Eyring parameters

Table 2.2 Calculated Values for the Evaluation of Eyring Parameters for the Data and the Theoretical Curve of Fig. 2.5...

Eyring Parameters for Add-Catalyzed Decomposition of Benzhydryl Azides and 1,1-DipbenyIethyl Azide... 

While all of the substrates discussed above are not shown in Fig. 2, the same analysis can be performed with all of them (alkynes, substituted methanes). One caveat that we encountered was that many of these substituted derivatives proved to be very stable. Loss of alkane from the n-pentyl hydride complex has a half-hfe of about an hour at 25°C. Methane loss from 3 has a half-life of about 5 h. Loss of benzene from 2, however, is extremely slow (months), and therefore, the rate of benzene reductive elimination at 25°C was determined by extrapolation from the rate at higher temperatures. The Eyring plot of hi( /T) vs. 1/T gave activation parameters for reductive elimination of benzene A// = 37.8 (1.1) kcal/mol and = 23 (3) e.u., which can be used to calculate the rate at other temperatures. As mentioned above, the substituted derivatives are much more stable. Reductive elimination of the alkynyl hydrides was examined at lOO C, as was the elimination of many of the substituted methyl derivatives. In these cases, the rate of benzene elimination was calculated from the Eyring parameters at the same temperature as that where the rate of reductive elimination was measured, so that the barriers could be directly compared as in Fig. 2. The determinatimi of AG° for all substrates allows Eq. 7 to be used to determine relative metal-carbon bond strengths for these compounds. Table 1 summarizes these data, giving A AG, AG°, and Drei(Rh-C) for all substrates. 

The method above is useful for estimating the Eyring parameters using only two data points in a test situation (hint), but for research we would want to use all the available data. In Figure 8.3, we plot the natural logarithms of the rate constants versus [ /T K) and get a very good fit to a straight line just as we did for the Arrhenius plot but here we will analyze the data in a different way (it is the same plot). 

Of the adjustable parameters in the Eyring viscosity equation, kj is the most important. In Sec. 2.4 we discussed the desirability of having some sort of natural rate compared to which rates of shear could be described as large or small. This natural standard is provided by kj. The parameter kj entered our theory as the factor which described the frequency with which molecules passed from one equilibrium position to another in a flowing liquid. At this point we will find it more convenient to talk in terms of the period of this vibration rather than its frequency. We shall use r to symbolize this period and define it as the reciprocal of kj. In addition, we shall refer to this characteristic period as the relaxation time for the polymer. As its name implies, r measures the time over which the system relieves the applied stress by the relative slippage of the molecules past one another. In summary. 

Of the various parameters introduced in the Eyring theory, only r—or j3, which is directly proportional to it-will be further considered. We shall see that the concept of relaxation time plays a central role in discussing all the deformation properties of bulk polymers and thus warrants further examination, even though we have introduced this quantity through a specific model. 

We have found an alternative to the power law, Eq. (2.14), which describes experimental data as well as the latter. In the Eyring approach, however, the curve-fitting parameters have a fundamental significance in terms of a model for the flow process at the molecular level. 

Eyring activation parameters for NaOH-catalyzed methylolation in relatively concentrated aqueous solutions... 

Some workers in this field have used Eyring s equation, relating first-order reaction rates to the activation energy d(7, whereas others have used the Arrhenius parameter E. The re.sults obtained are quite consistent with each other (ef. ref. 33) in all the substituted compounds listed above, AG is about 14 keal/mole (for the 4,7-dibromo compound an E value of 6 + 2 keal/mole has been reported, but this appears to be erroneous ). A correlation of E values with size of substituents in the 4- and 7-positions has been suggested. A/S values (derived from the Arrhenius preexponential factor) are... 

The trends of variation of the activation parameters are correlated with the solvation mechanism and dielectric behavior of the medium. Thus, AH, AG and A5 for the acidic resin-catalyzed hydrolysis of isopropyl acetate were calculated using the Wynne-Jones and Eyr-... 

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. 

Butler G., Stergiadis S., Eyre M. and Leifert C. (2006). Effect of production system and geographic location on milk quality parameters , Aspects of Applied Biology, 80, 189-193. 

Gschneidner Jr., K.A., and Calderwood, EW. (1986) Intra-rare earth binary alloys phase relationships, lattice parameters and systematics. In Handbook on the Physics and Chemistry of Rare Earths, eds. Gschneidner Jr., K.A. and Eyring, L. (North-Holland, Amsterdam), Vol. 8, p. 1. 

The idea that an activated complex or transition state controls the progress of a chemical reaction between the reactant state and the product state goes back to the study of the inversion of sucrose by S. Arrhenius, who found that the temperature dependence of the rate of reaction could be expressed as k = A exp (—AE /RT), a form now referred to as the Arrhenius equation. In the Arrhenius equation k is the forward rate constant, AE is an energy parameter, and A is a constant specific to the particular reaction under study. Arrhenius postulated thermal equilibrium between inert and active molecules and reasoned that only active molecules (i.e. those of energy Eo + AE ) could react. For the full development of the theory which is only sketched here, the reader is referred to the classic work by Glasstone, Laidler and Eyring cited at the end of this chapter. It was Eyring who carried out many of the... 

The Marcus classical free energy of activation is AG , the adiabatic preexponential factor A may be taken from Eyring s Transition State Theory as (kg T /h), and Kel is a dimensionless transmission coefficient (0 < k l < 1) which includes the entire efiFect of electronic interactions between the donor and acceptor, and which becomes crucial at long range. With Kel set to unity the rate expression has only nuclear factors and in particular the inner sphere and outer sphere reorganization energies mentioned in the introduction are dominant parameters controlling AG and hence the rate. It is assumed here that the rate constant may be taken as a unimolecular rate constant, and if needed the associated bimolecular rate constant may be constructed by incorporation of diffusional processes as ... 

Table 1 Arrhenius and Eyring activation parameters for the reductive elimination of halogens from chalcogenopyrylium dyes containing tellurium(IV) dihalide groups...

Table 2 Arrhenius and Eyring activation parameters for the second, Slow reaction observed by stopped-flow spectroscopy in the oxidative addition of halogens to diorgano tellurides 17, 20, and 23-25...

The second, slow reaction was followed for 17 and 23-25 in several solvents at several different reaction temperatures. Arrhenius and Eyring activation parameters for the second, slow reaction observed in the addition of iodine to 17 and 23-25 along with those for the addition of bromine to compound 20 are compiled in Table 2. In the examples of Table 2, the rate of reaction increases as the polarity of the solvent increases from CCI4 to EtOAc to CH3CN. The slow reaction remains first-order in all three solvents. For di-4-methoxyphenyltelluride (24), values of and A// in CH3CN are 20-40 kJ moP lower than in CCI4 or EtOAc. Again, the data from the kinetics studies are consistent with the formation of an ionic intermediate via a dissociative process. 

The reductive elimination reactions of halogen from 6-11 illustrate several examples of ligand loss from trigonal bipyramidal species B to generate onium species A. Activation parameters in these processes were of 73 to 100 kJ mol and Eyring activation parameters of 70-97 kJ molfor and —4 to... 

Table 3 Arrhenius and Eyring activation parameters for the debrominations of 2,3-dibromo-2-methylpentane (27) and 1,2-dibromodecane (29) with di-n-hexyltelluride (26) and tetra-n-butylammonium iodide...

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