Reactions in single-phase systems

In many respects, reactions between metals are simpler than reactions between ionic crystals. However, the discussion of metal reactions has been left until now since the main emphasis so far has been on the more chemical aspects of solid state reactions, and the reactions between ionic crystals serve as classical examples for this. 

The subscript defect refers to the site of repeatable growth. These equations can be compared to eq. (4-19) which is applicable for a homogeneous defect reaction in ionic crystals, and to eq. (6-6) which is applicable for an inhomogeneous defect reaction in ionic crystals. In these equations, in contrast to eq. (7-1), the pairwise formation of defects is evident. 

Accordingly, the simplest reaction which we can treat in homogeneous metallic systems is the equilibration of defects. After this comes the broad field of reactions in single-phase systems with spatially variable composition. These latter reactions are generally classified under the title Dilfusion in Metals . There is a number of excellent monographs on this topic [1, 2, 3, 4], The diffusional mechanisms and the fundamental phenomenological laws have already been treated in the introductory chapters, and especially in chapter 5. However, there are still a great many aspects of chemical reactions between metals which have not yet been discussed. These will be treated in detail in the present chapter. 

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Mixing and chemical reaction in single-phase systems... 

Situation a, comprising simultaneous mixing and reaction in single phase systems, is the most complicated one. In this case effective modelling is not always possible. Generally more experimental work is needed in order to predict the... 

Examples of significant temperature gradients in single phase systems are found in flames, and also in very viscous liquids where rapid exothermic reactions take place. The effect of temperature gradients in viscous systems was briefly indicated in section 5.2.3. But in general, the problem of homogeneous reactors with two- or three-dimensional temperature and concentration gradients is considered too specialized for this book therefore the interested reader is referred to the relevant literature (see, e.g., the comprehensive book by Rosner, 1986). 

Reaction System Polymerization reaction in single-phase flows. 

If the reaction order does not change, reactions with n < 1 wiU go to completion in finite time. This is sometimes observed. Solid rocket propellants or fuses used to detonate explosives can bum at an essentially constant rate (a zero-order reaction) until all reactants are consumed. These are multiphase reactions limited by heat transfer and are discussed in Chapter 11. For single phase systems, a zero-order reaction can be expected to slow and become first or second order in the limit of low concentration. 

Section 1.5 described one basic problem of scaling batch reactors namely, it is impossible to maintain a constant mixing time if the scaleup ratio is large. However, this is a problem for fed-batch reactors and does not pose a limitation if the reactants are premixed. A single-phase, isothermal (or adiabatic) reaction in batch can be scaled indefinitely if the reactants are premixed and preheated before being charged. The restriction to single-phase systems avoids mass... 

The motions of the individual fluid parcels may be overlooked in favor of a more global, or Eulerian, description. In the case of single-phase systems, convective transport equations for scalar quantities are widely used for calculating the spatial distributions in species concentrations and/or temperature. Chemical reactions may be taken into account in these scalar transport equations by means of source or sink terms comprising chemical rate expressions. The pertinent transport equations run as... 

Steefel, C. I. and A.C. Lasaga, 1994, A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. American Journal of Science 294, 529-592. 

The operational interpretation of rA, as opposed to this verbal definition, does depend on the circumstances of the reaction.1 This is considered further in Chapter 2 as a consequence of the application of the conservation of mass to particular situations. Furthermore, rA depends on several parameters, and these are considered in Section 1.4.2. The rate with respect to any other species involved in the reacting system may be related to rA directly through reaction stoichiometry for a simple, single-phase system, or it may require additional kinetics information for a complex system. This aspect is considered in Section 1.4.4, following a preliminary discussion of the measurement of rate of reaction in Section 1.4.3. 

In this chapter, we describe how experimental rate data, obtained as described in Chapter 3, can be developed into a quantitative rate law for a simple, single-phase system. We first recapitulate the form of the rate law, and, as in Chapter 3, we consider only the effects of concentration and temperature we assume that these effects are separable into reaction order and Arrhenius parameters. We point out the choice of units for concentration in gas-phase reactions and some consequences of this choice for the Arrhenius parameters. We then proceed, mainly by examples, to illustrate various reaction orders and compare the consequences of the use of different types of reactors. Finally, we illustrate the determination of Arrhenius parameters for die effect of temperature on rate. 

For a single-phase system, V always refers to the volume of the reacting system, but is not necessarily the volume of the reactor. For example, for a liquid-phase reaction in... 

Certain solvents are essentially immiscible at low temperature, but on heating, their relative solubility increases until they form a single phase. Such a biphasic system allows reactions to be conducted in single phase under homogeneous... 

As for a single phase system, the rate of the reaction is still dependent on the probability of reactants meeting and therefore on the concentration of the reagents. However, in the biphasic system, the critical concentration of these components is no longer their total concentration in the whole system but the concentration where the reaction takes place. This concentration will be dependent on a number of factors, and the most influential are the rate of diffusion of the reactants to the catalyst and the relative solubility of the reagents in each phase. These two factors are interdependent, and will be considered in turn. 

In the preceeding paragraphs we described the effect of surfactants in reactions proceeding in a single liquid phase. A logical extension of this concept is in the use of surfactants in two-phase systems where their... 

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