Polanyi relationships

Polanyi relationships also represent another useful method for the estimation of activation energies in metathesis reactions (Laidler, 1987). These methods rely on the assumption that activation energies are linearly related to the heats of reaction ... 

Semenov s empirical formulation represents a special case of a Polanyi relationship in which the activation energy for an exothermic hydrocarbon metathesis reaction is given by (Semenov, 1958)... 

Br0nsted-Evans-Polanyi relationships in heterogeneous catalysis... 

Apparently, these results implied an inverse relationship between reactivity and selectivity, with the reactivity of the carbocation measured by the inverse of the rate constant for solvolysis. This indeed was not unexpected in the context of a general perception that highly reactive reagents, especially reactive intermediates such as carbocations, carbanions, or carbenes are unselective in their reactions.257 259 Such a relationship is consistent with a natural inference from the Hammond postulate258 and Bell-Evans-Polanyi relationship,260 and is illustrated experimentally by the dependence of the Bronsted exponent for base catalysis of the enolization of ketones upon the reactivity of the ketone,261,262 and other examples21,263 including Richard s careful study of the hydration of a-methoxystyrenes.229... 

The thermolyses presented in this chapter are one example of a series of analogous reactions. The Bell-Evans-Polanyi relationship of Equation 1.3 also holds for many other series of analogous reactions. The general principle that can be extracted from Equation 1.3 is that, at least for a reaction series, the more exothermic the enthalpy of reaction, the faster it will be. But this doesn t mean that all reactions that are exothermic are fast, so be careful. 

The rate constant of HAT from 1 has been determined as (3.4 1.0) x 104 M-1 s-1 at 28 °C by using a cyclobutyl carbinyl radical as clock. Also, the log A term of the Arrhenius equation is normal for a second-order HAT and thus the entropic demand of the NHC boranes is similar to that of group 14 metal hydrides. From the rate constant a BDE of about 88 kcal mol 1 for 2 was estimated by applying an Evans-Polanyi relationship. This value is somewhat higher than the calculated value of 80 kcal mol-1. 

The thermolyses presented in this chapter are one example of a series of analogous reactions. The Bell-Evans-Polanyi relationship of Equation 1.3 also holds for many other series of analogous reactions. 

Ot Values" Derived from the Polanyi Relationship for various radicals... 

The most widely used correlation of this type is the Evans-Polanyi relationship... 

The Bell-Evans-Polanyi relationship, Hammond s postulate, and the Marcus equation are all approaches to analyzing, understanding, and predicting relationships between the thermodynamics and kinetics of a series of closely related reactions. This is an important issue in organic chemistry, where series of reactions differing only in peripheral substituents are common. Each of these approaches provides a sound basis for the intuitive expectation that substituents that favor a reaction in a thermodynamic... 

The Bell-Evans-Polanyi relationship and the Hammond postulate (see Section 3.3) provide a basic framework within which to discuss structure-reactivity relationships. The Bell-Evans-Polanyi equation implies that there will be a linear relationship between and the C-H BDE. 

Fig. 11.20. Quadratic Evans-Polanyi relationship In/ (298) =—1.368 X 10- - 0354AH, - 50.96 (a) CHjF, (b) CH3CI (c)CH3Br,...

Figure 16. Summary plot of activation parameters (enthalpy of activation, AH entropy of activation, AS ) for oxygen isotope exehange in siUeates reacted with either pure water or salt solntions. The Eyring-Polanyi relationship (Eqn. 102) was nsed with data described by Cole et al. (1983), Cole and Ohmoto (1986), Cole et al. (1987, 1992), and in Table 2 (see Appendix). Note that data falling on a hnear trend generally indieate that a conunon leaetion meehanism predominates, ab = albite, san = sanidine, eels = celsian, qtz = qnartz, mnsc = muscovite, bio = biotite, chi = chlorite, parag = paragonite, woll = wollastonite, diop = diopside, gran = granite, bas = basalt.

Figure 10.29 Schematic illustration of Brensted-Evans-Polanyi relationship between activation energy change and reaction energy (Ereact) change, proportionality constant...

The addition reactions shown in Table 2 have small barriers that correlate roughly with the stability of the produced alkyl radical. Such correlations are more obvious for other types of reactions, e.g., abstraction reactions. They are known as linear free-energy relationships (LFER), and the most prominent correlation is the Evans-Polanyi relationship... 

The latter takes a value between 0, corresponding to an early transition state and 1, corresponding to a late transition state. Typically reported values are around 0.5. Note that the Evans-Polanyi relationship as formulated in equation 87 holds for exothermic reactions. In the case of an endothermic reaction, the relationship becomes ... 

Transfer coefficient in Polanyi relationship Real values of the model parameter Curvature of internal catalyst temperature profile Effectiveness factor... 

Activation energy Br0nsted-Evans-Polanyi relationships ... 

In this section, we move from the elucidation of molecular and atomic adsorption to the fundamental features that control smface reactivity. We start by initially describing dissociative adsorption processes. We focus on elucidating surface chemistry as well as the understanding of how the metal substrate influences the intrinsic surface reactivity. We will also pay attention to geometric ensemble-size related requirements. The Brpnsted-Evans Polanyi relationship between transition-state energy and reaction energy discussed in Chapter 2 is particularly useful in understanding differences in reactivity between different metal surfaces. 

One can then assume a Brpnsted-Evans-Polanyi relationship to relate the dependence of rate constant fc i to the overpotential E ... 

Diatomic molecules adsorbed to transition-metal surfaces dissociate through tight transition states. A general Brpnsted-Evans-Polanyi relationship can then be defined which is valid for nearly all diatomic molecules that dissociate along a similar reaction path ... 

Other methods for calculating the activation energies of the ORR have been reported in the literature. Based on the linear Bronsted-Evans-Polanyi relationship, Norskov et al. [85] proposed a method to estimate the least activation energy by calculating the stability of the reaction intermediate. With this simple model, the study reported a Tafel slope of 60 mV at 300 K (71 mV at 357 K). The value was consistent with experimental results. 

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