Vapor-liquid coexistence diagram

Figure 3 Vapor pressure (a) and vapor-liquid coexistence diagram (b) for methyl fluoride from GEMC NVT simulations. The solid line indicates the experimental data and the symbols and dashed line are simulation results based on the ab initio pair potential. The closed symbol is the estimated critical point...

Fig. 2. Vapor pressure (a) and vapor-liquid coexistence diagram (b) for acetonitrile. The solid curve represents experimental data. Symbols are GEMC simulation results with the following potentials diamonds, potential by Bukowski et al. (1999) circles, potential by Cabaleiro-Lago and Rfos (1997).

The order of a transition can be illustrated for a fixed-stoichiometry system with the familiar P-T diagram for solid, liquid, and vapor phases in Fig. 17.2. The curves in Fig. 17.2 are sets of P and T at which the molar volume, V, has two distinct equilibrium values—the discontinuous change in molar volume as the system s equilibrium environment crosses a curve indicates that the phase transition is first order. Critical points where the change in the order parameter goes to zero (e.g., at the end of the vapor-liquid coexistence curve) are second-order transitions. 

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... 

Figure 1. Schematic phase diagram of a single-component substance showing the region of vapor-liquid coexistence. The full line is the coexistence locus (binodal). The dashed line is the locus of stability limits (spinodal), which separates the stable and unstable regions. Also shown are the destabilizing fluctuations in the metastable (nucleation), and unstable (spinodal decomposition) regions, with denoting the initial uniform density / , the radius of a nucleus, / , the radius of the critical nucleus. A, the wavelength of a density fluctuation, and the critical wavelength [109].

For fluids, the point on the phase diagram where the vapor-liquid coexistence curve ends. 

Fig. 27. Pressure—temperature projection of the phase diagram of a binary mixture of pentamer + monomer with = 1 (a) and = 0.9 (b). The filled symbols are simulation results for the critical line, while the empty symbols are simulation results for the vapor—liquid coexistence of the pure components. The short-dashed line is the critical line from TPTl, while the long-dashed line is the critical line from TPTl when parameters are rescaled to the critical point of the pure components. Full lines are TPTl predictions for the vapor pressure of the pure components (results from [244])...

The shaded region is that part of the phase diagram where liquid and vapor phases coexist in equilibrium, somewhat in analogy to the boiling line for a pure fluid. The ordinary liquid state exists on the high-pressure, low-temperature side of the two-phase region, and the ordinary gas state exists on the other side at low pressure and high temperature. As with our earlier example, we can transform any Type I mixture... 

In Fig. 8.8, we see that sulfur can exist in any of four phases two solid phases (rhombic and monoclinic sulfur), one liquid phase, and one vapor phase. There are three triple points in the diagram, where various combinations of these phases, such as monoclinic solid, liquid, and vapor or monoclinic solid, rhombic solid, and liquid, coexist. However, four phases in mutual equilibrium (such as the vapor, liquid, and rhombic and monoclinic solid forms of sulfur, all in mutual equilibrium) in a one-component system has never been observed, and thermodynamics can be used to prove that such a quadruple point cannot exist. 

The Density-Temperature Diagram. Consider the densities of the liquid and vapor that coexist in the two-phase region. If these densities are plotted as a function of temperature the curves AC and BO in Figure 22 are obtained. Points 4 and B represent the densities... 

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... 

Fig. 16. Calculated phase diagram of the soft-sphere plus mean-field model, showing the vapor-liquid (VLB), solid-liquid (SI.E ), and solid-vapor (SVE) coexistence loci, the superheated liquid spinodal (s), and the Kauzmann locus (K) in the pressure-temperature plane (P = Pa /e-,T =k T/ ). The Kauzmann locus gives the pressure-dependent temperature at which the entropies of the supercooled lit]uid and the stable crystal are equal. Note the convergence of the Kauzmann and spinodal loci at T = 0. See Debenedetti et al. (1999) for details of this calculation.

Figure 8.10 Schematic Pv diagram for a pure substance with the solid phase included. Shaded regions are metastable and unstable states. Vapor-liquid critical point (filled square) occurs at the maximum in the vapor-pressure curve. Filled circles are the triple-point voliunes at which solid, liquid, and vapor all coexist in three-phase equilibrium.

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