Phase diagrams, vapor-liquid

Fig. 3. Vapor—liquid-phase diagram for the HCl—H2 O system (5) where (-) represents the demarcation between the two-phase region and the gas...

The liquid line and vapor line together constitute a binary (vapor + liquid) phase diagram, in which the equilibrium (vapor) pressure is expressed as a function of mole fraction at constant temperature. At pressures less than the vapor (lower) curve, the mixture is all vapor. Two degrees of freedom are present in that region so that p and y2 can be varied independently. At pressures above the liquid (upper) curve, the mixture is all liquid. Again, two degrees of freedom are present so that p and. v can be varied independently/... 

Figure 8.14 Relationship between the (p. v) and (/. x) (vapor + liquid) phase diagrams for an ideal solution.

E8.8 (a) Construct the binary (vapor + liquid) phase diagram for an ideal... 

The influence of equilibrium chemical reactions on vapor-liquid phase diagrams. Chem. Engng. Sci.,... 

The principal tools have been density functional theory and computer simulation, especially grand canonical Monte Carlo and molecular dynamics [17-19]. Typical phase diagrams for a simple Lennard-Jones fluid and for a binary mixture of Lennard-Jones fluids confined within cylindrical pores of various diameters are shown in Figs. 9 and 10, respectively. Also shown in Fig. 10 is the vapor-liquid phase diagram for the bulk fluid (i.e., a pore of infinite radius). In these examples, the walls are inert and exert only weak forces on the molecules, which themselves interact weakly. Nevertheless,... 

Second, recall the many analogies that occur in the phase behavior of binary mixtures. For example, many features that occur on binary vapor-liquid phase diagrams have counterparts on liquid-solid diagrams. Some of those equivalent features are listed in Table 9.2. Furthermore, such equivalences include not only the kinds of behavior but may also extend to the general shapes of two-phase lines. That is, many... 

To have a simple example, we consider an alkane(l) + aromatic(2) mixture, modeled by the Redlich-Kwong equation (8.2.1). Certain vapor-liquid phase diagrams for this mixture were displayed and discussed in 9.3. Here our objective is to compute residual enthalpies for vapor and liquid that coexist in equilibrium in particular, we want to construct an isothermal plot of vs. x and y. (We will call this an hxy diagram, even though it is that is actually plotted.) To do so, we set the temperature, pick a liquid composition Xp and then perform a bubble-P calculation to obtain values... 

Barbosa, D., and M.F. Doherty, The Influence of Equilibrium Chemical Reactions on Vapor-Liquid Phase Diagrams, Chem. Eng. ScL, 43, 529 (1988a). 

FIGURE 8.4 Vapor-liquid phase diagrams of methane in a graphite pore with fluid-solid interaction of ejkg = 21.5 K and pore width of H = lOo, where o is diameter of methane. Temperature, T, and density, p, are in adimensional form in the plot. The open circles and dashed and solid lines represent the results from the simulations, MFT, and MFWDFT, respectively. The dotted curve represents the bulk vapor-liquid equilibrium obtained from simulation. (From Vishnyakov, A., et al. Langmuir 17 4451, 2001 Adapted from Peng, B. and Yu, Y.-X., J. Phys. Chem. B. 112 15407, 2008.)... 

A vapor-liquid phase diagram for a binary mixture of species 1 and 2 at 293 K is shown in the following figure. 

Data at two temperatures were obtained from Zeck and Knapp (1986) for the nitrogen-ethane system. The implicit LS estimates of the binary interaction parameters are ka=0, kb=0, kc=0 and kd=0.0460. The standard deviation of kd was found to be equai to 0.0040. The vapor liquid phase equilibrium was computed and the fit was found to be excellent (Englezos et al. 1993). Subsequently, implicit ML calculations were performed and a parameter value of kd=0.0493 with a standard deviation equal to 0.0070 was computed. Figure 14.2 shows the experimental phase diagram as well as the calculated one using the implicit ML parameter estimate. 

Chapter 14 describes the phase behavior of binary mixtures. It begins with a discussion of (vapor -l- liquid) phase equilibria, followed by a description of (liquid + liquid) phase equilibria. (Fluid + fluid) phase equilibria extends this description into the supercritical region, where the five fundamental types of (fluid + fluid) phase diagrams are described. Examples of (solid + liquid) phase diagrams are presented that demonstrate the wide variety of systems that are observed. Of interest is the combination of (liquid + liquid) and (solid 4- liquid) equilibria into a single phase diagram, where a quadruple point is described. 

Liquid-vapor TX phase diagram for an ideal solution of A in B. An isopleth isshown. The line segment D E F- G H represents the path of sequential fractional distillation steps through two and a half stages (or two and a half "theoretical plates"). 

The relationship between temperature and pressure for which two phases co-exist at equilibrium is called the vapor pressure curve. This diagram summarizes all the vapor-liquid phase behavior for a one-component system. 

If the temperature is raised to Tj, the phase behavior shown in figure 3.7e occurs. This temperature is greater than the UCEP temperature, therefore two phases exist as the pressure is increased as long as the critical mixture curve is not intersected. The two branches of the vapor-liquid phase envelope approach each other in composition at an intermediate pressure and it appears that a mixture critical point may occur. But as the pressure is further increased, a mixture critical point is not observed and the two curves begin to diverge. To avoid confusion, the phase behavior shown in figure 3.7e is not included in the P-T-x diagram. 

Generally, liquid-liquid phase equilibrium (or phase separation) occurs only over certain temperature ranges, bounded above by the upper consolute or upper critical solution temperature, and bounded below by the lower consolute or lower critical solution temperature. These critical solution temperatures are indicated on the liquid-liquid phase diagrams given here. All partially miscible mixtures should exhibit either one or both consolute temperatures however, the lower consolute temperature may be obscured by the freezing of the mixture, and the upper consolute temperature will not be observed if it is above the bubble point temperature of the mixture, as vaporization will have instead occurred. ... 

However, this maximum is for a solid phase, wherein spheres are so closely packed that long-range order is preserved and there is little, if any, net diffusion of spheres. For the pure hard-sphere Mid, the upper boxmd on T) is even less the fluid-solid phase transition occurs at ii = 2ii a /3 = 0.494 [12]. For it < 0.494 the substance is fluid and long-range order is disrupted by molecular motions. Without attractive forces between spheres, no vapor-liquid phase transition occurs and we refer to the material at Ti < 0.494 as merely "fluid." The hard-sphere phase diagram is shown in Figure 4.8. 

The equilibrium between a liquid and its vapor is not the only dynamic equilibrium that can exist between states of matter. Under appropriate conditions, a solid can be in equilibrium with its liquid or even with its vapor. A phase diagram is a graphic way to summarize the conditions under which equilibria exist between the different states of matter. Such a diagram also allows us to predict which phase of a substance is present at any given temperature and pressure. 

The dominant thermodynamically stable forms of carbon are graphite, diamond, liquid, and vapor. The phase diagram presented by Bundy [9] and adapted in Fig. 7... 

The SPC/E water model differs from the SPC only by reparametrization of the site electrostatic charges to account for the missing polarization correction [47]. The vapor-liquid phase envelope was determined through an indirect molecular dynamics approach [67] resulting in a better agreement with the phase diagram of real water in that the critical point of the SPC/E model is -65 IK and p 0.326g / cm. ... 

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