Inverse Arrhenius

Experiments were also performed at various temperatures in the presence of DPPH. Although the data fitted the conventional Arrhenius relationship (Eq. 5.39), it gave an activation energy which was negative i. e. inverse Arrhenius behaviour. 

Driscoll [67], Lorimer and Mason [79] and Price [65[ have also obtained inverse Arrhenius temperature dependencies for reactions performed in the presence of ultrasound. For example Driscoll has investigated the polymerisation of styrene and methyl methacrylate in the presence of their respective homopolymers and observed that the lower the reaction temperature the faster was the reaction rate and the higher the final polymer yield (Figs. 5.38 and 5.39). Price on the other hand using a non polymer system has sonicated methyl butyrate (MeOBu) and compared the rates of radical production in the absence and presence of the initiator azobisisobutyronitrile (AIBN) (Tab. 5.18). 

The primary KIEs on kcat also indicated a transition at 30 °C, below which the primary kn/ko ratio is very temperature dependent, extrapolating to Ah/Ad 1 [24]. This inverse Arrhenius prefactor ratio is predicted within the Bell tunnel correction for a moderate extent of tunneling, and is consistent with an elevated a-secondary RS exponent. Above 30 °C, the primary kn/ko ratio is nearly independent of temperature, resulting in an isotope effect on the prefactor of Ah /Ad = 2 [24]. A tunnel correction would also predict such an elevated Arrhenius prefactors ratio when both H and D react almost exclusively by turmeling however this condition requires a very small activation energy for k at, while a value of = 14 kcal mol is observed [24]. 

In all cases, the temperature dependence of R follows the inverse Arrhenius law with the linear in T pre-exponential factor (Zhu et al., 2005 Huang et al., 2000)... 

Arrhenius S 1889 Uber die Reaktionsgeschwindigkeit bei der inversion von Rohrzucker durch Sauren Z. Physik. Chem. 4 226-48... 

The non-Arrhenius behavior of the inversion rate constant has been detected by [Deycard et al. 1988] for the oxyranyl radical,... 

Figure 6-1. Arrhenius plot for (he chair-chair ring inversion of cyclohexane. ...

The temperature dependence of a reaction rate lies in the rate constant and, as we shall see in Section 13.12, that temperature dependence gives valuable insight into the origins of rate constants. In the late nineteenth century, the Swedish chemist Svante Arrhenius found that the plot of the logarithm of the rate constant (In k) against the inverse of the absolute temperature (1 IT) is a straight line. In other words,... 

The measured [ OH]/[ OH] branching ratio versus inverse temperature is plotted in Fig. 4. If the two species are produced by two parallel pathways, the total reaction rate is a simple sum of the two pathway-resolved rates. In this case, the data points in an Arrhenius plot should fall on a straight line with a slope proportional to the difference in activation energies for the two competing pathways. A fit to the data in Fig. 4 yields the result that the barrier to O atom abstraction is 1.0 0.4kcal mol larger than for H atom abstraction. Although... 

The parameter values were then plotted versus the inverse temperature and were found to follow an Arrhenius type relationship... 

Figure 10.2 Arrhenius plot of the natural logarithm of the relaxation time extracted from the ac susceptibility data as a function of the inverse temperature for 1 at different external fields as indicated. (Reprinted from Ref. [6]. Copyright (2009) American Chemical Society.)...

Figure 13. Arrhenius plots and activation energy E for the initial maximum or plateau rate of heat release, versus the inverse absolute temperature. All data refer to high density boards. The hardboard line represents a mean for the commercial Masonite and Asplund hardboards of Figure 14, with a caliper varying between 2.2 and 6 mm. (Reproduced with permission from ref. 10. Copyright 1989 De Gruyter.)...

Fig. 3 An Arrhenius plot of the logarithm of the spin-state relaxation rate observed in [Fe(HB(pz)3)2] versus the inverse temperature. Data obtained from Fig. 9 of [30]... 

Catalysis by itself is an older discipline than chemical reaction engineering. It was formally initiated by Berzelius [5], who first used this term in 1836. In 1889, Arrhenius [6] laid the foundation of the modem development of the theory of reaction rates by showing that the specific rate of the reaction grows exponentially with inverse temperature. However, it was only in the first decade of... 

The effect of monomer concentration on the dependence of the DP on temperature. Further studies [12,52, 62] of the temperature dependence of the DP showed that the Arrhenius plot was approximately linear over the temperature range -5° to -78° for all concentrations of isobutene from about half-molar to undiluted monomer, and that the slope of the line increased with decreasing concentration in such a way that all the lines crossed at approximately the same temperature, -50°. This means that at -50°, the inversion temperature , the DP is independent of monomer concentration at lower temperatures it decreases, at higher temperatures it increases with increasing monomer concentration. This behaviour was found for polymerisation in methyl, ethyl and vinyl chloride as solvents. 

Arrhenius s formulation is based on a prior idea and equation of van t Hoff in the Etudes de dynamique chimique (Amsterdam Frederik Muller, 1884). See Arrhenius, "Ueber die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Sauren," ZPC 4 (1889) 226248, partially translated in M. H. Back and K. J. Laidler, eds., Selected Readings, 3135 also see Laidler, "Chemical Kinetics," 4275, on 5557. 

Fig. 4.10 Critical current density JPS of (100) oriented silicon electrodes for different HF concentrations plotted versus the inverse absolute temperature 1/71 Arrhenius-type behavior, with an activation energy of 0.345 eV, is observed.

Quantitative measurements of simple and enzyme-catalyzed reaction rates were under way by the 1850s. In that year Wilhelmy derived first order equations for acid-catalyzed hydrolysis of sucrose which he could follow by the inversion of rotation of plane polarized light. Berthellot (1862) derived second-order equations for the rates of ester formation and, shortly after, Harcourt observed that rates of reaction doubled for each 10 °C rise in temperature. Guldberg and Waage (1864-67) demonstrated that the equilibrium of the reaction was affected by the concentration ) of the reacting substance(s). By 1877 Arrhenius had derived the definition of the equilbrium constant for a reaction from the rate constants of the forward and backward reactions. Ostwald in 1884 showed that sucrose and ester hydrolyses were affected by H+ concentration (pH). 

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... 

Using the same experimental approach, a family of enantiomerically pure oxonium ions, i.e., O-protonated 1-aryl-l-methoxyethanes (aryl = 4-methylphenyl ((5 )-49) 4-chlorophenyl ((5)-50) 3-(a,a,a-trifluoromethyl)phenyl ((5)-51) 4-(a,a,a-trifluoromethyl)phenyl ((S)-52) 1,2,3,4,5- pentafluorophenyl ((/f)-53)) and 1-phenyl-l-methoxy-2,2,2-trifluoroethane ((l )-54), has been generated in the gas phase by (CH3)2Cl -methylation of the corresponding l-arylethanols. ° Some information on their reaction dynamics was obtained from a detailed kinetic study of their inversion of configuration and dissociation. Figs. 23 and 24 report respectively the Arrhenius plots of and fc iss for all the selected alcohols, together with (/f)-40) of Scheme 23. The relevant linear curves obey the equations reported in Tables 23 and 24, respectively. The corresponding activation parameters were calculated from the transition-state theory. 

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