Second-order chemical

Slesser and Highet (S15) have proposed a theoretical model for the case of a second-order chemical reaction taking place in a slurry reactor. This model is based on concepts very similar to those employed by Sherwood and Farkas, apart from the obvious complications resulting when one treats a second-order reaction. 

Heeb, T. G. and R. S. Brodkey (1990). Turbulent mixing with multiple second-order chemical reactions. AlChE Journal 36, 1457-1470. 

Lee, J. (1966). Isotropic turbulent mixing under a second-order chemical reaction. 

Mao, K. W. and H. L. Toor (1971). Second-order chemical reactions with turbulent mixing. Industrial and Engineering Chemistry Fundamentals 10, 192-197. 

In the special case of ion exchange and unfavorable equilibrium, i.e. aA B < 1, with A originally in the solution, under the condition of sufficiently long bed, Walter s solution could be used. Walter s equation is a special case of the Thomas model for arbitrary isotherm and the kinetic law equivalent to a reversible second-order chemical reaction (Helfferich, 1962) ... 

What is the physical meaning of the rate constant of a chemical reaction What is the dimension of the rate constant of a first-(second-) order chemical reaction How does the rate constant depend on the temperature Write the Arrhenius equation. What is called the activation energy What substances are called catalysts and inhibitors ... 

These equations are similar to those of first- and second-order chemical reactions, I being a photon concentration. This applies only to isotropic radiation. The coefficients A and B are known as the Einstein coefficients for spontaneous emission and for absorption and stimulated emission, respectively. These coefficients play the roles of rate constants in the similar equations of chemical kinetics and they give the transition probabilities. 

The titanium-sapphire wavelength itself is too short for vibrational excitation in most molecules, and too long for electronic excitation. However, these high peak powers permit efficient frequency conversion. For example, certain crystals can convert two photons with frequency co into a single photon with frequency 2co. In many ways this can be viewed as similar to a second-order chemical reaction, such as the dimerization of NO2 to form N2O4. The rate of that reaction is proportional to the square of the NO2 concentration the rate of this frequency doubling is proportional to the square of the photon concentration (the intensity), so high powers are very useful. It is also possible to combine two photons with different frequencies co and o>i in either sum-... 

Compartmentalization allows the concentration of molecules so that the rates of second-order chemical reactions can be increased over what could be achieved in, for example, a bulk ocean. Modem cells concentrate molecules in the cytoplasm to an amazing level the concentrations of many metabolites are in the high micromolar or even millimolar range. 

Rate laws of the type which describe bimolecular second order chemical reactions might be expected to be a model for ion exchange reactions, and indeed this was the case for exchangers of both natural and synthetic origin. For example, the rate of ion exchange could be described by a bimolecular second order rate equation for irreversible reaction of the form ... 

Reactions that take place consecutive to the electrode process can be studied polarographioally only in those cases in which the electrode process is reversible. In these cases the wave-heights and the wave-shape remain unaffected by the chemical processes. However, the half-wave potentials are shifted relative to the equilibrium oxidation-reduction potential, determined e.g. potentiometrically. Hence, whereas in all above examples, limiting currents were measured to determine the rate constant, it is the shifts of half-wave potentials which are measured here. First- and second-order chemical reactions will be discussed in the following. 

Muonium has been observed in pure hydrocarbons ( ), alcohols (, 7 ), and water ( ). Because Mu reacts slowly with these pure liquids, giving observable reaction lifetimes of Mu up to 4us, they can be used as solvents to study various solutes of interest. As the free triplet Mu atom reacts with the solute its observed precession frequency is damped and a decay constant, X can be obtained. The concentration dependence of the decay constant provides second order chemical rate constants for Mu addition, abstraction, spin conversion, and oxidation-reduction reactions. When analogous hydrogen atom rate constants are available the kinetic isotope effect can also be calculated. 

In the EC2i process, an initial electron transfer step is followed by a second-order irreversible chemical reaction (typically a dimerization process, as considered in the practical examples in Sec. III.B). The use of SECM to characterize the kinetics of the second-order chemical reactions is based on the same principles as for the EQ case, discussed in Sec. II, with a generator electrode employed to electrogenerate the species of interest [B, see Eq. (1)], which is collected at a second electrode. The second-order process involving the consumption of B to form electroinactive products occurs in the gap between the two electrodes ... 

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