Homogeneous reaction defined

In order to exemplify the potential of micro-channel reactors for thermal control, consider the oxidation of citraconic anhydride, which, for a specific catalyst material, has a pseudo-homogeneous reaction rate of 1.62 s at a temperature of 300 °C, corresponding to a reaction time-scale of 0.61 s. In a micro channel of 300 pm diameter filled with a mixture composed of N2/02/anhydride (79.9 20 0.1), the characteristic time-scale for heat exchange is 1.4 lO" s. In spite of an adiabatic temperature rise of 60 K related to such a reaction, the temperature increases by less than 0.5 K in the micro channel. Examples such as this show that micro reactors allow one to define temperature conditions very precisely due to fast removal and, in the case of endothermic reactions, addition of heat. On the one hand, this results in an increase in process safety, as discussed above. On the other hand, it allows a better definition of reaction conditions than with macroscopic equipment, thus allowing for a higher selectivity in chemical processes. 

It may be recalled that in homogeneous reactions all reacting materials are found within a single phase, be it gas, liquid or solid if the reaction is catalytic, then the catalyst must also be present within the phase. Thus, there are a number of means of defining the rate of a reaction the intensive measure based on unit volume of the reacting volume (V) is used practically exclusively for homogeneous systems. The rate of reaction of any component i is defined as... 

In homogeneous reactions, the upper limits of concentration are determined by the (limited) solubility of the salts of periodic acid and by the low pH values produced by periodic acid itself. Apart from these considerations, the concentration conditions to be selected are governed by the type of information desired. A very dilute solution having a high oxidant substrate ratio is used in the exploratory or preliminary phase defined earlier (see p. 13), but a more concentrated solution, in which the oxidant is only slightly in excess of the theoretical, is recommended for the preparative phase. 

Central to catalysis is the notion of the catalytic site. It is defined as the catalytic center involved in the reaction steps, and, in Figure 8.1, is the molybdenum atom where the reactions take place. Since all catalytic centers are the same for molecular catalysts, the elementary steps are bimolecular or unimolecular steps with the same rate laws which characterize the homogeneous reactions in Chapter 7. However, if the reaction takes place in solution, the individual rate constants may depend on the nonreactive ligands and the solution composition in addition to temperature. 

The solid state reactions are extremely complex due to intervention of many physical parameters and it becomes often necessary to make some generalizations in the complex reactions. The rate in solid state reactions cannot be defined in the same way as that for a homogeneous reactions because the concept of concentration in solid state reactions has no significance. The energy of activation in a solid state reaction has also no significance, except in some rare cases. 

The above example considered a homogeneous reaction where all of the reactants and products are in the same state, i.e., in an aqueous solution. However, many reactions involve mixtures of gases, liquids, solids, etc. In this case they are defined as heterogeneous reactions. 

Any type of reactor with known contacting pattern may be used to explore the kinetics of catalytic reactions. Since only one fluid phase is present in these reactions, the rates can be found as with homogeneous reactions. The only special precaution to observe is to make sure that the performance equation used is dimensionally correct and that its terms are carefully and precisely defined. 

In discussing the mechanism of eliminations over solids, the nomenclature which has been developed for homogeneous reactions will be used. Therefore the basic mechanisms of olefin formation have first to be outlined and their meaning in heterogeneous catalysis defined. 

We have assumed above that the rate constant of the homogeneous reaction, fe2, is infinitely large so that the boundary between the A2 and X-dominated zones is clearly defined. When k2 is smaller, this boundary will be less clear. The modified convective-diffusion equations are difficult to solve and numerical solution is necessary. This has been performed at the RRDE making the assumptions that [221, 222]... 

Smoluchowski [M. v. Smoluchowski (1917)] treated the problem of diffusion controlled homogeneous reactions in which the reacting particles were initially distributed at random and were non-interacting (except for the collision process). If reaction occurs during the first encounter of the diffusing partners, it is diffusion controlled. If many encounters of the diffusing partner are needed before they eventually react with each other, the process is reaction controlled. If the particles interact already at some distance, one can nevertheless use the concept of diffusion controlled encounters. In this case, one has to carefully define an extended reaction volume as will be outlined later. 

