The Thermodynamics of Phase Equilibria

1 How many degrees of freedom are present in an enclosed system of boiling water  

4 An ideal liquid has a AT/yap that is independent of temperature. Its boiling point as a function of temperature was determined to be 100°C and lOHC at 101 kPA and 105 kPa, respectively. What is its AHyap  

This chapter from The Physical Basis of Biochemistry Solutions Manual to the Second Edition corresponds to Chapter 13 from The Physical Basis ofBiochemistiy, Second Edition 

5 Urea is considered an eco-friendly de-icer. How many grams of urea (MM = 60.06 g/mol) is required to prevent 3.3 kg of water from freezing at 4°( .  

6 At 1 atm pressure, how much does a tablespoon of table salt (18 g of NaCl) elevate the boiling point of a pot of water (1.1 1)  

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The thermodynamics of phase equilibria is reviewed in Chapter 17 and the fundamental thermodynamic differences between conserved and nonconserved order parameters are reinforced with a geometrical construction. These order parameters are used in the kinetic analyses of continuous and discontinuous phase transformations. 

The required height Z for the column can be calculated by integrating to the point y = ye. The evaluation of this integral is often only possible numerically as the mole fraction yeq is normally a complex function of the mole fraction x of the liquid, and therefore according to the balance equation (1.227) is still dependent on the mole fraction y. How the mole fractions at equilibrium are ascertained is dealt with in the thermodynamics of phase equilibria. 

In ideal chromatography, we assume that the column efficiency is infinite, or in other words, that the axial dispersion is negligibly small and the rate of the mass transfer kinetics is infinite. In ideal chromatography, the surface inside the particles is constantly at equilibrium with the solution that percolates through the particle bed. Under such conditions, the band profiles are controlled only by the thermodynamics of phase equilibria. In linear, ideal chromatography, all the elution band profiles are identical to the injection profiles, with a time or volume delay that depends only on the retention factor, or slope of the linear isotherm, and on the mobile phase velocity. This situation is unrealistic, and is usually of little importance or practical interest (except in SMB, see Chapter 17). By contrast, nonlinear, ideal chromatography is an important model, because the profiles of high-concentration bands is essentially controlled by equilibrium thermodynamics and this model permits the detailed study of the influence of thermodynamics on these profiles, independently of the influence of the kinetics of mass transfer... 

Chromatography is a powerful separation method because it can be carried out easily under experimental conditions such that the two phases of the system are always near equilibrium. This is because the kinetics of the mass transfers between these phases is usually fast. The separation power of a column, under a given set of experimental conditions, is directly a function of the rate of the mass transfer kinetics and of the axial dispersion coefficient. The scientists involved in the development of stationary phases for chromatography have produced excellent packing materials that permit the achievement of a very large number of equilibrium stages (i.e., theoretical plates) in a column. Thus, as we show later in Chapters 10 and 11, the thermodynamics of phase equilibria is often the main... 

A full treatment of the thermodynamics of phase equilibria may be found elsewhere. Only the terminology and some essential concepts will be reviewed in this section. 

It is easy to relate retention times to the thermodynamics of phase equilibria. In practice, however, it is difficult to measure many of the relevant thermodynamic parameters with sufficient accuracy, while retention times can be measured with great precision. Furthermore, it should be emphasized at the outset that even though very precise measurements can indeed be made in chromatography [38], the available stationary phases are often so poorly reproducible that such precision is unwarranted. Column-to-column reproducibility for silica-based phases is reasonable only for columns packed with material from a given supplier. For this reason, chromatographers prefer whenever possible to use relative retention data. 

This equation is very important in the thermodynamics of phase equilibria the condition of the equality of the fugacity of equilibrium phases and the above equation provide the phase composition. 

Equation (4-8) is the fundamental property relation for singlephase PVT systems, from which all other equations connecting properties of such systems are derived. The quantity is called the chemical potential of ecies i, and it plays a vital role in the thermodynamics of phase ana chemical equilibria. 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Freezing point depression follows the colligative laws of thermodynamics at low concentrations added to water. At the same time the boiling point generally will be increased. The freezing point depression can be readily explained from the theory of phase equilibria in thermodynamics. 

