Two and Multicomponent Systems

The basic equation for the vapor-liquid phase equilibrium forms the major design criteria for apparatus that separate liquid mixtures by distillation or selective absorption. 

In distillation, the process or actual working temperature is lower than the criti- 

R the universal gas constant Vj Q partial molar volume of component i at pressure p and temperature T yj activity coefficient of i in the liquid phase (see Eq. (1-31)) 

Vj I molar volume of liquid component i at temperature T and saturated vapor pressure Pg, 

The fugacity fj is defined by the chemical potential of a real gas, as postulated by Lewis  

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Adsorption characteristics of co-precipitated samples with the composition Fe(0H)3 -Cd(OH)2 and Fe(OH)3 - Cr(OH)3 confirm this statement and generality of the regularity found follows from the structural formation mechanism considered. This regularity inherent in all two- and multicomponent systems with different pH of initial and complete precipitation of components opens a broad perspective for scientifically justified and purposeful selection of conditions for the synthesis of adsorbents with the given structure and catalysts with the component precipitated first being a carrier and the other, an active phase. 

The low molecular mass binders have low solution viscosity and allow low-emission paints with high solids contents or even solvent-free paints to be produced. Here, the binder consists of a mixture of several reactive components, and film formation takes place by chemical drying after application of the paint. If chemical hardening occurs even at room temperature, the binder components must be mixed together shortly before or even during application (two- and multicomponent systems). 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

While the early work on molten NH4CI gave only some qualitative hints that the effective critical behavior of ionic fluids may be different from that of nonionic fluids, the possibility of apparent mean-field behavior has been substantiated in precise studies of two- and multicomponent ionic fluids. Crossover to mean-field criticality far away from Tc seems now well-established for several systems. Examples are liquid-liquid demixings in binary systems such as Bu4NPic + alcohols and Na + NH3, liquid-liquid demixings in ternary systems of the type salt + water + organic solvent, and liquid-vapor transitions in aqueous solutions of NaCl. On the other hand, Pitzer s conjecture that the asymptotic behavior itself might be mean-field-like has not been confirmed. 

The thermodynamic equations for the Gibbs energy, enthalpy, entropy, and chemical potential of pure liquids and solids, and for liquid and solid solutions, are developed in this chapter. The methods used and the equations developed are identical for both pure liquids and solids, and for liquid and solid solutions therefore, no distinction between these two states of aggregation is made. The basic concepts are the same as those for gases, but somewhat different methods are used between no single or common equation of state that is applicable to most liquids and solids has so far been developed. The thermodynamic relations for both single-component and multicomponent systems are developed. 

We consider a two-phase, multicomponent system in which there is one planar surface. The state of the system is defined by assigning values to the entropy and volume of the system, the area of the surface, and the mole numbers of the components. The differential of the energy of the system is... 

Extraction is a mass exchange process in a multiphase and multicomponent system that involves transfer and distribution of one or more components into two... 

These two equations are equivalent and either one can be used to calculate the compositions of a two-phase multicomponent system. These equations are most readily solved by trial and error. To simplify Ihe calculation, one mole of starting material is taken as a basis. In this case Ti. = 1 and ni + = 1. A reasonable valne of ni or ti is chosen... 

These data allow us to assume that tridymite is in fact a phase belonging to a two-or multicomponent system where its own stability field in the form of a solid solution can be considered. Binary phase diagrams of this type have been constructed by Holmquist (1961) and Wollast (1967). 

In this chapter, we introduce the concepts of molecular distribution function (MDF), in one- and multicomponent systems. The MDFs are the fundamental ingredients in the modern molecular theories of liquids and liquid mixtures. As we shall see, these quantities convey local information on the densities, correlation between densities at two points (or more) in the system, etc. 

The nearly two dozen phase diagrams shown below present the reader with examples of some important types of single and multicomponent systems, especially for ceramics and metal alloys. This makes it possible to draw attention to certain features like the kinetic aspects of phase transitions (see Figure 22, which presents a time-temperature-transformation, or TTT, diagram for the precipitation of a-phase particles from the [5-phase in a Ti-Mo alloy Reference 1, pp. 358-360). The general references listed below and the references to individual figures contain phase diagrams for many additional systems. 

A curious example is that of the distribution of benzene in water benzene will initially spread on water, then as the water becomes saturated with benzene, it will round up into lenses. Virtually all of the thermodynamics of a system will be affected by the presence of the surface. A system containing a surface may be considered as being made up of three parts two bulk phases and the interface separating them. Any extensive thermodynamic property will be apportioned among these parts. For example, in a two-phase multicomponent system, the extra amount of an i component that can be accom-mondated in the system due to the presence of the interface ( ) may be expressed as Qi Qii where is the total number of molecules of i in the whole system, Vj and Vjj are the volumes of phases I and II, respectively, and Q and Qn are the concentrations of i in phases I and II, respectively. The surface (excess) concentration of i is defined as Fj = A, where A is the surface area. At equilibrium, the chemical potential of any component is the same in each bulk phase and at the surface. The Gibbs adsorption equation, which is one of the most widely used expression in surface and colloid science is shown in Eq. (2) ... 

Azeotropes occur in binary, ternary, and multicomponent systems. They can be homogeneous (single liquid phase) or heterogeneous (two liquid phases). They can be minimum boiling or maximum boiling. The ethanol/water azeotrope is a minimumboiling homogeneous azeotrope. 

The various systems are treated in the order in which the alkali metals are listed in Group I of the Periodic Table. Most of the available solubility data are for the orthophosphates of sodium and potassium, and for these two systems an introductory chapter on the M0H-HjP0 -H20 (M = Na or K) system is given. Each of these chapters (chapters 2 and 7) also refers to compounds to be considered in later chapters. Following each of these introductory chapters there are chapters dealing with the solubility data for individual orthophosphates having different M/P ratios, and the ternary and multicomponent systems in which these orthophosphates are components. Only one chapter is devoted to each of the orthophosphates of lithium, rubidium and cesium. 

Szczepanik, Ryszard, 1963. Two- and multicomponent, solid-liquid systems formed by aromatic hydrocarbons, anthraquinone, and coal-tar fractions. Chem. Stosowana Ser. A 7,621-660. 

Phase diagrams of ternary systems usually contain two-phase regions in the solid state (see e.g., [2] and Figure 10.1). The diffusion mass transfer in ternary and multicomponent systems is essentially different from the case of a binary system in quasiequilibrium as there exists the possibility of two-phase zone formation in the diffusion process. Though two-phase formation is connected with the thermodynamic disadvantage of interphase boundaries formation, there are cases when any other diffusion mode is impossible. Formation of two-phase regions may also proceed at high reaction rates at interfaces, that is, the assumption of quasiequilibrium of the interdiffusion process is imposed. Subsequently, we can apply the apparatus of hnear thermodynamics for irreversible processes [3-5]. 

Because of the formation and growth of two-phase zones, the description of diffusion interaction in ternary and multicomponent systems is more complicated when compared to binary ones, in which the diffusion path in quasiequilibrium conditions is unambiguous and the resulting diffusion zone does not contain any two-phase regions. Diffusion processes in two-phase zones are difficult to... 

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