Vapor-liquid-solid equilibria

The critical point is unique for (vapor + liquid) equilibrium. That is, no equivalent point has been found for (vapor + solid) or (liquid + solid) equilibria. There is no reason to suspect that any amount of pressure would eventually cause a solid and liquid (or a solid and gas) to have the same //m, Sm, and t/m. with an infinite o and at that point. mC02 was chosen for Figure 8.1 because of the very high vapor pressure at the (vapor + liquid + solid) triple point. In fact, it probably has the highest triple point pressure of any known substance. As a result, one can show on an undistorted graph both the triple point and the critical point. For most substances, the triple point is at so low a pressure that it becomes buried in the temperature axis on a graph with a pressure axis scaled to include the critical point. 

Equations of State. Equations of state having adjustable parameters are often used to model the pressure—volume—temperature (PVT) behavior of pure fluids and mixtures (1,2). Equations that are cubic in specific volume, such as a van der Waals equation having two adjustable parameters, are the mathematically simplest forms capable of representing the two real volume roots associated with phase equilibrium, or the three roots (vapor, liquid, solid) characteristic of the triple point. 

An extensive process data base has been accumulated which includes (1) vapor-liquid-solid equilibrium data for binary... 

Equilibrium calculations for electrolyte solutions include speciation equilibrium, vapor-liquid equilibrium, solid-liquid equilibrium, and liquid-liquid equilibrium. As an example of the first three types of equilibria, we will consider the ternary H2O-NH3-CO2 system. 

Many industrial separation processes are based on phase equilibria. By this we mean that the various components of the mixtures present in the (vapor, liquid, solid) phases are in equilibriinn. This is a dynamic equilibriinn and equal mnnbers of components are being transferred continuously from one phase to the other thus the concentrations at equilibriinn do not change. To design the separation processes in industry, e.g., finding the height and number of trays of a distillation column, we need to know the concentrations at equilibrium at any temperature and pressure. 

Consider first the schematic P-T and P-x diagrams for the naphthalene-ethylene system. Figure 3.18b depicts the solubility behavior of naphthalene in supercritical ethylene at a temperature greater than the UCEP temperature. Solid-gas equilibria exist at low pressures until the three-phase SLV line is intersected. The equilibrium vapor, liquid, and solid phases are depicted as points on the horizontal tie line at pressure Pj. As the pressure is further increased a vapor-liquid envelope is observed for overall mixture concentrations less than Xl- A mixture critical point is observed for this vapor-liquid envelope, as described earlier. If the overall mixture composition is greater than Xl, then solid-gas equilibria are observed as the pressure is increased above Pj. 

P8.14 The vapor pressures of liquid anthracene and phenanthrene can be described by the Antoine equation using the Antoine parameters given below. Calculate the vapor-liquid-solid equilibrium (VLSE) along the solid-liquid saturation curve assuming ideal mixture behavior in the liquid phase. Melting points and heats of fusion of both components are given in example P8.1 above. Compare the vapor-liquid separation factors to those of an isothermal VLE data set at 220 "C (calculate assuming ideal liquid mixture behavior). 

In the previous chapter the necessary conditions for equilibrium were introduced in terms of the chemical potentials of the constituent species in the various phases. In this chapter we will relate these chemical potentials to a more convenient form, that of the equilibrium constant. Furthermore, we will discuss the application of equilibrium constants to the three types of equilibria which occur in our overall vapor-liquid-solid model ... 

The Equilibrium Compositions of Electrolyte Solutions (ECES) Program is an extensive general purpose vapor-liquid-solid prediction program for aqueous electrolyte systems. The package has a number of special features, including ... 

The Vapor-Liquid Equilibrium in Mixtures and Solutions Bibliographic Database covers the literature published between January 1900 and December 1995. It gives references on experimental vapor-liquid, vapor-liquid-liquid, and vapor-liquid-solid equilibrium measurements for 2- to 9-component system.s. Data on 2588 substances (and 80 other materials, e.g., polymers) in 30118 systems from 10878 references are stored in the database. 

The major application of vapor-liquid equilibrium (VLE) is distillation. The uses of liquid-liquid equilibrium (LLE), liquid-solid equilibrium (LSE), and gas-solid equilibrium (GSE) are much more diverse. They include extraction (both solid and liquid), decantation as a phase separation, vapor-phase deposition (the heart of the semiconductor business), and a host of environmental applications. In all of these applications the equilibrium state and the rate of approaching it are both important. This book discusses only the equiUb-rium state, normally asking what are the compositions of the equilibrium phases when the system has minimized its Gibbs energy, subject to the external constraints and the starting conditions. As with VLE, the working criterion for LLE, LSE, and GSE is that the fugacity of any individual species must be the same in aU the phases at equilibrium (Eq. 7.4). 

