Second-order chemical reaction

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. 

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 ... 

Example 3.3 Chemical Reaction Rate Constants Expressed in Terms of Mixing Ratios In the cgs unit system the rate constant k for a second-order chemical reaction,... 

Let Ze be the maximum time over which an eddy maintains its integrity, that is, so that Ze > Zj for nearly all eddies. Also, let r, be a characteristic timescale for the second-order chemical reaction. 

Notice that the rate law becomes dimensionless via division by 2 (Ca, surface), which is exactly the same as the dimensional scaling factor for irreversible second-order chemical reaction in the numerator of the intrapellet Damkohler... 

One-Dimensional Diffusion and Either Zeroth-, First-, or Second-Order Chemical Reaction in Catalytic Pellets with Rectangular, Cylindrical, or Spherical Geometry... 

The sequence of equations presented below is required to solve the isothermal gas-liquid CSTR problem for the chlorination of benzene in the liquid phase at 55°C. After some simplifying assumptions, the problem reduces to the solution of nine equations with nine unknowns. Some of the equations are nonlinear because the chemical kinetics are second-order in the liquid phase and involve the molar densities of the two reactants, benzene and chlorine. The problem is solved in dimensionless form with the aid of five time constant ratios that are generated by six mass transfer rate processes (1) convective mass transfer through the reactor, (2) molecular transport in the liquid phase across the gas-liquid interface for each of the four components, and (3) second-order chemical reaction in the liquid phase. 

Some typical results obtained for reserpine, methyl testosterone, and prednisolone with dry ACN and DMF will be given here, including composite and single tablet assays. Reserpine and methyl testosterone may be considered as representative of nearly ideal systems for analysis. Prednisolone in dry DMF and ACN shows clear evidence for a follow-up second order chemical reaction, making it a nonideal system. 

Figure 33 depicts a prednisolone calibration curve in dry ACN. The nonlinearity of this profile is obvious. Because there is absolutely no indication of adsorption effects, we hypothesize that there is a following second order chemical reaction. Hydrocortisone gives similar behavior in dry aprotic solvents. Both of these steroids are characterized by an aliphatic alcohol groip which is not associated with the other three ideally behaving steroids. This circumstantial evidence suggests that the anion radical electrode reaction product is being protonated by reactant diffusing toward the electrode. The likelihood that this is the process occurring is further enhanced by the fact that addition of sufficient amounts of a weak proton donor (e.g., H2O) leads to a linear calibration curve with lower sensitivity, as shown in Figure 34. The latter figure illustrates calibration curves for dry and wet ACN and DMF, as well as aqueous base.

This iteration method is fundamentally different from all other methods discussed in Chapter 7. It basically produces iterated solutions that are valid over the whole domain of interest. As the iteration increases, the iterated solution is (hc fully) getting closer to the exact solution. This method is known as the Picard method. The fundamental disadvantage of this technique, which mitigates its usefiilness, is that the iterated solutions must be found analytically, so that they can be applied to subsequent iteration steps (which involves the evaluation of an integral), (a) Show that the modeling of a second order chemical reaction in a fixed bed reactor would give rise to the following differential... 

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