Equilibria coexisting liquid-vapor

Liquids Vapor pressure is the most important of the basic thermodynamic properties of fluids. It is the pressure of equilibrium, coexisting liquid and vapor phases at a specified temperature. The vapor pressure curve is a monotonic function of temperature from its minimum value (the triple point pressure) at the triple point temperature T, to its maximum value (the critical pressure) at Tc. 

Figure 4. The equilibrium fraction of monomers in the coexisting liquid-vapor phase of an associating fluid with one square-well bonding site. The liquid-phase fractions of monomers are on the left-hand side of the figure. The circles are data from RCMC-Gibbs ensemble simulations, and the lines are calculations from three different implementations of a theory for associating fluids. The solid line uses exact values of the reference fluid radial distribution function the dashed and long dashed-short dashed lines use the WCA and modified WCA approximations to the radial distribution function, respectively. (Reprinted with permission from Muller et al. [43]. Copyright 1995 American Institute of Physics.)...

The lines separating the regions in a phase diagram are called phase boundaries. At any point on a boundary between two regions, the two neighboring phases coexist in dynamic equilibrium. If one of the phases is a vapor, the pressure corresponding to this equilibrium is just the vapor pressure of the substance. Therefore, the liquid-vapor phase boundary shows how the vapor pressure of the liquid varies with temperature. For example, the point at 80.°C and 0.47 atm in the phase diagram for water lies on the phase boundary between liquid and vapor (Fig. 8.10), and so we know that the vapor pressure of water at 80.°C is 0.47 atm. Similarly, the solid-vapor phase boundary shows how the vapor pressure of the solid varies with temperature (see Fig. 8.6). 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

It has been proposed to define a reduced temperature Tr for a solution of a single electrolyte as the ratio of kgT to the work required to separate a contact +- ion pair, and the reduced density pr as the fraction of the space occupied by the ions. (M+ ) The principal feature on the Tr,pr corresponding states diagram is a coexistence curve for two phases, with an upper critical point as for the liquid-vapor equilibrium of a simple fluid, but with a markedly lower reduced temperature at the critical point than for a simple fluid (with the corresponding definition of the reduced temperature, i.e. the ratio of kjjT to the work required to separate a van der Waals pair.) In the case of a plasma, an ionic fluid without a solvent, the coexistence curve is for the liquid-vapor equilibrium, while for solutions it corresponds to two solution phases of different concentrations in equilibrium. Some non-aqueous solutions are known which do unmix to form two liquid phases of slightly different concentrations. While no examples in aqueous solution are known, the corresponding... 

What does it mean that (25°C, 23.8 Torr) is a point on the liquid-vapor coexistence line Consider a beaker of liquid water at 25°C, covered with a lid and allowed to come into equilibrium with its own vapor ... 

Fractional distillation can be represented on a liquid/vapor phase diagram by plotting temperature versus composition, as shown in Figure 11.18. The lower region of the diagram represents the liquid phase, and the upper region represents the vapor phase. Between the two is a thin equilibrium region where liquid and vapor coexist. 

Solid-liquid, solid-vapor and liquid-vapor equilibrium curves for pure water (solid curves) and for a solution (dashed curves). The triple point (where solid, liquid, and vapor coexist and at nearly the same temperature as the freezing point) is shifted to lower temperature for the solution. 

The minimum number of degrees of freedom for any system is zero. When F = 0, the system is invariant, and Eq. (2.12) becomes ir = 2 + N. This value of tt is the maximum number of phases which can coexist at equilibrium for a system containing N chemical species. When N - 1, this number is 3, and we have a triple point For example, the triple point of water, where liquid, vapor, and the common form of ice exist together in equilibrium, occurs at 0.01°C and 0.00610 bar. Any change from these conditions causes at least one phase to disappear. 

