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Rate coefficients

This is the situation exploited by the so-called isolation method to detennine the order of the reaction with respect to each species (see chapter B2.1). It should be stressed that the rate coefficient k in (A3,4,10) depends upon the definition of the in the stoichiometric equation. It is a conventionally defined quantity to within multiplication of the stoichiometric equation by an arbitrary factor (similar to reaction enthalpy). [Pg.763]

It is clear from figure A3.4.3 that the second-order law is well followed. Flowever, in particular for recombination reactions at low pressures, a transition to a third-order rate law (second order in the recombining species and first order in some collision partner) must be considered. If the non-reactive collision partner M is present in excess and its concentration [M] is time-independent, the rate law still is pseudo-second order with an effective second-order rate coefficient proportional to [Mj. [Pg.769]

In a fourth step the cross section is related to a state-selected specific bimolecular rate coefficient... [Pg.774]

This rate coefficient can be averaged in a fifth step over a translational energy distribution P (E ) appropriate for the bulk experiment. In principle, any distribution P (E ) as applicable in tire experiment can be introduced at this point. If this distribution is a thennal Maxwell-Boltzmann distribution one obtains a partially state-selected themial rate coefficient... [Pg.774]

In a final, sixth step one may also average (sum) over a thennal (or other) quantum state distribution I (and F) and obtain the usual thennal rate coefficient... [Pg.774]

A completely analogous derivation leads to the rate coefficient for bimolecular reactions, where dare partition fiinctions per unit volume. ... [Pg.780]

The exponential fiinction of the matrix can be evaluated tln-ough the power series expansion of exp(). c is the coliinm vector whose elements are the concentrations c.. The matrix elements of the rate coefficient matrix K are the first-order rate constants W.. The system is called closed if all reactions and back reactions are included. Then K is of rank N- 1 with positive eigenvalues, of which exactly one is zero. It corresponds to the equilibrium state, witii concentrations r detennined by the principle of microscopic reversibility ... [Pg.790]

As an example we take again the Lindemaim mechanism of imimolecular reactions. The system of differential equations is given by equation (A3.4.127T equation (A3.4.128 ) and equation (A3.4.129T The rate coefficient matrix is... [Pg.790]

Quack M 1984 On the mechanism of reversible unimolecular reactions and the canonical ( high pressure ) limit of the rate coefficient at low pressures Ber. Bunsenges. Phys. Chem. 88 94-100... [Pg.794]

According to Kramers model, for flat barrier tops associated with predominantly small barriers, the transition from the low- to the high-damping regime is expected to occur in low-density fluids. This expectation is home out by an extensively studied model reaction, the photoisomerization of tran.s-stilbene and similar compounds [70, 71] involving a small energy barrier in the first excited singlet state whose decay after photoexcitation is directly related to the rate coefficient of tran.s-c/.s-photoisomerization and can be conveniently measured by ultrafast laser spectroscopic teclmiques. [Pg.820]

Ciary D C, Smith D and Adams N G 1985 Temperature dependence of rate coefficients for reactions of ions with dipolar molecules Chem. Phys. Lett. 119 320-6... [Pg.824]

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. [Pg.831]

In the sections below a brief overview of static solvent influences is given in A3.6.2, while in A3.6.3 the focus is on the effect of transport phenomena on reaction rates, i.e. diflfiision control and the influence of friction on intramolecular motion. In A3.6.4 some special topics are addressed that involve the superposition of static and transport contributions as well as some aspects of dynamic solvent effects that seem relevant to understanding the solvent influence on reaction rate coefficients observed in homologous solvent series and compressed solution. More comprehensive accounts of dynamics of condensed-phase reactions can be found in chapter A3.8. chapter A3.13. chapter B3.3. chapter C3.1. chapter C3.2 and chapter C3.5. [Pg.832]

For analysing equilibrium solvent effects on reaction rates it is connnon to use the thennodynamic fomuilation of TST and to relate observed solvent-mduced changes in the rate coefficient to variations in Gibbs free-energy differences between solvated reactant and transition states with respect to some reference state. Starting from the simple one-dimensional expression for the TST rate coefficient of a unimolecular reaction a— r... [Pg.833]

