation of the deterministic rate equation, but the reaction process far from the stationary state behaves in essentially different way from that of `near the stationary state.'

A Kinetic study of the reaction of nitrogen dioxide with tetrafluoroethylene

Abstract: The reaction of NO2 with C2F4 was studied at 30°, 68°, 114°, and 157°C by in situ monitoring the infrared absorption bands of the products. The major primary products of the reaction are O2NCF2CFO and FNO. Smaller amounts of CF2O (and presumably NO) are also produced. There was no evidence for other primary products, though they may have been produced in minor amounts. The rate laws for the production of both O2NCF2CFO and CF2O are first order in both [NO2] and [C2F4]. CF2O production is at least partly heterogeneous as demonstrated by packing the quartz reaction vessel with Pyrex beads and by using a Monel cell. The homogeneous rate constant obtained from the high-temperature results gives a rate constant of 3.4 × 108 exp (minus;17000/RT) M−1sec−1 for CF2O production. Actually these Arrhenius parameters represent lower limits, since the heterogeneous reaction may still be playing a significant role. The production rate of O2NCF2CFO is not much affected by changing the nature of the surface or the surface to volume ratio. However the reaction may be heterogeneous, since the rate constant for its formation of 1.3 × 104 e×p (−7500/RT) M−1sec−1 has an abnormally low pree×ponential factor. E×periments in the presence of NO indicate that the mechanism for O2NCF2CFO formatlon is The intermediate can also react with NO: with k13/k12 = 1.3.

A study of the liquid-vapor phase change of mercury based on irreversible thermodynamics.

Abstract: The object of this work is to determine the transport coefficients which appear in linear irreversible-thermodynamic rate equations of a phase change. An experiment which involves the steady-state evaporation of mercury was performed to measure the principal transport coefficient appearing in the mass-rate equation and the coupling transport coefficient appearing in both the mass-rate equation and the energy-rate equation. The principal transport coefficient sigma, usually termed the 'condensation' or 'evaporation' coefficient, is found to be approximately 0.9, which is higher than that measured previously in condensation-of-mercury experiments. The experimental value of the coupling coefficient K does not agree with the value predicted from Schrage's kinetic analysis of the phase change. A modified kinetic analysis in which the Onsager reciprocal law and the conservation laws are invoked is presented which removes this discrepancy but which shows that the use of Schrage's equation for predicting mass rates of phase change is a good approximation.