The application of Eq. (10.3) to specific phase-equilibrium problems requires use of models of solution behavior, which provide expressions for G or for the Hi as functions of temperature, pressure, and composition. The simplest of such expressions are for mixtures of ideal gases and for mixtures that form ideal solutions. These expressions, developed in this chapter, lead directly to Raoult s law, the simplest realistic relation between the compositions of phases coexisting in vapor/liquid equilibrium. Models of more general validity are treated in Chaps. 11 and 12. 

In most industrial processes coexisting phases are vapor and liquid, although liquid/liquid, vapor/solid, and liquid/solid systems are also encountered. In this chapter we present a general qualitative discussion of vapor/liquid phase behavior (Sec. 12.3) and describe the calculation of temperatures, pressures, and phase compositions for systems in vapor/liquid equilibrium (VLE) at low to moderate pressures (Sec. 12.4).t Comprehensive expositions are given of dew-point, bubble-point, and P, T-flash calculations. 

For a pure species coexisting liquid and vapor phases are in equilibrium when they have the same temperature, pressure, and fugacityJ... 

It is well known that the vapor pressure curves of the solid and liquid phases of a given substance meet at the triple point thus, in Fig. 16 the curve AO represents solid-vapor equilibria, OB is for liquid-vapor, and OC for solid-liquid equilibria. The three curves meet at the triple point O where solid, liquid and vapor can coexist in equilibrium. It will be observed that near the triple point, at least, the slope of the curve AO on the pressure-temperature diagram is greater than that of OB , in other words, near the... 

Figure 2.12 is the classic pressure-temperature (FT) representation of the phase changes of a pure component. There are three primary phases of pure components solid liquid, and vapor solid-solid transitions, liquid crystal phases, and so on, are also possible but will not be considered here. The solid lines represent the sublimation curve (solid —> vapor), the vapor pressure curve (liquid —> vapor) and the melting curve (solid liquid) of the pure component. The triangle represents the triple point, at which a solid, liquid and vapor coexist in equilibrium. The circle represents the pure component critical point, where the supercritical region begins. 

For ascertaining the process conditions of RESS and PGSS, it is essential to have knowledge of the equilibrium solubility of the solute in dense gas (SCF phase) and vice versa, and also the P-T trace for the solid-liquid-vapor (S-L-V) phase transition of the drug substance. If all three phases coexist, there is only a single degree of freedom for a binary system, and a P-T trace of the S-L-V equilibrium is sufficient to determine the phase equilibrium compositions. 

The extreme limit of high density of s is the pure liquid. Normally, the liquids of interest are either at room temperature and 1 atm pressure or along the liquid-vapor coexistence equilibrium line. Let l and g be the liquid and the gaseous phases of a pure component s at equilibrium. The Gibbs energy of... 

Figure 4.2 Variation of the vapor pressure, Pv, of a substance with the temperature, 7, showing the phase transition between solid, liquid and vapor phases. Two phases can coexist in equilibrium only at pressures and temperatures defined by the phase boundary lines in the phase diagram, such as liquid-vapor, solid-liquid and solid-vapor lines. The liquid-vapor phase boundary terminates at the critical point, 7C. All three phases can coexist in equilibrium only at the triple point, 73, which is the intersection of the three two-phase boundaries.

Comparison with experimental data shows that the complete local-composition equation preserves the quality of Wilson s equation in describing vapor-liquid equilibrium of completely miscible systems. There are no more than slight differences between the complete equation and Wilson s equation in the fitting of data. But the complete local-composition (CLC) equation extends Wilson s local-composition equation to partially miscible solutions. Good predictions of the coexistent liquid compositions of ternary mixtures based on the binary parameters have been found for water + ethyl acetate + ethanol, for water + methyl acetate + acetone, and for water + acrylonitrile + acetonitrile. 

One experimental observation in phase equilibrium is that the two coexisting equilibrium phases must have the same temperature and pressure. Clearly, the arguments given in Secs. 7.1 and 7.2 establish this. Another experimental observation is that as the pressure is lowered along an isotherm on which a liquid-vapor phase transition occurs, the actual volume-pressure behavior is as shown in Fig. 7.3-3, and not as in Fig. 7.3-2. 

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