Phase equilibria, homogeneous fluids

Because the macroscopic-intensive properties of homogeneous fluids in equilibrium states ate functions of T, P, and composition, it follows that the total property of a phase fiM can be expressed functionally as in equation 113 ... 

The formulas presented here are valid for fluids at a homogeneous one-phase equilibrium state. They are not to be directly apphed to a fluid at an unstable state, for ordinary interest is not on the unstable fluid as a homogeneous phase, but on the saturated phases that separate from the unstable fluid. Separate calculations on the separated phases need to be performed with the eos-derived formulas for the individual saturated phases, and summed if desired. The calculations to find the saturated equilibrium phases are the subject of Section 4.4. 

As pointed out in the previous chapter, the separation of a homogeneous fluid mixture requires the creation of another phase or the addition of a mass separation agent. Consider a homogeneous liquid mixture. If this liquid mixture is partially vaporized, then another phase is created, and the vapor becomes richer in the more volatile components (i.e. those with the lower boiling points) than the liquid phase. The liquid becomes richer in the less-volatile components (i.e. those with the higher boiling points). If the system is allowed to come to equilibrium conditions, then the distribution of the components between the vapor and liquid phases is dictated by vapor-liquid equilibrium considerations (see Chapter 4). All components can appear in both phases. 

Fig. 2. Phase diagram describing lateral phase separations in the plane of bilayer membranes for binary mixtures of dielaidoylphosphatidylcholine (DEPC) and dipalmitoyl-phosphatidylcholine (DPPC). The two-phase region (F+S) represents an equilibrium between a homogeneous fluid solution F (La phase) and a solid solution phase S presumably having monoclinic symmetry (P(J. phase) in multilayers. This phase diagram is discussed in Refs. 19, 18, 4. The phase diagram was derived from studies of spin-label binding to the membranes.

Some components in a gas or liquid interact with sites, termed adsorption sites, on a solid surface by virtue of van der Waals forces, electrostatic interactions, or chemical binding forces. The interaction may be selective to specific components in the fluids, depending on the characteristics of both the solid and the components, and thus the specific components are concentrated on the solid surface. It is assumed that adsorbates are reversibly adsorbed at adsorption sites with homogeneous adsorption energy, and that adsorption is under equilibrium at the fluid- adsorbent interface. Let (m" ) be the number of adsorption sites and (m 2) the number of molecules of A adsorbed at equilibrium, both per unit surface area of the adsorbent. Then, the rate of adsorption r (kmol m s ) should be proportional to the concentration of adsorbate A in the fluid phase and the number of unoccupied adsorption sites. Moreover, the rate of desorption should be proportional to the number of occupied sites per unit surface area. Here, we need not consider the effects of mass transfer, as we are discussing equilibrium conditions at the interface. At equilibrium, these two rates should balance. Thus,... 

In Chap. 6 we treated the thermodynamic properties of constant-composition fluids. However, many applications of chemical-engineering thermodynamics are to systems wherein multicomponent mixtures of gases or liquids undergo composition changes as the result of mixing or separation processes, the transfer of species from one phase to another, or chemical reaction. The properties of such systems depend on composition as well as on temperature and pressure. Our first task in this chapter is therefore to develop a fundamental property relation for homogeneous fluid mixtures of variable composition. We then derive equations applicable to mixtures of ideal gases and ideal solutions. Finally, we treat in detail a particularly simple description of multicomponent vapor/liquid equilibrium known as Raoult s law. 

When a pure liquid is placed in an evacuated bulb, molecules will leave the liquid phase and enter the gas phase until the pressure of the vapor in the bulb reaches a definite value, which is determined by the nature of the liquid and its temperature. This pressure is called the vapor pressure of the liquid at a given temperature. The equilibrium vapor pressure is independent of the quantity of liquid and vapor present, as long as both phases exist in equilibrium with each other at the specified temperature. As the temperature is increased, the vapor pressure also increases up to the critical point, at which the two-phase system becomes a homogeneous, one-phase fluid. 

As indicated earlier, the state of a pure homogeneous fluid is fixed whenever two intensive tliemiodynamie properties are set at definite values. In contrast, when two phases are in equilibrium, the state of the system is fixed when only a single property is speeified. For example, a mixture of steam and liquid water in equilibrium at 101.325 kPa ean exist only at 373.15 K (100°C). It is impossible to change the temperature without also ehanging the pressure if vapor and liquid are to eontinue to exist in equilibrium. 

In general, any substance that is above the temperature and pressure of its thermodynamic critical point is called a supercritical fluid. A critical point represents a limit of both equilibrium and stability conditions, and is formally delincd as a point where the first, second, and third derivatives of the energy basis function for a system equal zero (or, more precisely, where 9P/9V r = d P/dV T = 0 for a pure compound). In practical terms, a critical point is identifled as a point where two or more coexisting fluid phases become indistinguishable. For a pure compound, the critical point occurs at the limit of vapor-Uquid equilibrium where the densities of the two phases approach each other (Figures la and lb). Above this critical point, no phase transformation is possible and the substance is considered neither a Uquid nor a gas, but a homogeneous, supercritical fluid. The particular conditions (such as pressure and temperature) at which the critical point of a substance is achieved are unique for every substance and are referred to as its critical constants (Table 1). 

Table I. lists a few possible advantages for conducting chemical synthesis in a supercritical environment. For example, supercritical fluids might provide a means to manipulate reaction environments by altering density and temperature to influence both reaction rate and selectivity. Futhermore, in a homogeneous supercritical phase, one can, in principle, eliminate interfacial transport limitations. Effectively, temperature and pressure are used to alter density in a way to influence both solvation dynamics and equilibrium solubility. With supercritical fluid solvents, there is the possibility of integrating both reaction and separation processes, which could lead to economic advantages over conventional synthetic processes carried out in liquid solvents.

In synthetic methods, a mixture of known composition is prepared and the phase equilibrium is observed subsequently in an equilibrium cell (the problem of analyzing fluid mixtures is replaced by the problem of synthesizing them). After known amounts of the components have been placed into an equilibrium cell, pressme and temperature are adjusted so that the mixture is homogeneous. Then temperature or pressure is varied until formation of a new phase is observed. This is the common way to observe cloud points in demixing polymer systems. No sampling is necessary. Therefore, the experimental equipment is often relatively simple and inexpensive. For multicomponent systems, experiments with synthetic methods yield less information than with analytical methods, because the tie lines carmot be determined without additional experiments. This is specially trae for polymer solutions where fractionation accompanies demixing. 

For type 4b the pressure maximum of the LGSn curve is so pronounced that the critical curve LG is cut twice at the critical end points C and E between C and E pure solid component II is in equilibrium with a homogeneous, highly compressed, fluid phase. This type has been detected in the HjO + SiOz system, the critical end point E being situated at 1080 °C, 970 MPa, and 74 mass per cent Si02. ... 

A method of sharp drop in the amplitude of vibration of the tube in a vibrating tube densimeter (VTFD in Table 1.1) was suggested by Crovetto and Wood (1991) for experimental determination of phase boundary and phase transition from homogeneous fluid to liquid-gas equilibrium. 

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