Phases and Components

Unfortunately, this does not nearly encompass all we need to say about components. We will have more to say in Chapter 11, but we should at least point out that the definition of eomponents given above ( smallest set of chemical formulas... ) is used for phases in our models, not in real systems. For example, analysis of any ealeite crystal will reveal the presence of many elements besides those in the formulas CaCOj. Nevertheless, component CaCOj is very often used to represent ealeite, whatever its actual composition. 

Equilibrium, phases, and components are terms that appear to apply to real systems, not just to the model systems that we said thermodynamics applies to, and in general conversation, they do. But real phases, especially solids, are never perfectly homogeneous. And real systems don t really have components, only our models of them do. Seawater, for example, has an incredibly complex composition, containing dozens of elements. But our thermodynamic models might model seawater as having two, three, or more components, depending on the application. As for equilibrium, real systems do often achieve equilibrium as we have defined it, but it is never a perfeet equilibrium. 

However, the fact that real phases are more or less homogeneous, and that real systems achieve an approximate equilibrium, is what makes thermodynamics useful. The model is perfect, but real life comes close enough in 

The components of a system are the smallest number of formulae required to describe all the phases in the system. The word formula refers here to any assemblage of elemental symbols, each having any stoichiometry, positive or negative. The problem here is, what are we to regard as the composition of the phase Do we include trace elements Again, we postpone discussion, and will discuss the Phase Rule for fairly simple cases where these problems do not appear to arise. 

A system having a fixed composition may have a number of equivalent sets of components. For example, the compositions of all phases in the system ABC can be described by the components (A,B,C) (A,ABC,AC) (A2B, B, B iC) or any other three points lying in the ABC plane. Any two compositions are insufficient and any four are too many, because one of the four could always be described by a suitable combination of the other three. ABC is therefore a three-component system. 

We continue to use the term constituent in the sense defined in Chapters 3 and 11. A constituent is any combination of the components of a system, in other words. 

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Phase solubility analysis is a technique to determine the purity of a substance based on a careful study of its solubility behavior [38,39]. The method has its theoretical basis in the phase mle, developed by Gibbs, in which the equilibrium existing in a system is defined by the relation between the number of coexisting phases and components. The equilibrium solubility of a material in a particular solvent, although a function of temperature and pressure, is nevertheless an intrinsic property of that material. Any deviation from the solubility exhibited by a pure sample arises from the presence of impurities and/or crystal defects, and so accurate solubility measurements can be used to deduce the purity of the sample. 

Eutectic diagrams (from Greek svtt]ktoo- easily melted ) represent the T-x melting behavior for binary systems with completely immiscible solid phases a, /3. The solid a, /3 phases often correspond to (virtually) pure components A, B, respectively, so we may treat phase and component labels (rather loosely) as interchangeable in this limit. 

J.W. Gibbs developed the thermodynamic methods for the characterisation of equilibrium states of heterogeneous systems involving any number of substances. Before deriving a thermodynamic method for the characterisation of equilibrium states of heterogeneous systems, we define two important terms i.e., phase and component. 

Problem 10 Determine the number of phases and components in the following systems ... 

In a distillation column, vapor and liquid flow in countercurrent directions to each other. Liquid is vaporized at the bottom, and vapor is condensed from the top product and withdrawn from the column. A number of trays are placed in the column, or the column is packed with open material, so that the vapor phase contacts the liquid phase, and components are transferred from one phase to the other. As you proceed up the column the temperature decreases, and the net effect is an increase in the more volatile component(s) in the vapor and a decrease in the less volatile components in the liquid. Vapor is withdrawn from the top of the column and liquid from the bottom. Feed to the column usually enters part way up the column. 

Chapter 6, Separator Design, considers only the most common phase and component separators. Because plates and column packings are contained in ves-... 

Membrane technology is variously used for separating phases and component—starting, say, with suspensions and colloidal suspensions, and solutions, and moving on to liquids and gases. A brief overview follows. 

