Arrhenius equation extensions

These methods are based on extensions of the Arrhenius equation, which we can write... 

It can be shown, through substitution of appropriate values into Eq. (5), that variations in the values of x in a series of related reactions results in compensatory behavior, subject to certain further conditions. Since the properties of Eq. (5) have been described particularly extensively in previous articles (73, 34-38), the analysis will not again be repeated here. It is worth mentioning, however, that the composite reaction does not strictly obey the Arrhenius equation, although the error present may be below the limits that can be... 

Feb. 19,1859, Wijk, Sweden - Oct. 2,1927, Stockholm, Sweden). Arrhenius developed the theory of dissociation of electrolytes in solutions that was first formulated in his Ph.D. thesis in 1884 Recherches sur la conductibilit galvanique des dectrolytes (Investigations on the galvanic conductivity of electrolytes). The novelty of this theory was based on the assumption that some molecules can be split into ions in aqueous solutions. The - conductivity of the electrolyte solutions was explained by their ionic composition. In an extension of his ionic theory of electrolytes, Arrhenius proposed definitions for acids and bases as compounds that generate hydrogen ions and hydroxyl ions upon dissociation, respectively (- acid-base theories). For the theory of electrolytes Arrhenius was awarded the Nobel Prize for Chemistry in 1903 [i, ii]. He has popularized the theory of electrolyte dissociation with his textbook on electrochemistry [iv]. Arrhenius worked in the laboratories of -> Boltzmann, L.E., -> Kohlrausch, F.W.G.,- Ostwald, F.W. [v]. See also -> Arrhenius equation. 

Rate constants for these key reactions have been studied extensively and are given in Table 1.33. Reaction (82) is of particular interest [50] because, first, flame-speed simulations are very sensitive to the rate of this reaction and secondly, the establishment of its non-linear temperature coefficient in the late 60s first raised doubts about the validity of the simple Arrhenius equation over wide temperature ranges. 

The sucrose inversion has been extensively studied from the viewpoint of electrolyte effects (Guggenheim and Wiseman, 2), the application of the Arrhenius equation to the reaction (Leininger and Kilpatrick, 3), and the catalytic effects of acid molecules (Hammett and Paul, 4). It is probable that, in aqueous solution, we are dealing with a case of specific hydrogen ion catalysis and can postulate the equilibrium (Gross, Steiner, and Suess, 5)... 

In the opinion of the authors this equation may be considered as the Arrhenius-parallel emerging at high temperatures. Noteworthy is the difference from the classical Arrhenius equation recalled in the introduction. There is an extensive evidence for the crossover from the VET- to the Arrhenius-type behavior on heating above the melting temperature. " However, the analysis of high resolution experimental data for glass forming liquids indicate also the... 

Ions are extensively used as reagents and as catalysts because they are highly reactive. In solution, ions have a strong interaction with the solvent and, as we discuss in Chapter 11, this behavior leads to essential modifications of the dynamics. Therefore, to study their intrinsic behavior we examine here ion-molecule reactions in the gas phase, continuing from the discussion in Section 3.2.6. Specifically, we consider nucleophilic displacement reactions of the type X + RY XR + Y . Such gas-phase Sn2 ion-molecule reactions proceed with reaction rate constants that vary from almost capture-controlled to so slow that they can barely be detected. Moreover, the rate constant exhibits an inverse temperature dependence, that is, the rate of nucleophilic displacement slows down with increasing temperature. This behavior is in marked contrast to the predictions of the Arrhenius equation. 

Although the protonic theory is not confined to aqueous solutions, it does not cover aprotic solvents. The solvent system theory predates that of Bronsted-Lowry and represents an extension of the Arrhenius theory to solvents other than water. It may be represented by the defining equation ... 

Au is the difference between the liquid and glassy volumetric expansion coefficients and the temperatures are in kelvin. "The WLF equation holds between I], or / f 10 K and abftut 100 K above 7A,. Above this temperature, for thermally stable polymers, Berry and Fox (28) have shown that a useful extension of the WLF equation is the addition of an Arrhenius term with a low activation energy. 

If the correlating line in Figure 4 is extrapolated to zero residence time, a value is obtained for the b parameter in the methane yield equation b = 0.0165. An extension to higher temperatures of the Arrhenius plot for b obtained by Zahradnik and Glenn shows this value... 

The main differences between Hopfield s theory and the earlier theory of Marcus are the explicit use of the spectral shape functions D E) (though this difference is removed when Gaussian functions are used), the lack of reference to a transition state, and the extension to lower temperatures where equation (16) is replaced by a non-Arrhenius form, not quoted here. Jortner, however, later argued that at low temperatures the Hopfield theory is inapplicable, since... 

The importance of polymer segmental motion in ion transport has already been referred to. Although classical Arrhenius theory remains the best approach for describing ion motion in solid electrolytes, in polymer electrolytes the typical curvature of the log a vs. 1/T plot is usually described in terms of Tg-based laws such as the Vogel-Tamman-Fulcher (VTF) [61] and Williams-Landel-Ferry (WLF) [62] equations. These approaches and other more sophisticated descriptions of ion motion in a polymer matrix have been extensively reviewed [6, 8, 63]. 

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