Eyring equations

Combining equation (A3,4,95). equation (A3,4,96) and equation (A3.4.97) one obtains the first Eyring equation for iinimolecular rate constants ... 

In a fiormal analogy to the expressions for the thenuodynamical quantities one can now defiine the standard enthalpy // and entropy ofiactivation. This leads to the second Eyring equation. ... 

This guarded assessment does not mean that the effort involved in deriving the Eyring equation was wasted-far from it. Several points might be noted ... 

The effect of temperature on diffusivities in zeolite ciystals can be expressed in terms of the Eyring equation (see Ruthven, gen. refs.). 

The free enthalpy of activation, aG, of the ring inversion at 253 K is calculated from the logarithmic form of the Eyring equation ... 

The values of the apparent rate constants kj for each temperature and the activation enthalpies calculated using the Eyring equation (ref. 21) are summarized in Table 10. However, these values of activation enthalpies are only approximative ones because of the applied simplification and the great range of experimental errors. Activation entropies were not calculated in the lack of absolute rate constants. Presuming the likely first order with respect to 3-bromoflavanones, as well, approximative activation entropies would be between -24 and -30 e.u. for la -> Ih reaction, between -40 and - 45 e.u. for the Ih la reaction and between -33 and -38 e.u. for the elimination step. These activation parameters are in accordance with the mechanisms proposed above. 

Values of AH and A of Eyring Equation for Blends Modified with the Interfacial Agents K1 and K2... 

Various statistical treatments of reaction kinetics provide a physical picture for the underlying molecular basis for Arrhenius temperature dependence. One of the most common approaches is Eyring transition state theory, which postulates a thermal equilibrium between reactants and the transition state. Applying statistical mechanical methods to this equilibrium and to the inherent rate of activated molecules transiting the barrier leads to the Eyring equation (Eq. 10.3), where k is the Boltzmann constant, h is the Planck s constant, and AG is the relative free energy of the transition state [note Eq. (10.3) ignores a transmission factor, which is normally 1, in the preexponential term]. 

According to the Eyring equation [In P= — AAH RT + AAS R, where P -A (major diol)/ /c(minor diol)], an asymmetric reaction proceeding through a pair of diastereomeric transition states shows a linear temperature effect on the enantioselectivity. However, if the asymmetric... 

The Arrhenius theory (above) was wholly empirical in terms of it derivation. A more rigorous, but related, form of the theory is that of Eyring (also called the theory of absolute reaction rates). The Eyring equation is... 

It is extremely common, but wrong, to see the Eyring equation written in a similar form, with the Arrhenius ordinate of ln(fc) (as y ) and the final logarithmic term written as In(fcBr -t-fi). Although such an equation might be readily achieved from the brief derivation in Justification Box 8.6, it is seen straightaway to be nonsensical, for the following three reasons ... 

We will employ the form of the Eyring equation written as Equation (8.56). 

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Experimental values.b Calculated from the Eyring equation. 

It is important to remember that the Marcus model refers to a weakly electronically coupled model, as embodied in the term outer-sphere ET. Thus it must be assumed that the electronic overlap between the two reactants is so small that no quantum-chemical effects ensue, yet that there must be enough overlap for the transmission coefficient k of the Eyring equation to be equal to 1 (the reaction must be adiabatic). Usually, this minimum overlap requirement is put at a fairly low level, around 0.1 kcal mol-1, which causes no problems for most reactions involving at least one organic species. 

In simple chemical kinetics, the rate of a reaction is a simple function of temperature increasing the temperature T causes an exponential increase in the rate constant k, as described within the Arrhenius and Eyring equations. 

Eyring equation physchem An equation, based on statistical mechanics, which gives the specific reaction rate for a chemical reaction in terms of the heat of activation, entropy of activation, the temperature, and various constants. T-rir i,kwa-zhon ... 

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