RMD Simulation of Chemical Nucleation (22). A series of microscopic computer experiments was performed using the cooperative isomerization model (Eq. 2). This system was selected for the trial simulations for several reasons First, only two chemical species are involved, so that a minimal number of particles is needed. Second, the absence of buffered chemicals (e.g., A and B in the Trimolecular reaction of the next section) eliminates the need for creation or destruction of particles in order to maintain constant populations (19., 22j. Third, the dynamical model of the cooperative mean-field interaction can be examined as a convenient means of introducing cubic or higher nonlinearity into molecular models based on binary collisions. Finally, the need for a microscopic simulation is most apparent for transitions between multi -pie macroscopic states. Indeed, the characterization of spatially localized fluctuations is of obvious importance to the understanding of nucleation phenomena. As for the equilibrium vapor-liquid and liquid-solid transitions, detailed simulations at the molecular level should provide deep physical insight into chemical nucleation processes whkh is unattainable from theory, higher-level simulation, or experiment. 

There are well-established methods for the characterization of membranes such as microscopic, bubble point, mercury porosimetry, liquid vapor equilibrium, gas-liquid equilibrium and liquid- solid equilibrium method. 

In this chapter, we shall discuss equilibrium liquid shapes on solid substrates, which demands equilibrium of liquid-vapor, liquid-solid, and vapor-solid. Not always do authors take into account all the three equilibria. The vapor-solid equilibrium determines the presence of adsorbed liquid layers on solid surfaces for both complete and partial wetting. Even at this moment, we and everything around are covered by a thin water film. The thickness of aqueous films depends on the humidity in the room, and the adsorption is exactly at equilibrium with the surrounding humidity, no matter how low or high. 

The maximum-likelihood method is not limited to phase equilibrium data. It is applicable to any type of data for which a model can be postulated and for which there are known random measurement errors in the variables. P-V-T data, enthalpy data, solid-liquid adsorption data, etc., can all be reduced by this method. The advantages indicated here for vapor-liquid equilibrium data apply also to other data. 

Vapor pressure is an important property of liquids, and to a much lesser extent, of solids. If a liquid is allowed to evaporate in a confined space, tlie pressure of Uie vapor phase increases as Uie amount of vapor increases. If Uiere is sufficient liquid present, Uie pressure in Uie vapor space eventually comes to equal exacUy Uie pressure exerted by the liquid at its own surface. At Uiis point, a dynamic equilibrium exists in wliich vaporization and condensation take place at equal rates and Uie pressure in Uie vapor space remains constant. The pressure exerted at equilibrium is called Uie vapor pressure of the liquid. Solids, like liquids, also exert a vapor pressure. EvaporaUon of solids (sublimaUon) is noUccable only for Uie few solids characterized by appreciable vapor pressures. 

The vapor pressure (P ) of a pure liquid at a given temperature (T) is the pressure exerted by its vapor in equilibrium with the liquid phase in a closed system. All liquids and solids exhibit unique vapor pressure-temperature curves. For instance, in Figure 2-79, lines BA and AC represent the equilibrium vapor pressure curves of the solid and liquid phases, respectively. 

Point A on a phase diagram is the only one at which all three phases, liquid, solid, and vapor, are in equilibrium with each other. It is called the triple point. For water, the triplepoint temperature is 0.01°C. At this temperature, liquid water and ice have the same vapor pressure, 4.56 mm Hg. 

The bulbs contain tleft to right) gaseous chlorine and the vapors in equilibrium with liquid bromine and solid iodine. 

The equilibrium pressure when (solid + vapor) equilibrium occurs is known as the sublimation pressure, (The sublimation temperature is the temperature at which the vapor pressure of the solid equals the pressure of the atmosphere.) A norma) sublimation temperature is the temperature at which the sublimation pressure equals one atmosphere (0.101325 MPa). Two solid phases can be in equilibrium at a transition temperature (solid + solid) equilibrium, and (liquid + liquid) equilibrium occurs when two liquids are mixed that are not miscible and separate into two phases. Again, "normal" refers to the condition of one atmosphere (0.101325 MPa) pressure. Thus, the normal transition temperature is the transition temperature when the pressure is one atmosphere (0.101325 MPa) and at the normal (liquid + liquid) solubility condition, the composition of the liquid phases are those that are in equilibrium at an external pressure of one atmosphere (0.101325 MPa). 

More than two phases can exist at equilibrium. For example, solid ice, liquid water, and water vapor exist together at the triple point of water. Various combinations of solid, liquid, and vapor can exist together to give triple points. ... 

Example 5.3 Predict the degrees of freedom for (a) pure liquid water and solid ice in equilibrium (b) pure liquid water, solid ice, and water vapor in equilibrium, and (c) solid ice in equilibrium with a liquid mixture of (ethanol + water). 

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