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Kinetic theory 492 kinetics

Langmuir adsorption isotherm A theoretical equation, derived from the kinetic theory of gases, which relates the amount of gas adsorbed at a plane solid surface to the pressure of gas in equilibrium with the surface. In the derivation it is assumed that the adsorption is restricted to a monolayer at the surface, which is considered to be energetically uniform. It is also assumed that there is no interaction between the adsorbed species. The equation shows that at a gas pressure, p, the fraction, 0, of the surface covered by the adsorbate is given by ... [Pg.234]

It must also be realized that this thin surface region is in a very turbulent state. Since the liquid is in equilibrium with its vapor, then, clearly, there is a two-way and balanced traffic of molecules hitting and condensing on the surface from the vapor phase and of molecules evaporating from the surface into the vapor phase. From the gas kinetic theory, the number of moles striking 1 cm of surface per second is... [Pg.56]

It is instructive to consider just how mobile the surface atoms of a solid might be expected to be. Following the approach in Section III-2, one may first consider the evaporation-condensation equilibrium. The number of molecules hitting a 1-cm surface per second is from kinetic theory... [Pg.258]

Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. [Pg.282]

J. Frenkel, Kinetic Theory of Liquids, Clarendon Press, Oxford, 1946. [Pg.343]

In evaluating if a site can be regarded as a two-dimensional potential box, then the rate of adsorption will be given by the rate of molecules impinging on the site area oq- From gas kinetic theory. [Pg.605]

The acconunodation coefficient for Kr on a carbon filament is determined experimentally as follows. The electrically heated filament at temperature 72 is stretched down the center of a cylindrical cell containing Kr gas at 7. Gas molecules hitting the filament cool it, and to maintain its temperature a resistance heating of Q cal sec cm is needed. Derive from simple gas kinetic theory the expression... [Pg.672]

Mention was made in Section XVIII-2E of programmed desorption this technique gives specific information about both the adsorption and the desorption of specific molecular states, at least when applied to single-crystal surfaces. The kinetic theory involved is essentially that used in Section XVI-3A. It will be recalled that the adsorption rate was there taken to be simply the rate at which molecules from the gas phase would strike a site area times the fraction of unoccupied sites. If the adsorption is activated, the fraction of molecules hitting and sticking that can proceed to a chemisorbed state is given by exp(-E /RT). The adsorption rate constant of Eq. XVII-13 becomes... [Pg.705]

It turns out that there is another branch of mathematics, closely related to tire calculus of variations, although historically the two fields grew up somewhat separately, known as optimal control theory (OCT). Although the boundary between these two fields is somewhat blurred, in practice one may view optimal control theory as the application of the calculus of variations to problems with differential equation constraints. OCT is used in chemical, electrical, and aeronautical engineering where the differential equation constraints may be chemical kinetic equations, electrical circuit equations, the Navier-Stokes equations for air flow, or Newton s equations. In our case, the differential equation constraint is the TDSE in the presence of the control, which is the electric field interacting with the dipole (pemianent or transition dipole moment) of the molecule [53, 54, 55 and 56]. From the point of view of control theory, this application presents many new features relative to conventional applications perhaps most interesting mathematically is the admission of a complex state variable and a complex control conceptually, the application of control teclmiques to steer the microscopic equations of motion is both a novel and potentially very important new direction. [Pg.268]

Substances at high dilution, e.g. a gas at low pressure or a solute in dilute solution, show simple behaviour. The ideal-gas law and Henry s law for dilute solutions antedate the development of the fonualism of classical themiodynamics. Earlier sections in this article have shown how these experimental laws lead to simple dieniiodynamic equations, but these results are added to therniodynaniics they are not part of the fonualism. Simple molecular theories, even if they are not always recognized as statistical mechanics, e.g. the kinetic theory of gases , make the experimental results seem trivially obvious. [Pg.374]

Born M and Green H S 1946 A general kinetic theory of liquids I. The molecular distribution functions Proc. R. Soc. A 188 10... [Pg.551]

Born M and Green H S 1949 A General Kinetic Theory of Liquids (Cambridge Cambridge University Press)... [Pg.552]

We will almost always treat the case of a dilute gas, and almost always consider the approximation that the gas particles obey classical, Flarniltonian mechanics. The effects of quantirm properties and/or of higher densities will be briefly commented upon. A number of books have been devoted to the kinetic theory of gases. Flere we note that some... [Pg.664]

The kinetic theory of transport processes in gases rests upon three basic assumptions. [Pg.671]

Statistical mechanics and kinetic theory, as we have seen, are typically concerned with the average behaviour of an ensemble of similarly prepared systems. One usually hopes, and occasionally can demonstrate, that the variations of these properties from one system to another in the ensemble, or that the variation with time of the properties of any... [Pg.687]