Calculation, thermodynamic optimization of phase diagrams. The knowledge of phase equilibria, phase stability, phase transformations is an important reference point in the description and understanding of the fundamental properties of the alloys and of their possible technological applications. This interest has promoted a multi-disciplinary and multi-national effort dedicated not only to experimental methods, but also to techniques of optimization, calculation and prediction of... 

The role of a thermodynamic approach is well known a thermodynamic check, optimization and prediction of the phase diagram may be carried out by using methods such as those envisaged by Kubaschewski and Evans (1958), described by Kaufman and Nesor (1973), Ansara et al. (1978), Hillert (1981) and very successfully implemented by Lukas et al. (1977, 1982), Sundman et al. (1985). The knowledge (or the prediction) of the intermediate phases which are formed in a certain alloy system may be considered as a preliminary step in the more general and complex problem of assessment and prediction of all the features of phase equilibria and phase diagrams. See also Aldinger and Seifert (1993). 

Design of extraction processes and equipment is based on mass transfer and thermodynamic data. Among such thermodynamic data, phase equilibrium data for mixtures, that is, the distribution of components between different phases, are among the most important. Equations for the calculations of phase equilibria can be used in process simulation programs like PROCESS and ASPEN. 

The history of CALPHAD is a chronology of what can he achieved in the field of phase equilibria by combining basic thermodynamic principles with mathematical formulations to describe the various thermodynamic properties of phases. The models and formulations have gone through a series of continuous improvements and, what has become known as the CALPHAD approach, is a good example of what can be seen as a somewhat difficult and academic subject area put into real practice. It is indeed the art of the possible in action and its applications are wide and numerous. 

Urszula Domahska has been professor. Faculty of Chemistry, Warsaw University of Technology since February 1995. She has been the Head of the Physical Chemistry Division since September 1991 and vice director of the Institute of Fundamental Chemistry (1988-1990). She had long-term scientific visits as visiting professor Laboratoire De Thermodynamique Ft D Analyse Chimique, University of Metz, France University of Turku, Finland Faculty of Science, Department of Chemistry, University of Natal, South Africa Department of Chemical Engineering, Louisiana State University, United States. Her interests have included such areas of physical chemistry as thermodynamics, especially thermodynamics of phase equilibria, VLE, LLE, SLE, high-pressure SLE, separation science, calorimetry, correlation and prediction of physical-chemical properties, and ionic liquids. She is a member of the Polish Chemical Society member of the Polish Association of Calorimetry and Thermal Analysis member of lUPAC Commission on Solubility member of International Association of Chemical Thermodynamics and scientific advisor at the Journal of Chemical Engineering Data. 

The purpose of phase equilibria calculations is to predict the thermodynamic properties of mixtures, avoiding direct experimental determinations, or to extrapolate the existing data to different temperatures and pressures. The basic requirements for performing any thermodynamic calculation are the choice of the appropriate thermodynamic model and knowledge of the parameters required by the model. In the case of high pressure phase equilibria, the thermodynamic model used is generally an equation of state which is able to describe the properties of both phases. 

In the next two chapters, we use thermodynamic relationships summarized in Chapter 1 la to delve further into the world of phase equilibria, using examples to describe some interesting effects. As we do so, we must keep in mind that our discussion still describes only relatively simple systems, with a much broader world available to those who study such subjects as critical phenomena, ceramics, metal alloys, purification processes, and geologic systems. In this chapter, we will limit our discussion to phase equilibria of pure substances. In Chapter 14, we will expand the discussion to describe systems containing more than one component. 

Oonk,H.A. 1981. Phase Theory The Thermodynamics of Heterogeneous Equilibria. Amsterdam Elsevier. 

In principle, mixtures containing a very large number of components behave in a way described by the same general laws that regulate the behavior of mixtures containing only a comparatively small number of components. In practice, however, the procedures for the description of the thermodynamic and kinetic behavior of mixtures that are usually adopted for mixtures of a few components rapidly become cumbersome in the extreme as the number of components grows. As a result, alternate procedures have been developed for multicomponent mixtures. Particularly in the field of kinetics, and to a lesser extent in the field of phase equilibria thermodynamics, there has been a flurry of activity in the last several years, which has resulted in a variety of new results. This article attempts to give a reasoned review of the whole area, with particular emphasis on recent developments. 

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