Energy rate coefficients

The Energy Rate Coefficients / Xk and Axk- Pxk, a rate coefficient analogous to aXK but specifying the rate of absorption of electron energy in effecting any particular Reaction, Rl, is given by... 

E. T. Denisov and T. Denisova, Handbook of antioxidants Bond dissociation energies, rate coefficients, activation energies, and enthalpies of reactions, CRC Press, Boca Raton, 2nd ed., 2000... 

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... 

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. 

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... 

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]. 

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... 

The master equation treatment of energy transfer in even fairly complex reaction systems is now well established and fairly standard [ ]. However, the rate coefficients kjj or the individual energy transfer processes must be established and we shall discuss some aspects of this matter in tire following section. 

The amount of energy lost in unit time, the energy-loss frequency, is Vgg = kpN (t). The energy-loss rate coefficient for two-temperature Maxwellian distributions is... 

The probability for a particular electron collision process to occur is expressed in tenns of the corresponding electron-impact cross section n which is a function of the energy of the colliding electron. All inelastic electron collision processes have a minimum energy (tlireshold) below which the process cannot occur for reasons of energy conservation. In plasmas, the electrons are not mono-energetic, but have an energy or velocity distribution,/(v). In those cases, it is often convenient to define a rate coefficient /cfor each two-body collision process ... 

In summary, the so-called Einstein A and B rate coefficients connecting a lower-energy initial state i and a final state f are related by the following conditions ... 

Benson [499] and Livingstone [500] considered the influence of experimental accuracy on measured rate and temperature coefficients. To measure the rate coefficient to 0.1%, the relative errors in each ctj value must be <0.1% and the reaction interval should be at least 50%. Temperature control to achieve this level of precision must be 0.003% or 0.01 K at 300 K. For temperature control to 1 K, the minimum error in the rate coefficient is 5% and in the activation energy, measured over a 20 K interval, is 10%. No allowance is included in these calculations for additional factors such as self-heating or cooling. 

The vast majority of the kinetic detail is presented in tabular form. Amassing of data in this way has revealed a number of errors, to which attention is drawn, and also demonstrated the need for the expression of the rate data in common units. Accordingly, all units of rate coefficients in this section have been converted to mole.l-1.sec-1 for zeroth-order coefficients (k0), sec-1 for first-order coefficients (kt), l.mole-1.sec-1 for second-order coefficients (k2), l2.mole-2.sec-1 for third-order coefficients (fc3), etc., and consequently no further reference to units is made. Likewise, energies and enthalpies of activation are all in kcal. mole-1, and entropies of activation are in cal.deg-1mole-1. Where these latter parameters have been obtained over a temperature range which precludes the accuracy favoured by the authors, attention has been drawn to this and also to a few papers, mainly early ones, in which the units of the rate coefficients (and even the reaction orders) cannot be ascertained. In cases where a number of measurements have been made under the same conditions by the same workers, the average values of the observed rate coefficients are quoted. In many reactions much of the kinetic data has been obtained under competitive conditions such that rate coefficients are not available in these cases the relative reactivities (usually relative to benzene) are quoted. 

RATE COEFFICIENTS (INITIAL) AND ACTIVATION ENERGIES FOR REACTION OF H2S04... 

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