Dispersion chemical kinetics

In general, the sensitivity of FIA is less than that for conventional methods of analysis for two principal reasons. First, as with chemical kinetic methods, measurements in FIA are made under nonequilibrium conditions when the signal has yet to reach its maximum value. Second, dispersion of the sample as it progresses through the system results in its dilution. As discussed earlier, however, the variables that influence sensitivity are known. As a result the FIA manifold can be designed to optimize the sensitivity of the analysis. 

Measurement of the absorption rate of carbon dioxide in aqueous solutions of sodium hydroxide has been used in some of the more recent work on mass-transfer rate in gas-liquid dispersions (D6, N3, R4, R5, V5, W2, W4, Y3). Although this absorption has a disadvantage because of the high solubility of C02 as compared to 02, it has several advantages over the sulfite-oxidation method. For example, it is relatively insensitive to impurities, and the physical properties of the liquid can be altered by the addition of other liquids without appreciably affecting the chemical kinetics. Yoshida and... 

Chemical Kinetics, Tank and Tubular Reactor Fundamentals, Residence Time Distributions, Multiphase Reaction Systems, Basic Reactor Types, Batch Reactor Dynamics, Semi-batch Reactors, Control and Stability of Nonisotheimal Reactors. Complex Reactions with Feeding Strategies, Liquid Phase Tubular Reactors, Gas Phase Tubular Reactors, Axial Dispersion, Unsteady State Tubular Reactor Models... 

Pollutants emitted by various sources entered an air parcel moving with the wind in the model proposed by Eschenroeder and Martinez. Finite-difference solutions to the species-mass-balance equations described the pollutant chemical kinetics and the upward spread through a series of vertical cells. The initial chemical mechanism consisted of 7 species participating in 13 reactions based on sm< -chamber observations. Atmospheric dispersion data from the literature were introduced to provide vertical-diffusion coefficients. Initial validity tests were conducted for a static air mass over central Los Angeles on October 23, 1968, and during an episode late in 1%8 while a special mobile laboratory was set up by Scott Research Laboratories. Curves were plotted to illustrate sensitivity to rate and emission values, and the feasibility of this prediction technique was demonstrated. Some problems of the future were ultimately identified by this work, and the method developed has been applied to several environmental impact studies (see, for example, Wayne et al. ). 

A change in size on scale-up is not the sole determinant of the seal-ability of a unit operation or process. Scalability depends on the unit operation mechanism(s) or system properties involved. Some mechanisms or system properties relevant to dispersions are listed in Table 2 (59). In a number of instances, size has little or no influence on processing or on system behavior. Thus, scale-up will not affect chemical kinetics or thermodynamics although the thermal effects of a reaction could perturb a system, e.g., by affecting convection (59). Heat or mass transfer within or between phases is indirectly affected by changes in size while convection is directly... 

It is important to study chemical kinetics of catalysis in dispersed liquid-liquid systems. Therefore it is necessary to consider the following (14-16) ... 

Its obvious peculiarity as compared with the standard chemical kinetics, equation (2.1.10), is the emergence of the fluctuational second term in r.h.s. The stochastic reaction description by means of equation (2.2.37) permits us to obtain the equation for dispersions crjj which, however, contains higher-order momenta. It leads to the distinctive infinite set of deterministic equations describing various average quantities, characterizing the fluctuational spectrum. 

Chemical kinetics deductions are, in some circumstances, possible from a reaction system using a dispersed solid. If the solid is entirely insoluble, for example a supported catalyst, true surface kinetics can be obtained provided (i) it can be shown that the chemical reaction on the surface is much slower than the associated mass transfer, and (ii) the surface area of the solid can be obtained. These conditions applied in the case of the oxidation of an aqueous solution of hydrazine using a dispersion of insoluble barium chromate [16]. Another case is where it can be shown that an increase in the amount of the solid component does not increase the reaction rate. In this case, exemplified by the formation of benzyl acetate from benzyl bromide and solid sodium acetate in toluene solvent, it is likely that the reaction occurs in the solution phase and that the reaction is proceeding at the saturation concentration of the solid reactant in the liquid phase [17]. 

