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Concept# Arrhenius equation

Summary

In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that the van 't Hoff equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and reverse reactions. This equation has a vast and important application in determining the rate of chemical reactions and for calculation of energy of activation. Arrhenius provided a physical justification and interpretation for the formula. Currently, it is best seen as an empirical relationship. It can be used to model the temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes/reactions. The Eyring equation, developed in 1935, also expresses the relationship between rate and energy.
Equation
The Arrheniu

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This article is part of the project to model the kinetics of high-temperature combustions, occurring behind shock waves and in detonation waves. The "conventional" semi-empirical correlations of ignition delays have been reformulated, by keeping the Arrhenius equation form. It is shown how it polynomial with 3(N) Coefficients (where N is an element of [1, 4] is the number of adjustable kinetic parameters, likely to be simultaneously chosen among the temperature T, the pressure P, the inert fraction X-Ar, and the equivalence ratio Phi) can reproduce the delays predicted by the Curran et al. [H.J. Curran, P. Gaffuri, W.J. Pitz. C.K. Westbrook, Combust. Flame 129 (2002) 253-280] detailed mechanism (565 species and 22538 reactions), over it wide range of conditions (comparable with the validity domain). The deviations between the simulated times and their fits (typically 1%) are definitely lower than the Uncertainties related to the mechanism (at least 25%). In addition. using, this new formalism to evaluate these durations is about 10(6) times faster than simulating them With SENKIN (CHEMKIN III package) and only 10 times slower than using the classical correlations. The adaptation of the traditional method for predicting delays is interesting, for modeling. because those performances are difficult to obtain simultaneously with Other reduction methods (either purely mathematical, chemical, or even mixed). After a physical and mathematical justification of the proposed formalism, some of its potentialities for n-heptane combustion are presented. In particular, the trends of simulated delays and activation energies are shown for T is an element of [1500 K, 1900 K], P is an element of [10 kPa, 1 MPa] X-Ar is an element of [0, 0, 7], and Phi is an element of [0.25, 4.0]. (C) 2008 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

2008Paul Joseph Dyson, Kishore Kondamudi

Novel and environmentally benign Bronsted acidic ionic liqs. with SO3-H functionality were prepd. using N-methylimidazole, pyridine, triethylamine and 1,4-butanesultone as the source chems. The prepd. ionic liq. catalysts were characterized by NMR and their catalytic activity in tert-butylation of p-cresol with tert-Bu alc. was investigated. The effects of reaction time, reaction temp., reactant mole ratio and the recyclability of the catalysts on the conversion of p-cresol and selectivity to 2-tert-butyl-p-cresol and 2,6-di-tert-butyl-p-cresol called butylated hydroxytoluene (BHT) were investigated. Lower alc. to p-cresol mole ratios, lower ionic liq. to p-cresol ratio and temps. as low as 70°C gave 80% conversion of p-cresol. The catalyst activity was found to be almost completely retained even after 5 recycles. The extended Arrhenius equation was used to calc. the rate consts. for this reaction.

Carrier kinetics in the density range of N = 10(17) - 10(20) cm(-3) is investigated inside the bulk of crystalline silicon. Most conventional experimental techniques used to study carrier mobility are indirect and lack sensitivity because of charging effects and recombination on the surface. An all optical technique is used to overcome these obstacles. By focusing 1.3-mu m femtosecond laser pulses in the volume, we inject an initial free-carrier population by two-photon absorption. Then, we use pump-and-probe infrared microscopy as a tool to obtain simultaneous measurements of the carrier diffusion and recombination dynamics in a microscale region deep inside the material. The rate equation model is used to simulate our experimental results. We report a constant ambipolar diffusion coefficient D-a of 2.5 cm(2) s(-1) and an effective carrier lifetime tau(eff) of 2.5 ns at room temperature. A discussion on our findings at these high-injection levels is presented. (C) 2016 AIP Publishing LLC.

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