In the thennodynamic fomiiilation of TST the pressure dependence of the reaction rate coefficient defines a volume of activation [24, 25 and 26]... [Pg.840]

There is one important caveat to consider before one starts to interpret activation volumes in temis of changes of structure and solvation during the reaction the pressure dependence of the rate coefficient may also be caused by transport or dynamic effects, as solvent viscosity, diffiision coefficients and relaxation times may also change with pressure [2]. Examples will be given in subsequent sections. [Pg.841]

Instead of concentrating on the diffiisioii limit of reaction rates in liquid solution, it can be histnictive to consider die dependence of bimolecular rate coefficients of elementary chemical reactions on pressure over a wide solvent density range covering gas and liquid phase alike. Particularly amenable to such studies are atom recombination reactions whose rate coefficients can be easily hivestigated over a wide range of physical conditions from the dilute-gas phase to compressed liquid solution [3, 4]. [Pg.845]

As discussed above, one may try to represent the density dependence of atom recombhiation rate coefficients k in the spirit of equation (A3.6.24) as... [Pg.845]

If Other fall-off broadening factors arising m unimolecular rate theory can be neglected, the overall dependence of the rate coefficient on pressure or, equivalently, solvent density may be represented by the expression [1, 2]... [Pg.848]

Sometimes it may be convenient to use an even simpler interpolation fomuila that coimects the different rate coefficient limits [4]... [Pg.849]

Multidimensionality may also manifest itself in the rate coefficient as a consequence of anisotropy of the friction coefficient [M]- Weak friction transverse to the minimum energy reaction path causes a significant reduction of the effective friction and leads to a much weaker dependence of the rate constant on solvent viscosity. These conclusions based on two-dimensional models also have been shown to hold for the general multidimensional case [M, 59, and 61]. [Pg.851]

Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely... [Pg.852]

Wahnstrom G and Metiu H 1988 Numerical study of the correlation function expressions for the thermal rate coefficients in quantum systems J. Phys. Chem. JPhCh 92 3240-52... [Pg.1004]

Thachuk M and Schatz G C 1992 Time dependent methods for calculating thermal rate coefficients using flux correlation functions J. Chem. Phys. 97 7297-313... [Pg.1004]

From these equations one also finds the rate coefficient matrix for themial radiative transitions including absorption, induced and spontaneous emission in a themial radiation field following Planck s law [35] ... [Pg.1048]


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A lower bound on the rate coefficient