In a long series of papers on the master equation, Pritchard and his coworkers elucidated for the first time the effects of rotational and vibrational disequilibrium on the dissociation and recombination of a dilute diatomic gas. Ultrasonic dispersion in a diatomic gas was analyzed by similar computational experiments, and the first example of the breakdown of the linear mixture rule in chemical kinetics was demonstrated. A major difficulty in these calculations is that the eigenvalue of the reaction matrix (corresponding to the rate constant) differs from the zero eigenvalue (required by species conservation) by less than... 

Schnabel, R. R., and Fitting, D. J. (1988). Analysis of chemical kinetics data from dilute, dispersed, well-mixed flow-through systems. Soil Sci. Soc. Am. J. 52, in press. 

The simplest mechanisms leading to the dispersion (spreading) of a zone s molecules can be described by the classical random-walk model [9], as noted in Section 5.3. However this model does not fully account for the complexities of migration. It gives, instead, a simple approximation which inherits the most essential and important properties (foremost of all the randomness) of the real migration process. The random-walk model has been used in a similar first-approximation role in many fields (chemical kinetics, diffusion, polymer chain configuration, etc.) and is thus important in its own right. 

In traditional chemical kinetics A = 0, the rate constant is time-invariant, and the effective kinetic order 7 equals the molecularity 2. As the reaction becomes increasingly diffusion-limited or dimensionally restricted, A increases, the rate constant decreases more quickly with time, and the kinetic order in the time-invariant rate law increases beyond the molecularity of the reaction. When the reaction is confined to a 1-dimensional channel, 7 = 3.0, or it can be as large as 50 when isolated on finely dispersed clusters or islands [9,21]. The kinetic order is no longer equivalent to the molecularity of the reaction. The increase... 

Benson. The Foundations of Chemical Kinetics Djerassi. Optical Rotatory Dispersion Hill. Statistical Mechanics IIiNE. Physical Organic Chemistry Laitinen. Chemical Amilysis... 

Even when the laboratory test reactor is intended to be representative in a reaction kinetic sense only (thus waiving the demand for correspondence in terms of pressure drop and hold-ups), the process performance data can be affected by differences in mass transfer and dispersion caused by scale reduction. When interphase mass transfer and chemical kinetics are both important for the overall conversions, the above test reactor, which is a relatively large pilot plant reactor, cannot be further reduced in size unless one accepts deviations in test results. 

The chemical method for obtaining coalescence frequencies has the disadvantage of the influence of the mass transfer that takes place on the physicochemical properties of the dispersion. Further, the intrinsic chemical kinetics must be known. 

Invironmental chemists are most often concerned with the response of an environmental system to change. This change may be natural (such as the diurnal cycle of solar irradiation) or caused by human intervention (such as the dispersion of a pesticide). Since change is such a major concern, it should not be nui prising that chemical kinetics is an integral component of models of natural Nystems. Intrinsically kinetic questions concerning the nature and behavior of mloral systems include ... 

J.M. Hungerford, G.D. Christian, Chemical kinetics with reagent dispersion in single-line flow injection systems, Anal. Chim. Acta 200 (1987) 1. 

Most FIA methods are based on the use of chemical reactions, the products of which are measurable by a detector of choice. Indeed, FIA is useful only because it can accommodate such a wide variety of chemistries. Thus, in most cases, a FIA peak is a result of two processes of the physical dispersion, discussed in previous sections, and of subsequent chemical reactions. These two kinectic processes occur simultaneously in any flow system yet, in FIA their mutual interaction is very complex, since the dispersed zones are not homogeneously mixed, but are composed from concentration gradients formed by gradual penetration of reacting species in both axial and radial directions. An exact description of chemical kinetics taking place in FIA system is therefore very difficult, and this is why so few papers dealing with the theory of chemical kinetics in FIA systems have been published [150, 151, 181, 391, 541, 554, 1064, 1065], although this problem is central to further development of FIA. 

In this section some observations will be made on the influence of chemical kinetics on the FIA response curve and general principles will be outlined, while the published attempts to analyze theoretically the physical dispersion and chemical conversion of an analyte in a FIA system will be discussed in Chapter 3. 

However, the stopped-flow FIA technique allows the fractional conversion to be measured experimentally for any FIA system by resolving the contribution of the dispersion process and of chemical kinetics. By stopping the flow (cf. Sections 2.4.3 and 4.3) any element of the dispersed sample zone can be selected and arrested in the flow cell, where the change of response with time [i.e., rf(response)/[Pg.81]

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