Phase diagrams for water

FIGURE 8.6 The phase diagram for water (not to scale). The solid blue lines define the boundaries of the regions of pressure and temperature at which each phase is the most stable. Note that the freezing point decreases slightlv with increasing pressure. The triple point is the point at which three phase boundaries meet. The letters A and B are referred to in Example 8.3. 

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). 

FIGURE 8.9 The phase diagram for water drawn with a logarithmic scale for pressure, in order to show the different solid phases of water in the high-pressure region. 

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. 

FIGURE 8.12 A quantitative version of the phase diagram for water close to the critical point. Pressures are in atmospheres, except for point A. 

As discussed in Chapter 6, water forms strong hydrogen bonds and these lead to a number of important features of its atmospheric behavior. All three phases of water exist in the atmosphere, and the condensed phases can exist in equilibrium with the gas phase. The equilibria between these phases is summarized by the phase diagram for water. Fig. 7-9. 

The phase diagram for water, shown in Figure 11-39. illustrates these features for a familiar substance. The figure shows that liquid water and solid ice coexist at the normal freezing point, T = 273.15 K and P = 1.00 atm. Liquid water and water vapor coexist at the normal boiling point, P — 373.15 K and P — 1.00 atm. The triple point of water occurs at 7 = 273.16 K and P = 0.0060 atm. The figure shows that when P is lower than 0.0060 atm, there is no temperature at which water is stable as a liquid. At sufficiently low pressure, ice sublimes but does not melt. 

The phase diagram for water. The critical point is at 647 K, 218 atm, well off-scale on this graph. ... 

These effects can be displayed on a phase diagram that compares the behavior of pure solvent and a solution. Figure 12-13 shows such a phase diagram for water and aqueous solutions. 

The phase diagram for water, showing how the phase boundaries change when a nonvolatile solute dissolves in the liquid. 

C14-0133. The enthalpy of sublimation of Ice at 273.15 K Is not the simple sum of the enthalpies of fusion and vaporization of water, but it can be calculated using Hess law and an appropriate path that Includes fusion and vaporization. Devise such a path, show it on a phase diagram for water, and carry out the calculation, making reasonable assumptions If necessary (C(liquid water) = 75.3 7 mol K , and C(water vapor) = 33.6 K ). 

We now look at the phase diagram for water in Figure 5.10. Ice melts at 0 °C if the pressure is p° (as represented by T and Pi respectively on the figure). If the pressure exerted on the ice increases to P2, then the freezing temperature decreases to 7). (The freezing temperature decreases in response to the negative slope of the liquid-solid phase boundary (see the inset to Figure 5.10), which is most unusual virtually all other substances show a positive slope of (lp/dT.)... 

FIGURE 8.1 Phase diagram for water-gelatin-ethanol as a function of temperature. (Reprinted with permission from Elysee-Collen, B. and Lencki, R. (1996). J. Agric. Food Chem., 44, 1651-1657.)... 

Figure 8.7 shows the ternary phase diagram for water, hexanoic acid, and sodium dodecyl sulfate at 25 °C. Seven different areas are shown in the figure, which has been used to describe the solubilization of polar dirt by surfactant solutions in detergency applications. The following comments refer to these seven different regions and explain the labeling used in Figure 8.7 ...

FIG. 8.7 Ternary phase diagram for water (W), hexanoic acid (A), sodium dodecyl sulfate (S) at 25°C. See text for a description of the various regions. (Redrawn, with permission, from A. S. C. Lawrence, Chem. Ind., 44, 1764 (1961).)... 

FIG. 8.12 Rectangular figure shows the phase diagram for water-cyclohexane (at 5% surfactant) versus temperature. Superimposed ternary phase diagrams offer an interpretation of the phases present. (Redrawn, with permission, from M. L. Robbins, In Solution Chemistry of Surfactants, Vols. 1 and 2 (K. L. Mittal, Ed.), Plenum, New York, 1979.)... 

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 with each other. For example, the point at 80°C and 0.47 atm in the phase diagram for water... 

FIGURE 8.9 The phase diagram for water and the cooling curve for a sample initially at point A. The sample cools at constant pressure through B to ice at C. The pause in the decline of the cooling curve at B is due to the release of heat when the liquid freezes. 

FIGURE 8.10 The phase diagram for water shown with more numerical detail. C is the critical point. 

Distillation processes have a degree of flexibility not available to freezing processes in the choice of an operating temperature. The almost vertical ice-water line in the temperature-pressure phase diagram for water indicates essentially a fixed operating temperature. Similarly this is true for the hydrate-water line in the hydrate systems. The effect on vapor volume resulting from the relationship between vapor pressure and... 

Hydrate phase diagrams for water-hydrocarbon systems provide a convenient overview of the calculation types. These diagrams differ substantially from the normal hydrocarbon phase diagrams primarily due to hydrates and the hydrogen bonds inherent in aqueous systems. The phase diagrams of Section 4.1 provide an overview for the calculation methods in this chapter and the next. 

Hydrate Phase Diagrams for Water + Hydrocarbon Systems... 

Under some circumstances, (liquid + liquid) equilibria occur under conditions where it is also important to consider the (vapor + liquid) effects. For example, Figure 14.8 shows the phase diagram for (water + 1-butanol) at p = 101.3 kPa. Lines ac and be give the normal boiling temperatures for the mixtures. Since... 

A Quadruple Point Figure 14.20 shows phase diagrams for (water + acetonitrile) at five different pressures.16 The diagram in (a) at / = 0.1 MPa for this system is very similar to the (cyclohexane + methanol) diagram shown in Figure 14.19a that we described earlier, with a (liquid-I-liquid) equilibrium region present above the (solid + liquid) equilibrium curve for water. 

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