For example, if heat supplied to a system consisting of several phases and components (increase in entropy) causes the temperature to rise by T, the phases otherwise remaining unaltered, then the same amount of heat (increase in entropy) will raise the temperature by the smaller amount dT if we keep the system in equilibrium throughout. The displacement of the equilibrium, therefore, acts as a brake on the imposed change in the intensity factor, in this case the temperature. 

Since all points on a tie line have the same temperature, pressure, component concentration in one phase, and component concentration in the other phase, one more variable must be specified to define the relative amounts of the phases at equilibrium. The specihed variable could itself be either the fraction of one phase out of the total or the mixture composition. Note that only two component concentrations are independent in a ternary. In the single-phase region there are four degrees of freedom according to the phase rule. Therefore, if the fraction of one phase or whether one or two phases exist is unknown, four independent variables must be specihed to completely dehne the system. 

The angstrom unit is named for the famous Swedish scientist, and currently the nm (10 ) unit is mainly used. Because colloidal systems consist of two or more phases and components, the interfacial area-to-volume ratio becomes very signihcant. Colloidal particles have a high ratio of surface area to volume compared with bulk materials. A signihcant proportion of the colloidal... 

Having defined the terms phase and component we have now to consider a further term, namely, the degrees of freedom1 of a system... 

Equilibrium in simplified systems with several phases and components... 

Further discussion of these topics is found in Chapters 10 and 14. We leave these other considerations until later because a full discussion is much easier when other thermodynamic concepts such as activity and fugacity have been introduced. One of these considerations will be found to be that although as defined here phases and components appear to be entities that occur in rocks, minerals, solutions, and other parts of the real world, we will show that they are in fact parts of the thermodynamic model, just as much as are equilibrium and reversible processes. 

If the catalyst particles are not completely wetted by the liquid phase and the pores consequently not completely filled with liquid phase (static holdup gives some indication of whether this is the case or not), the situation is considerably more complex. In addition to being a function of the Thiele modulus, the catalytic effectiveness will now depend on the fraction of external wetting, rjcs, and the fraction of pore volume filled with liquid, rji. Dudokovic [M.P. Dudokovic, Amer. Inst. Chem. Eng. Jl., 23, 940 (1977)] proposed a reasonable approach that accounts for all three factors. If the reaction proceeds only on the catalyst surface effectively wetted by the liquid phase and components of the reaction mixture are nonvolatile, then one can in principle modify the definition of the Thiele modulus to... 

If the system in question contains several phases and components and, for a particular component, there are molecules in phase f, in phase 7 and so on, then the chemical potential of molecules of this component in phase i is defined to be... 

Shan Xiaowen, Chen Hudong. 1993. Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E, 47 (3) 1815. 

Sbragaglia, M., R. Benzi, L. Biferale, S. Sued, K. Sugiyama, and F. Toschi. Generalized Lattice Boltzmann Method with Multirange Pseudopotential. Phys. Rev. E 75 026702 (2007). Shan, X. and H. Chen. Lattice Boltzmann Model of Simulating Flows with Multiple Phases and Components. Phys. Rev. E 47 1815-1819 (1993). 

A review paper included selected references on methods for extraction from paper, layers, mobile phases, and component characterization methods used in TLC and HPTLC for separation of ink components and identification and comparison of ink formulations from ballpoint, fountain, and fiber-tipped pens and typewriter ribbons published between 1960 and 1996. This entry describes standard TLC methods for ink analysis published by the ASTM International (West Conshohocken, Pennsylvania, U.S.A.) and advances in the field of forensic ink analysis using these and other TLC and HPTLC procedures published since 1996. 

The U.S. Army Corps of Engineers requires contractors who perform construction work for the federal government to prepare a safety and occupational health plan (SOH). The idea is to analyze the potential work on a specific job or project and to plan accident prevention measures for each phase and component of the work. The plan includes work performed by subcontractors. It includes contractor hazard control measures. The plan must include frequent and regularly scheduled safety inspections of work sites, materials and equipment by competent persons. 

Shan and He [130,131] described a method for performing LBM simulations of flows with multiple phases and components. A eentral idea of their method is the use of an interparticle potential ... 

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