Phases and Multicomponent Systems

An ideal gas exists only as a gas because there are no intermolecular forces between the particles. However, intermolecular forces do exist in real substances with the result that real substances condense into liquids and freeze into solids. Liquids and solids are different phases than gases, and their thermod5mamic description introduces added complexity to the machinery of thermodynamics. This chapter is concerned with the generalization of the thermod5mamic principles for application to systems with more than one phase and more than one component. It also explains some of the important phenomena associated with phase changes. 

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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-... 

The material in this section is divided into three parts. The first subsection deals with the general characteristics of chemical substances. The second subsection is concerned with the chemistry of petroleum it contains a brief review of the nature, composition, and chemical constituents of crude oil and natural gases. The final subsection touches upon selected topics in physical chemistry, including ideal gas behavior, the phase rule and its applications, physical properties of pure substances, ideal solution behavior in binary and multicomponent systems, standard heats of reaction, and combustion of fuels. Examples are provided to illustrate fundamental ideas and principles. Nevertheless, the reader is urged to refer to the recommended bibliography [47-52] or other standard textbooks to obtain a clearer understanding of the subject material. Topics not covered here owing to limitations of space may be readily found in appropriate technical literature. 

Roberts et al. (1940), Barrer and Edge (1967), Skovborg and Rasmussen (1994) present similar, detailed derivations to consider the use of the Clapeyron equation for hydrate binary and multicomponent systems. The reader is referred to the work of Barrer and Edge (1967) for the precise meaning of dP/dT and the details of the derivation. Barrer and Stuart (1957) and Barrer (1959) point out that the problem in the use of the Clapeyron equation evolves from the nonstoichio-metric nature of the hydrate phase. Fortunately, that problem is not substantial in the case of hydrate equilibrium, because the nonstoichiometry does not change significantly over small temperature ranges. At the ice point, where the hydrate number is usually calculated, the nonstoichiometry is essentially identical for each three-phase system at an infinitesimal departure on either side of the quadruple point. 

In addition, a change of phase in multicomponent systems does not take place, in general, under conditions of both constant temperature and constant pressure, or with constant composition of the individual phases. We consider, as an example, a change of state represented as... 

Governing equations are the continuity equation, the chemical reactions and their thermodynamic relationships, and the heat, mass, and momentum equations. Elastic behavior of an expanding bed of particles sometimes must be included. These equations can be many and complex because we are dealing with both multiphase and multicomponent systems. Correlations are often in terms of phase-based dimensionless groups such as Reynolds numbers, Froude numbers, and Weber numbers. 

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. 

In 1926 Kohnstamm extended the Gibbs phase rule to encompass the appearance of critical points in one- and multicomponent systems. He assumed that the critical point may be considered as a specific, additional phase. If / phases coexist, and next become critical, p l meniscuses disappear in a solution consisting of c components. Hence, the Gibbs phase mle supplemented by the critical phase has the following form =c- p + p-l) + 2 = c-2p + > Consequently, for / -critical point at least c = 2p- component system is required. This yields for = 0, i.e. a single critical point, following conditions ... 

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. 

The equilibrium = f(c ) or the partition between an ionic component in the solid or resin phase and in the fluid phase of multicomponent systems depends on many material properties and the temperature and has to be measured. Things are easier for binary systems in which the ionic species a is exchanged. With the concentration q and the mass fraction in the solid or resin phase and the concentration C3 and the mass fraction in the liquid or solution phase the equilibrium =/(Ca) or a = f (y ) cau be described by the mass actiou equilibriiun Constant or selectivity coefficient (see (9.3-3)) ... 

Relative volatilities can be applied to both binary and multicomponent systems. In the binary case, the relative volatility a between the light component and the heavy component can be used to give a simple relationship between the composition of the liquid phase (x is the mole fraction of the light component in the liquid phase) and the composition of the vapor phase (y is the mole fraction of the light component in the vapor phase). 

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. 

Thermodynamic calculations were performed using THERMO software package to calculate the adiabatic combustion temperatures and product phase distribution. This program is based on optimization of Gibbs free energy of multiphase and multicomponent systems. The gases are assumed to be ideal and condensed phases completely immiscible [19],... 

With the help of the binary parameters kn or g -model parameters now the phase equilibrium behavior, densities, enthalpies, Joule-Thomson coefficients, and so on, for binary, ternary and multicomponent systems can be calculated. For the calculation of the VLE behavior the procedure is demonstrated in the following example for the binary system nitrogen-methane using classical mixing rules. The same procedure can be applied to calculate the VLE behavior of multicomponent systems and with g -mixing rules as well. 

Assuming that 1000 compounds are of technical interest, phase equilibrium information for about 500000 binary systems are required to fit the required binary parameters to describe aU possible binary and multicomponent systems. Although more than 64500 VLE data sets for nonelectrolyte systems have been published up lo now, VLE data are available for only 10300 binary systems, since for a few systems a large number of data sets were published, for example, for the systems ethanol-water, ammonia-water, water-carbon dioxide, methanol-water, methane-nitrogen more than 150 data sets are available. This means that only for 2% of the required systems at least one VLE data set is available. If only... 

The most complete theoretical treatment of MaxwellAVagner polarization process in polymer blends was done by Steeman and coworkers (Steeman and van Tumhout 2003) especially also for higher concentrations of the dispersed phase and multicomponent polymer blends (Steeman et al. 1994 Steeman and Maurer 1990, 1992). Quantitative conclusions about the phase structure of the different systems can be drawn including the modeling also of interfaces. This has also some impact on blend compatibilization by grafted copolymers (Eklind et al. 1997). 

In this chapter we are going to discuss the Langmuir adsorption isotherm (LAI) and several of its generalizations for single- and multicomponent systems in Sect. 2. This isotherm has proved to he most useful to describe adsorption in microporous materials. In Sect. 3 we will provide some information on a few empirical adsorption isotherms used to describe gas adsorption in micro- and mesoporous materials, i. e. showing pore condensation leading to an unlimited amount of mass in the adsorbed phase. 

Processes of formation and growth of intermediate phases in the diffusion zone of binary and multicomponent systems are controlled by the following multiscale processes [2, 4, 6, 8] ... 

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