Topic
Rate equation
About: Rate equation is a research topic. Over the lifetime, 4249 publications have been published within this topic receiving 90524 citations. The topic is also known as: rate law.
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TL;DR: In this article, the coupled vibration-dissociation-recombination process for molecules and atoms has been examined and techniques for solving the appropriate master equations for both quantum (discrete) and classical (continuous) models are given.
Abstract: The coupled vibration—dissociation—recombination process for molecules and atoms has been examined. Techniques for solving the appropriate master equations for both quantum (discrete) and classical (continuous) models are given. It is shown that the process is most easily treated classically and that in this case the master equation can be reduced to an equivalent diffusion equation. It is assumed that, after an initial vibration transient, during which reactions are negligible, the process may be treated using the steady‐state approximation. During the steady‐state phase, the usual phenomenological rate equations are valid and the ratio of the forward and reverse rate constants is the equilibrium constant, though the individual rate constants are depressed below their equilibrium values.Comparison of the results with other theoretical work shows general agreement for similar models; comparison with shock‐tube experiments on molecular dissociation and stellarator experiments on ionic recombination is enco...
283 citations
TL;DR: In this article, a theory of unimolecular reactions induced by coherent, monochromatic infrared radiation (URIMIR) in the absence of collisions is presented, where it is shown that the set of first order linear differential equations for the amplitudes of molecular states (Schrodinger equation) can be reduced, under specified conditions, to a much smaller set of First Order Linear Differential Equations for the coarse grained populations of levels for polyatomic molecules (master equation), and four limiting situations are identified in which such linear rate equations provide a reasonable approximation.
Abstract: A theory of unimolecular reactions induced by coherent, monochromatic infrared radiation (URIMIR) in the absence of collisions is presented. It is shown that the set of first order linear differential equations for the amplitudes of molecular states (Schrodinger equation) can be reduced, under specified conditions, to a much smaller set of first order linear differential equations for the coarse grained populations of levels for polyatomic molecules (master equation). Four limiting situations are identified in which such linear rate equations provide a reasonable approximation. Rate coefficients are obtained as a function of spectroscopic parameters (energy levels and transition moments). Solutions for the master equations are given as a function of time and at steady‐state. Simple limiting cases (Strong Field Limit, Weak Field Limit, Reaction Threshold Bottleneck, etc.) are identified and very simple rate expressions are obtained for these cases. A complete statistical mechanical theory of URIMIR is form...
281 citations
TL;DR: In this paper, a decrease of light transmission with increasing excitation intensity was observed in tetraphenylporphyrin/toluene solutions irradiated with 80 ps pulses at λ=532 nm.
277 citations
TL;DR: In this article, a study of CO formation for steam reforming of methanol on a commercial CuO/ZnO/Al2O3 catalyst has been performed in the temperature range 230-300°C and at atmospheric pressure.
Abstract: A study of CO formation for steam reforming of methanol on a commercial CuO/ZnO/Al2O3 catalyst has been performed in the temperature range 230–300 °C and at atmospheric pressure. The reaction schemes considered in this work are the methanol–steam reforming (SR) reaction and the reverse water gas-shift (rWGS) reaction. Power rate laws for the SR and reverse WGS reactions were used in a refinement of rate equations to the experiment data. For the temperature range studied the reaction order of methanol was determined under differential conversion (less than 10%) and was found to be 0.2. The integral method (partial pressure of the reactants and products measured as a function of contact time) was then applied to determine the reaction rate constants, activation energies, and pre-exponential factors for both reactions. The experimental results of CO partial pressure as a function of contact time at different reaction temperatures show very clearly that CO was formed as a consecutive product. The implications of the reaction scheme, in particular with respect to the production of CO as a secondary product, are discussed in the framework of on-board production of H2 for fuel cell applications in automobiles. Potential chemical engineering solutions for minimizing CO production are outlined.
274 citations
TL;DR: A model describing the free-electron generation in transparent solids under high-intensity laser irradiation that follows the nonstationary energy distribution of electrons on ultrashort time scales as well as the transition to the asymptotic avalanche regime for longer irradiations.
Abstract: We develop a model describing the free-electron generation in transparent solids under high-intensity laser irradiation. The multiple rate equation model unifies key points of detailed kinetic approaches and simple rate equations to a widely applicable description, valid on a broad range of time scales. It follows the nonstationary energy distribution of electrons on ultrashort time scales as well as the transition to the asymptotic avalanche regime for longer irradiations. The role of photoionization and impact ionization is clarified in dependence on laser pulse duration and intensity.
272 citations