Phases, heterogeneous systems

In Chapter 3 we described the structure of interfaces and in the previous section we described their thermodynamic properties. In the following, we will discuss the kinetics of interfaces. However, kinetic effects due to interface energies (eg., Ostwald ripening) are treated in Chapter 12 on phase transformations, whereas Chapter 14 is devoted to the influence of elasticity on the kinetics. As such, we will concentrate here on the basic kinetics of interface reactions. Stationary, immobile phase boundaries in solids (e.g., A/B, A/AX, AX/AY, etc.) may be compared to two-phase heterogeneous systems of which one phase is a liquid. Their kinetics have been extensively studied in electrochemistry and we shall make use of the concepts developed in that subject. For electrodes in dynamic equilibrium, we know that charged atomic particles are continuously crossing the boundary in both directions. This transfer is thermally activated. At the stationary equilibrium boundary, the opposite fluxes of both electrons and ions are necessarily equal. Figure 10-7 shows this situation schematically for two different crystals bounded by the (b) interface. This was already presented in Section 4.5 and we continue that preliminary discussion now in more detail. 

A two-phase heterogeneous system with multiple inputs, multiple outputs, and multiple reactions in each phase and with mass transfer between the two phases... 

A two-phase heterogeneous system with single input, single output, and a single reaction in each phase Figure 6.9... 

Analysis of Multi-Component-Multi-Phase Heterogeneous System... 

The vapor is thea withdrawa from the stiH as distillate. The changing Hquid composition is most coavenieafly described by foUowiag the trajectory (or residue curve) of the overall composition of all the coexistiag Hquid phases. An exteasive amouat of valuable experimental data for the water—acetoae—chloroform mixture, including biaary and ternary LLE, VLE, and VLLE data, and both simple distillation and batch distillation residue curves are available (93,101). Experimentally determined simple distillation residue curves have also been reported for the heterogeneous system water—formic acid—1,2-dichloroethane (102). 

The phase rule is a mathematical expression that describes the behavior of chemical systems in equilibrium. A chemical system is any combination of chemical substances. The substances exist as gas, liquid, or solid phases. The phase rule applies only to systems, called heterogeneous systems, in which two or more distinct phases are in equilibrium. A system cannot contain more than one gas phase, but can contain any number of liquid and solid phases. An alloy of copper and nickel, for example, contains two solid phases. The rule makes possible the simple correlation of very large quantities of physical data and limited prediction of the behavior of chemical systems. It is used particularly in alloy preparation, in chemical engineering, and in geology. 

There are a large number of processes in the chemical industries that handle a variety of suspensions of solid particles in liquids. The application of filtration techniques for the separation of these heterogeneous systems is sometimes very costly. If, however, the discrete phase of the suspension largely contains settleable particles, the separation can be effected by the operation of sedimentation. The process of sedimentation involves the removal of suspended solid particles from a liquid stream by gravitational settling. This unit operation is divided into thickening,... 

Heterogeneous reaetions involve two or more phases. Examples are gas-liquid reaetions, solid eatalyst-gas phase reaetions and produets, and reaetions between two immiseible liquids. Catalytie reaetions as illustrated in Chapter 1 involve a eomponent or speeies that par-tieipates in various elementary reaetion steps, but does not appear in the overall reaetion. In heterogeneous systems, mass is transferred aeross the phase. 

In heterogeneous systems AP must be critically reviewed, especially if the reaction involves a two-phase mixture of liquid and gas, or if the gas flows through a deep bed of catalyst particles as in the FCC systems. AP should be checked early in the design process to assess its influence on the overall plant integrity. 

Our interest is in solution kinetics, so we will concern ourselves only with homogeneous reactions, which take place in a single phase. Heterogeneous reactions take place, at least in part, at interfaces between phases.) Further, we will mainly work with closed systems, those in which matter is neither gained nor lost during the period of observation. 

On the other hand, operations such as distilling or freezing usually tend to separate solutions into the pure substances that were the components of the solution. The nearer alike the components are, the harder it is to separate them from the solution, but even in difficult cases, a variety of methods in succession usually brings about a separation. In nature, solutions are much more common than pure substances, and heterogeneous systems are more common than solutions. When we want pure substances, we often must prepare them from solutions through successive phase changes. 

According as it consists of one or of more phases, a system in equilibrium is said to be homogeneous or heterogeneous. 

This is an equation which fixes the relation existing between the number of phases (/ ), the number of components ( i), and the variance, or number of degrees of f reedom (F), of a heterogeneous system in equilibrium, subject to certain conditions which are usually satisfied in practice. The rule states that... 

Heterogeneous systems may differ in respect of the number of phases and their state of aggregation and composition. 

All points on the two tangents HRi, HR2, to the curve of solutions represent heterogeneous systems composed of solid hydrate in contact with solutions. If the curve between Ri and R2 is convex the heterogeneous systems are stable, and inversely. At a given temperature and pressure the hydrate can be in equilibrium with two liquid phases of different composition, one containing relatively more, the other relatively less, salt than the hydrate. With rise of temperature the form of the curve and the altitude of H change ... 

On a microscopic scale, a microemulsion is a heterogeneous system and, depending on the relative amounts of the constituents, three main types of structures can be distinguished [69] oil in water (OAV, direct micellar structure), water in oil (W/O, reverse micellar structure) and a bicontinuous structure (B) (Figure 6.1). By adding oil in water, OAV dispersion evolves smoothly to a W/O dispersion via bicontinuous phases. 

Many semibatch reactions involve more than one phase and are thus classified as heterogeneous. Examples are aerobic fermentations, where oxygen is supplied continuously to a liquid substrate, and chemical vapor deposition reactors, where gaseous reactants are supplied continuously to a solid substrate. Typically, the overall reaction rate wiU be limited by the rate of interphase mass transfer. Such systems are treated using the methods of Chapters 10 and 11. Occasionally, the reaction will be kinetically limited so that the transferred component saturates the reaction phase. The system can then be treated as a batch reaction, with the concentration of the transferred component being dictated by its solubility. The early stages of a batch fermentation will behave in this fashion, but will shift to a mass transfer limitation as the cell mass and thus the oxygen demand increase. 

Bearing in mind that most asymmetric reactions take place in the liquid phase, we have considered two general types of heterogeneous systems a liquid phase that is immiscible with the reaction phase and a solid phase. 

Both substrate and product have suface-active properties and favor mass transfer across the liquid-liquid interface. Their physicochemical properties modulate the behavior of the reaction in the heterogeneous system. Saturating substrate concentration in the aqueous phase (L aq) was not constant. It increased when using a high initial concentration of LA LA and when the HP concentration increased. The percentage of transferred LA T = LA qlLAf) depended on LA, and HP concentrations ... 

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