Brush S 1966-1972 Kinetic Theory vols 1 -3 (New York Pergamon)... [Pg.690]

Resibois P and de keener M 1977 Ciassicai Kinetic Theory of Fiuids (New York Wiley)... [Pg.690]

Present R D 1958 Kinetic Theory of Gases (New York McGraw-Hill)... [Pg.690]

Dorfman J R and van Bei]eren H 1977 The kinetic theory of gases Statisticai Mechanics, Part B Time-Dependent Processes ed B J Berne (New York Plenum)... [Pg.690]

Cohen E G D 1993 Fifty years of kinetic theory Physica A 194 229... [Pg.691]

Ernst M FI 1998 Bogoliubov-Choh-Uhlenbeck theory cradle of modern kinetic theory Progress in Statistical Physics ed W Sung et al (Singapore World Scientific)... [Pg.691]

The current frontiers for the subject of non-equilibrium thennodynamics are rich and active. Two areas dommate interest non-linear effects and molecular bioenergetics. The linearization step used in the near equilibrium regime is inappropriate far from equilibrium. Progress with a microscopic kinetic theory [38] for non-linear fluctuation phenomena has been made. Carefiil experiments [39] confinn this theory. Non-equilibrium long range correlations play an important role in some of the light scattering effects in fluids in far from equilibrium states [38, 39]. [Pg.713]

The foundations of the modem tireory of elementary gas-phase reactions lie in the time-dependent molecular quantum dynamics and molecular scattering theory, which provides the link between time-dependent quantum dynamics and chemical kinetics (see also chapter A3.11). A brief outline of the steps hr the development is as follows [27],... [Pg.772]

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. [Pg.774]

Figure A3.4.7. Sunnnary of statistical theories of gas kinetics with emphasis on complex fomiing reactions (m the figure A.M. is the angular momentum, after Quack and Troe [27, 36, 74]). The indices refer to the following references (a) [75, 76 and 77] (b) [78] (c) [79, and M] (d) [31, 31 and M] (e) [, 31 and... Figure A3.4.7. Sunnnary of statistical theories of gas kinetics with emphasis on complex fomiing reactions (m the figure A.M. is the angular momentum, after Quack and Troe [27, 36, 74]). The indices refer to the following references (a) [75, 76 and 77] (b) [78] (c) [79, and M] (d) [31, 31 and M] (e) [, 31 and...
Although the field of gas-phase kinetics remains hill of challenges it has reached a certain degree of maturity. Many of the fiindamental concepts of kinetics, in general take a particularly clear and rigorous fonn in gas-phase kinetics. The relation between fiindamental quantum dynamical theory, empirical kinetic treatments, and experimental measurements, for example of combustion processes [72], is most clearly established in gas-phase kmetics. It is the aim of this article to review some of these most basic aspects. Details can be found in the sections on applications as well as in the literature cited. [Pg.794]

Piiiing M J and Smith i W M (eds) 1987 Modern Gas Kinetics. Theory, Experiment and Application (Qxford Biackweii) Giibert R G and Smith S C (eds) 1990 Theory of Unimolecular and Recombination Reactions (Qxford Biackweii) Fioibrook K A, Piiiing M J and Robertson S Fi (eds) 1996 Unimolecular Reactions 2nd edn (Chichester Wiiey)... [Pg.797]


See other pages where Kinetic theory 492 kinetics is mentioned: [Pg.510]    [Pg.231]    [Pg.751]    [Pg.436]    [Pg.664]    [Pg.664]    [Pg.664]    [Pg.665]    [Pg.665]    [Pg.666]    [Pg.666]    [Pg.669]    [Pg.669]    [Pg.687]    [Pg.690]    [Pg.691]    [Pg.741]    [Pg.754]    [Pg.778]    [Pg.781]    [Pg.782]   
See also in sourсe #XX -- [ Pg.660 , Pg.743 ]




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Activation energy kinetic theory

Application of Kinetic-Molecular Theory to the Gas Laws

Application of Perturbation Theory to Chemical Kinetic Systems

Assumptions of the Kinetic Theory—A Second Look

Avogadro’s law kinetic molecular theory

Basic Concepts of Kinetic Theory

Bimolecular reactions kinetic theory

Bound states in kinetic theory

Boyle’s law kinetic-molecular theory and

Chapman-Enskog kinetic theory

Charles’s law kinetic-molecular theory and

Chemical Kinetics Collision Theory

Chemical action, kinetic theory

Chemical reaction kinetics activation theory)

