Phase equilibria systems

In this study, the stable phase equilibria system (NaCl - KQ - Na2B407 - K2B4O7 - H2O) at 298.15 K, a thermostatic shaker (model HZC2-C) whose temperature was controlled within 0.1 K was used for the measurement of phase equilibrium. 

In this example of the metastable phase equilibria system (NaCl - KCl - Na2B407 - K2B4O7 -H2O) at 308.15 K, the isothermal evaporation box was used. In an air-conditioned laboratory, a thermal insulation material box (70 cm long, 65 cm wide, 60 cm high) with an apparatus to... 

Palko AA, Drury JS, Begun GM (1976) Lithium isotope separation factors of some two-phase equilibrium systems. J Chem Phys 64 1828-1837... 

Phase of a two-phase equilibrium system, consisting of a polymer molecular-weight material, in which the polymer concentration is lower. 

Partial Miscibility in the Solid State So far, we have described (solid + liquid) phase equilibrium systems in which the solid phase that crystallizes is a pure compound, either as one of the original components or as a molecular addition compound. Sometimes solid solutions crystallize from solution instead of pure substances, and, depending on the system, the solubility can vary from small to complete miscibility over the entire range of concentration. Figure 14.26 shows the phase diagram for the (silver + copper) system.22 It is one in which limited solubility occurs in the solid state. Line AE is the (solid -I- liquid) equilibrium line for Ag, but the solid that crystallizes from solution is not pure Ag. Instead it is a solid solution with composition given by line AC. If a liquid with composition and temperature given by point a is... 

This equation is the well-known Clapeyron equation, and expresses the pressure of the two-phase equilibrium system as a function of the temperature. Alternatively, we could obtain dp/dT or dp/dP. When three phases are present, solution of the three equations gives the result that dT, dP, and dp are all zero. Thus, we find that the temperature, pressure, and chemical potential are all fixed at a triple point of a one-component system. 

The linear energy of the contact line in three-phase equilibrium system could have either positive or negative values. This does not violate the mechanical equilibrium stability condition in such systems. This is proved experimentally by determining k in the case of liquid black films in equilibrium with bulk solutions. The absolute values of k obtained are less than about 10 9 J m 1 (10 4 dyn) they are positive at lower and negative at higher electrolyte (NaCl) concentrations. 

Thus far we have not considered the fact that the initial composition of a chemical or phase equilibrium system may be known. Such information can be used in the formulation of species mass balances and the energy balance, which lead to additional equations relating the phase variables. Depending on the extent of initial information available and the number of phases present, the initial state information may or may not reduce the number of degrees of freedom of the system. This point is most easily demonstrated by reference to specific exapiples. so the effect of initial state information will be considered in the illustrations of the following chapters, not here. 

Toshev, B.V., Platikanov, D., and Scheludko, A., Line tension in three-phase equilibrium systems, Langmuir, 4, 489, 1988. 

For phase equilibrium study in this phase equilibrium system (NaCl - KCl - Na2B407 -K2B4O7 - H2O), the composition of the potassium ion in liquids and their corresponding wet... 

This section considers a binary liquid mixture of components A and B in equilibrium with either pure solid A or pure gaseous A. The aim is to find general relations among changes of temperature, pressure, and mixture composition in the two-phase equilibrium system that can be applied to specific situations in later sections. 

In a recent article [5] dealing with the properties of adsorbed water layers and the effect of adsorbed layers on interparticle forces, it was clearly stated that even under common room conditions (relative humidity in the region 40-60%), two or three adsorbed monolayers of water are often present on particles, dominating the interactions, and therefore the physical characteristics of the material. For a two-phase equilibrium system containing hydrophilic silica plates (surface of a-quartz covered by silanol groups) and water molecules, a molecular dynamic simulation expected at least one adsorbed monolayer to be present. Quite different behavior would be expected for less hydrophilic surfaces. The material character and chemical properties of solid materials are of crucial importance in the hydration interaction. Therefore, some common adsorbents which are Irequently used in aqueous electrolyte solutions are discussed separately. 

Chemical potential gradient driven phase-equilibrium systems... 

In headspace SPME a three-phase equilibrium system—the liquid, the headspace, and the fiber coating—is present in the sampling vial. Each equilibrium is governed by a partition coefficient the coating-headspace partition coefficient [Kf, headspace-sample partition coefficient (/Tfc) and coating-sample partition coefficient (/Q. The total mass of an analyte after equilibrium is distributed among the three phases ... 

When only the total system composition, pressure, and temperature (or enthalpy) are specified, the problem becomes a flash calculation. This type of problem requires simultaneous solution of the material balance as well as the phase-equilibrium relations. 