The mean residence time for a continuous stirred-tank reactor of volume Vc may be defined as Vc/v in just the same way as for a tubular reactor. However, in a homogeneous reaction mixture, it is not possible to identify particular elements of fluid as having any particular residence time, because there is complete mixing on a molecular scale. If the feed consists of a suspension of particles, it may be shown that, although there is a distribution of residence times among the individual particles, the mean residence time does correspond to Vc v if the system is ideally mixed. 

Dispersion polymerization is defined as a type of precipitation polymerization by which polymeric microspheres are formed in the presence of a suitable steric stabilizer from an initially homogeneous reaction mixture. Under favorable circumstances, this polymerization can yield, in a batch process, monodisperse, or nearly monodisperse, latex particles with a relatively large diameter (up to 15 pm) [103]. The solvent selected as the reaction medium is a good solvent for both the monomer and the steric stabilizer, but a non-solvent for the polymer being formed and therefore a selective solvent for the graft copolymer. This restriction on the choice of solvent means that these reactions can be carried out... 

The dimerization of 28 has also been studied by Prasad, who used Raman spectroscopy to monitor both changes in intermolecular vibrations and lattice phonon modes [73]. The Raman spectrum shows the disappearance of alkene stretches at 997, 1180, 1593, and 1625 cm-1 as expected, and the appearance of cyclobutane modes at 878,979, and 1001 cm-1. Phonon modes broadened as the reaction progressed, and bands around 15-40 cm-1 showed a shift in frequency. Between about 50 and 66% conversion it was difficult to define distinct bands, but after that point product bands grew in distinctly. This amalgamation behavior is good evidence for a homogeneous reaction mechanism. 

E will be different from 1 only if R4 is small relative to / 2, resulting in a bulk concentration of c — 0 and in a real parallel mechanism of the enhancement. The advantage of the concept of the enhancement factor as defined by eq 33 is the separation of the influence of hydrodynamic effects on gas-liquid mass transfer (incorporated in Al) and of the effects induced by the presence of a solid surface (incorporated in E ), indeed in a similar way as is common in mass transfer with homogeneous reactions. The above analysis shows that an adequate description of mass transfer with chemical reaction in slurry reactors needs reliable data on ... 

Example 8.1 Equilibrium constant of a reaction Consider a homogeneous reaction between species B and P B = E An ideal solution of 1L containing 1 mol of B initially has the concentration 1M. Define the equilibrium constant K. The Gibbs energy of the reaction is... 

Define the following expressions empirical method, metastable equilibrium, kindling temperature, thermostat, interface, dynamic steady state, unimolecular reaction, bimolecular reaction, homogeneous reaction, heterogeneous reaction. 

The principal difference between teactor design calculations involving homogeneous reactions and those involving fluid-solid heterogeneous reactions is that for the latter, the reaction rate is based on mass of solid catalyst, W, rather than on reactor volume, V. For a fluid-solid heterogeneous system, the rate of reaction of a substance A is defined as... 

The literature of catalysis is so vast that it is impossible to do full justice in one part of a chapter, even to the experimental methods that are in use. Most catalytic reactions are quite complex and a complete reaction mechanism can rarely be determined from a measurement of kinetics alone. It is safe to say that no catalytic gas-solid reaction has yet been fully characterised. Because of the many difficulties, work on catalytic reactions tends to veer towards two opposite poles. One of these can be described as the clean surface approach ", which uses the simplest reactions under high vacuum conditions and attempts to define the catalyst surface completely. The other approach is to study much more complex reactions in order to obtain overall kinetic information which describes the process. Where the mechanism is not understood, it is common to employ expressions similar to those used for homogeneous reactions, or even purely empirical equations. 

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