Absolute rate coefficients for termination

Absorption rate coefficients

Abstraction rate coefficient

Additivity of rate coefficients

An upper bound on the rate coefficient

Approximate forms of the macroscopic rate coefficient

Arrhenius plot rate coefficient data

Arrhenius rate expression, diffusion coefficient

Attachment rate coefficients

Average rate coefficient

Bimolecular rate coefficients

Burning Rate Coefficients

Butler-Volmer type rate coefficients

CLD Termination Rate Coefficients Theory Validation

Calculation of rate coefficient

Capture rate coefficients

Carpets, formaldehyde release rate coefficients

Chain cleavage rate coefficients

Chemical reaction rate coefficients

Chemical reactions, kinetics rate coefficients

Clockwise rate coefficients

Coagulation rate coefficient

Coefficient decomposition rate

Coefficient propagation rate

Coefficient termination rate

Composition-dependent rate coefficients

Copolymer averaged rate, coefficient for

Copolymer averaged rate, coefficient for propagation

Counter-clockwise rate coefficients

Cross-Sections and Rate Coefficients

Crystal-growth rate coefficient, data

Crystallization rate coefficient

Deactivation kinetics rate coefficients

Decay rate exponential coefficient

Detachment rate coefficients

Diffusion coefficient, and reaction rate

Dissolution rate coefficient

Effective rate coefficients

Einstein rate coefficients

Electron transfer rate coefficient

Energy rate coefficients

Escape-rate theory coefficients

Estimation of Rate Coefficient for Protein Adsorption

Falsification of Rate Coefficients and Activation Energies by

Film diffusion rate coefficient

First order rate coefficient

Flow rate fugacity coefficient

Formaldehyde release rate coefficient

Function Expressions for Rate Coefficients

Further estimates of the rate coefficient

General kinetic observations overall rate coefficient

Heat transfer coefficient mass flow rate

High-pressure rate coefficients

Kinetic rate coefficient

Kinetic rate coefficient , for

Kinetic relations and rate coefficients

Langevin rate coefficient

Mass transport rate coefficient

Mass-transfer coefficients, analogy with rates

Measurement of absolute rate coefficients

Microcanonical rate coefficient

Microscopic Rate coefficient

Modeling the Rate Coefficient

Nature of the Measurements Rate Coefficients and Branching Ratios or Cross Sections

Negative temperature coefficients reaction rate

Neutralisation, rate coefficient

Nucleophilic substitution rate coefficients

Parameterising Rate Coefficients

Peeling rate coefficients

Pesticide degradation rates rate coefficients

Photodissociation rate coefficients

Photolysis rate coefficient

Photolytic rate coefficient

Plasma-chemical reaction rate coefficient

Polymerization rate coefficients

Primary normal stress coefficient shear rate dependence

Properties of Rate Coefficients

Pseudo-coefficient rate

RRKM rate coefficients

Radiative rate coefficient

Radical entry rate coefficient

Rate Equations in Coefficient Form

Rate coefficient calculation

Rate coefficient cationic polymerization

Rate coefficient cyclic oxides

Rate coefficient diffusive

Rate coefficient dioxolane

Rate coefficient epoxides

Rate coefficient equivalence order

Rate coefficient flocculation

Rate coefficient for chemical reactions

Rate coefficient for desorption

Rate coefficient for water exchange

Rate coefficient hexene

Rate coefficient isoprene

Rate coefficient lactams

Rate coefficient matrix

Rate coefficient overall

Rate coefficient pseudo first-order

Rate coefficient temperature effects

Rate coefficient temperature variation

Rate coefficient tetrahydrofuran

Rate coefficient time dependent

Rate coefficient total

Rate coefficient with excited species

Rate coefficient with nitro compounds

Rate coefficient with olefins

Rate coefficient with radicals

Rate coefficient — continued

Rate coefficient, defined

Rate coefficient, definition

Rate coefficient, definitions determination

Rate coefficient, for

Rate coefficient, thermalized

Rate coefficients and constants

Rate coefficients and equilibrium constant

Rate coefficients and parameters for inhibition

Rate coefficients apparent

Rate coefficients determination

Rate coefficients for free-radical

Rate coefficients for free-radical polymerization

Rate coefficients for propagation

Rate coefficients in the intermediate fall-off range

Rate coefficients of elementary processes

Rate coefficients of elementary processes in the hydrogen—nitrogen oxide systems

Rate coefficients ratios

Rate coefficients temperature dependence

Rate constant coefficient

Rate equations exponential coefficients

Rate-determining step transfer coefficient

Reaction first-order rate coefficient

Reaction rate coefficient

Reaction rate coefficient Langevin

Reaction rate coefficient definition

Reaction rate coefficient trajectory calculation

Reaction rate constant and regression coefficient

Reaction rate, temperature coefficient

Reactions and reaction rate coefficients for the formation of water in star forming regions

Recommended rate coefficients

Second-order rate coefficient

Single event rate coefficients

Stability growth rate coefficient

State specific rate coefficients

Systematic Determination of Reaction Mechanism and Rate Coefficients

Teller Formula for VT-Relaxation Rate Coefficients

Temperature Dependence of Rate Coefficients

Temperature dependence of the rate coefficient

The Smoluchowski rate coefficient

The rate coefficient for a partially reflecting boundary condition

The rate coefficient including hydrodynamic repulsion

The rate coefficients

The steady-state density and rate coefficient

The steady-state rate coefficient

The time-dependent rate coefficient

Thermal rate coefficient

Transient experiments, rate coefficients

Uncertainty of the Rate Coefficients

Units and other forms of the reaction rate coefficient

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