In this brief review of dynamics in condensed phases, we have considered dense systems in various situations. First, we considered systems in equilibrium and gave an overview of how the space-time correlations, arising from the themial fluctuations of slowly varying physical variables like density, can be computed and experimentally probed. We also considered capillary waves in an inliomogeneous system with a planar interface for two cases an equilibrium system and a NESS system under a small temperature gradient. 

Landolt-Bornstein Physikalische-chemische TabeUen, Eg. I, p. 303, 1927. Phase-equilibrium data for the binary system NH3-H2O are given by Clifford and Hunter,y. Fhys. Chem., 37, 101 (1933). 

Enthalpy and phase-equilibrium data for the binary system HCI-H2O are given by Van Nuys, Trans. Am. Inst. Chem. Engts., 39, 663 (1943). 

Critical Temperature The critical temperature of a compound is the temperature above which a hquid phase cannot be formed, no matter what the pressure on the system. The critical temperature is important in determining the phase boundaries of any compound and is a required input parameter for most phase equilibrium thermal property or volumetric property calculations using analytic equations of state or the theorem of corresponding states. Critical temperatures are predicted by various empirical methods according to the type of compound or mixture being considered. 

For the case of equilibrium with respect to chemical reaciion within a single-phase closed system, combination of Eqs. (4-16) and (4-271) leads immediately to... 

Vapor/liquid equilibrium (XT E) relationships (as well as other interphase equihbrium relationships) are needed in the solution of many engineering problems. The required data can be found by experiment, but such measurements are seldom easy, even for binaiy systems, and they become rapidly more difficult as the number of constituent species increases. This is the incentive for application of thermodynamics to the calculation of phase-equilibrium relationships. 

The N equations represented by Eq. (4-282) in conjunction with Eq. (4-284) may be used to solve for N unspecified phase-equilibrium variables. For a multicomponent system the calculation is formidable, but well suited to computer solution. The types of problems encountered for nonelectrolyte systems at low to moderate pressures (well below the critical pressure) are discussed by Smith, Van Ness, and Abbott (Introduction to Chemical Engineering Thermodynamics, 5th ed., McGraw-Hill, New York, 1996). 

All these processes are, in common, liquid-gas mass-transfer operations and thus require similar treatment from the aspects of phase equilibrium and kinetics of mass transfer. The fluid-dynamic analysis ofthe eqmpment utihzed for the transfer also is similar for many types of liquid-gas process systems. 

Ternary-phase equilibrium data can be tabulated as in Table 15-1 and then worked into an electronic spreadsheet as in Table 15-2 to be presented as a right-triangular diagram as shown in Fig. 15-7. The weight-fraction solute is on the horizontal axis and the weight-fraciion extraciion-solvent is on the veriical axis. The tie-lines connect the points that are in equilibrium. For low-solute concentrations the horizontal scale can be expanded. The water-acetic acid-methylisobutylketone ternary is a Type I system where only one of the binary pairs, water-MIBK, is immiscible. In a Type II system two of the binary pairs are immiscible, i.e. the solute is not totally miscible in one of the liquids. 

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

Most simulations have been performed in the mieroeanonieal, eanonieal, or NPT ensemble with a fixed number of moleeules. These systems typieally require an iterative adjustment proeess until one part of the system exhibits the required properties, like, eg., the bulk density of water under ambient eonditions. Systems whieh are equilibrated earefully in sueh a fashion yield valuable insight into the physieal and, in some eases, ehemieal properties of the materials under study. However, the speeifieation of volume or pressure is at varianee with the usual experimental eonditions where eontrol over the eomposition of the interfaeial region is usually exerted through the ehemieal potential, i.e., the interfaeial system is in thermodynamie and ehemieal equilibrium with an extended bulk phase. Sueh systems are best simulated in the grand eanonieal ensemble where partiele numbers are allowed to fluetuate. Only a few simulations of aqueous interfaees have been performed to date in this ensemble, but this teehnique will undoubtedly beeome more important in the future. Partieularly the amount of solvent and/or solute in random disordered or in ordered porous media ean hardly be estimated by a judieious equilibration proeedure. Chemieal potential eontrol is mandatory for the simulation of these systems. We will eertainly see many applieations in the near future. 

As an acidic oxide, SiOj is resistant to attack by other acidic oxides, but has a tendency towards fluxing by basic oxides. An indication of the likelihood of reaction can be obtained by reference to the appropriate binary phase equilibrium diagram. The lowest temperature for liquid formation in silica-oxide binary systems is shown below ... 

---