Chemical reaction rate theory, relaxation kinetics

Chromatography kinetic theory

Classical Theory of Homogeneous Nucleation Kinetic Approach

Coagulation kinetics, Smoluchowski theory

Collision dynamics simple kinetic theory

Collision interparticle kinetic theory modeling

Collision kinetic theory applied

Collisions, kinetic theory

Combination with kinetic theory

Constrained Brownian motion phase space kinetic theory

Conventional kinetic theory

Crystalline polymers kinetic nucleation theory

Crystallization kinetics theory

Cyclization, kinetic theory

Dalton’s law of partial pressures kinetic-molecular theory and

Diffusion kinetic theory

Dilute gas kinetic theory

Electrode-electrolyte interface, kinetic theory

Electrode-kinetics theory

Elementary Kinetic Theory of Gases

Elementary kinetic theory

Emulsion type kinetic theory

Energetic Kinetic Theory

Energy state distributions, kinetics, microscopic theories

Example Chapman-Enskog reduction of kinetic theory to fluid mechanics

Extending the Kinetic Theory of Granular Flow to Reactive Systems

Extending the Kinetic Theory to Denser Gases

Extension of Molten Polymers and Molecular-Kinetic Theories

Formulation of the Kinetic Theory

Fracture Zhurkov kinetic theory

Fracture kinetic theory

From kinetic theory

Gas Laws and Kinetic Theory

Gas Properties Relating to the Kinetic-Molecular Theory

Gas kinetic theory of transport processes

Gases and the Kinetic-Molecular Theory

Gases kinetic molecular theory

General Theory of Adsorption Kinetics

Glass transition theory kinetic theories

Glass-rubber transition kinetic theory

Granular flow kinetic theory application

Granular flow, kinetic theory

Granular kinetic theory

Homogeneous kinetic measurements theory

Homopolymers, crystallization kinetic nucleation theory

Hybridization kinetics theory

Hydrodynamic model kinetic theory

Ideal gas kinetic theory

Inclusion of a chemical reaction into kinetic theory

Kinetic Considerations Collision Theory

Kinetic Isotope Effects Continued Variational Transition State Theory and Tunneling

Kinetic Molecular Theory A Model for Gases

Kinetic Molecular Theory and the Ideal Gas Law

Kinetic Molecular Theory of matter

Kinetic Theories of Elementary Reactions

Kinetic Theory Boltzmans Equation

Kinetic Theory Expression for the Rate Kernel

Kinetic Theory of Diffusion

Kinetic Theory of Glass

Kinetic Theory of Glass Formation

Kinetic Theory of Ideal Gases

Kinetic Theory of Macroemulsion Type

Kinetic Theory of Polymers

Kinetic Theory of Swelling

Kinetic Theory of an Ideal Gas

Kinetic crystallization growth theories

Kinetic energy collision theory

Kinetic energy collision theory component

Kinetic energy release distributions theory

Kinetic energy theory

Kinetic energy transition state theory

Kinetic gas theory

Kinetic isotope effect general theory

Kinetic isotope effects theory

Kinetic modeling biochemical systems theory

Kinetic molecular theory

Kinetic molecular theory A model that

Kinetic molecular theory postulates

Kinetic molecular theory quantitative

Kinetic molecular theory quantitative model

Kinetic molecular theory real gases and

Kinetic molecular theory root mean square velocity

Kinetic nucleation theory

Kinetic parameter distribution theory

Kinetic rate constant encounter theory

Kinetic theories for radical recombination

Kinetic theory

Kinetic theory (also Chap

Kinetic theory Boltzmann equation

Kinetic theory Chapman-Enskog expansion

Kinetic theory Subject

Kinetic theory absolute Maxwellian

Kinetic theory analysis

Kinetic theory applicable formulas

Kinetic theory assumptions

Kinetic theory calculations

Kinetic theory chemistry

Kinetic theory dense fluids

Kinetic theory description

Kinetic theory dynamics

Kinetic theory effects

Kinetic theory electrode-electrolyte interface, models

Kinetic theory for granular flow

Kinetic theory high densities

Kinetic theory initial density dependence

Kinetic theory intermediate density range

Kinetic theory laboratory experiments

Kinetic theory mesoscale model

Kinetic theory modeling

Kinetic theory modeling constitutive relations

Kinetic theory modeling energy dissipation rate

Kinetic theory modeling for collision-dominated dense suspensions

Kinetic theory modeling for interparticle collisions

Kinetic theory modeling hydrodynamic equations

Kinetic theory moment method

Kinetic theory of collisions

Kinetic theory of dense gases

Kinetic theory of fracture

Kinetic theory of gases

Kinetic theory of gases and

Kinetic theory of granular flow

Kinetic theory of liquids

Kinetic theory of matter

Kinetic theory of molecules

Kinetic theory of plasma

Kinetic theory of rubber elasticity

Kinetic theory of stopping

Kinetic theory of the biochemical switch

Kinetic theory of the glass transition

Kinetic theory of transport

Kinetic theory of transport phenomena

Kinetic theory polarization correction

Kinetic theory quantum mechanical

Kinetic theory research background

Kinetic theory small particles

Kinetic theory, definition of temperature

Kinetic theory, evaporation-condensation

Kinetic theory, evaporation-condensation equilibrium

Kinetic theory, renormalized

Kinetic-molecular theory defined

Kinetic-molecular theory diffusion

Kinetic-molecular theory effusion

Kinetic-molecular theory phase changes

Kinetics Langmuir theory

Kinetics Marcus theory

Kinetics basic theory

Kinetics competing reactions, theory

Kinetics free-volume theories

Kinetics gas theory

Kinetics microscopic theories

Kinetics molecular theory

Kinetics theory

Kinetics theory

Kinetics theory of gases

Kinetics transition state theory

Kinetics, chemical transition-state theory

Kinetics, molecular collision theory

Langmuir adsorption isotherm kinetic theory

Limited Kinetics—Debye Theory

Liquid kinetic theory

Liquids molecular kinetic theory

Marcus Theory and Butler-Volmer Kinetics

Marcus kinetic theory

Marcus kinetic theory maximum rate

Marcus kinetic theory reorganization energy

Matter kinetic molecular theory

Matter kinetic theory

Maxwell-Boltzmann kinetic theory

Membrane-bound kinetics theory

Mixed potential theory kinetic approach

Mixtures kinetic molecular theory

Mode-Coupling Theory relaxation kinetics

Models kinetic molecular theory

Molecular Theories of Chemical Kinetics

Molecular dynamics simulations kinetic theory

Momentum density kinetic theory

Nonequilibrium Kinetic Theory

Particles kinetic theory

Phase space theory, reaction kinetics

Phenomenological Coefficients and Kinetic Theory

Polymeric fluids, kinetic theories

Polymerization kinetic theory

Postulates of kinetic molecular theory

Postulates of the Kinetic Molecular Theory

Potential-relaxation method kinetic theory

Pressure kinetic molecular theory

Pressure kinetic theory

Problems Connected with the Kinetic Theory of Dense Gases

Rate constant kinetic theory

Reaction Rate Theory and Kinetics

Reaction kinetics, theories

Reactive Islands Kinetic Theory

Relaxation kinetic theories

Remarks on the Kinetic Theory of Granular Flows

Renormalization fully renormalized kinetic theory

Renormalized kinetic theory, mode coupling

Rubber elasticity, kinetic theory

Simulations kinetic theory

Simulations kinetic-molecular theory

Skill 11.5 Apply kinetic theory to explain interactions of energy with matter, including conceptual questions on changes in state

Solids molecular kinetic theory

State, changes molecular kinetic theory

States of Matter with the Kinetic Molecular Theory

Statistical Kinetic Theories

Steady state hot atom kinetic theory

Steady state kinetic theory model calculations

Steady-state kinetics basic theory

Swelling Kinetic Theory of Gel Networks

Temperature Dependence of Reaction Kinetics Activation Theory

Temperature kinetic molecular theory

Temperature kinetic-molecular theory and

The Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory of Liquids and Solids

The Kinetic Molecular Theory of Matter

The Kinetic Theory of Dense Gases

The Kinetic Theory of Fracture

The Kinetic Theory of Gases

The Kinetic-Molecular Theory

The Kinetic-Molecular Theory A Model for Gas Behavior

The kinetic theory applied to chemical reactions in solutions

The kinetic theory of fluids

The kinetic theory of matter

Theories kinetic-molecular theory

Theories of reaction kinetics

Theory of Chemical Kinetics

Theory of Scavenging and Recombination Kinetics

Theory of Transient State Kinetics and Dynamics

Theory of Translocation Kinetics

Theory of chemical kinetics in bulk and on the surface

Theory of enzyme kinetics

Theory of solid state reaction kinetics

Thermal analysis kinetic theory

Thermal conductivity kinetic theory expression

Thermochemical and Kinetic Theory Calculations

Three-Fluid Model with Kinetic Theory of Granular Flow Closure

Time-dependent density functional theory kinetic energy

Tracer kinetic theory

Transient state kinetics, theory

Transition state theory kinetic rates

Transition state theory kinetic treatment

Transition state theory of kinetic

Transition state theory statistical kinetic models

Transport properties, kinetic theory

Two-Fluid Model with Kinetic Theory of Granular Flow Closures

Unimolecular reaction kinetics isomerization theory

Vacuum and the Kinetic Theory of Gases

Viscosity kinetic theory expression

Volume kinetic molecular theory

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