The Phase Diagram of Water

A schematic representation of the phase diagram for pure H20 (not to scale) is shown in Fig. 7.1. Let us examine the topological features of this diagram in terms of increasing complexity from single- to multiphase character. 

Homogeneous Areas For p = 1, the phase rule establishes that 

Heterogeneous Lines and Points For p — 2, the phase rule requires that 

On such a two-phase coexistence curve, the system has only a single degree of freedom, so that, for a given T, the pressure P is fixed, and vice versa. For example, if the temperature of a liquid-vapor system is chosen as T = 25°C, the corresponding P (read from the vapor-pressure curve) must be 23.8 Torr, as shown by the dotted line in Fig. 7.1. 

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  

Moving along any of the boundary lines, e.g. the vapor-solid line, we observe two phases at equilibrium. This is true until we reach a point, denoted TP in the diagram, at which a third phase appears. We now have three phases, vapor, liquid, and solid, at equilibrium. At this point, the phase-rule of thermodynamics tells us that there are zero degrees of freedom. In other words, we cannot move in the phase diagram while observing the three phases at equilibrium. The point at which the three phases exist at equilibrium is called the triple point (TP). This is a unique point in the phase diagram, and is characterized by P = 0.006 atm and t = O.OrC. o 

Note that since three phases are at equilibrium at the triple point, it must be the intersection of the three boundary lines. In other words, at the triple point, we have the equalities  

In Fig. 1.17, we have noted one more unique point labeled CP. This is the vapor-liquid critical point. When we increase the temperature but follow the vapor-liquid boundary line, i.e. when we move along the curve P = fviiT), we eventually reach a point where there is no distinction between the vapor and the liquid phases. The two phases become one. This point is characterized by the pressure Pcp = 218 atm and Tcp = 374.15°C. The molar volume of the water at the critical point is 59.1 cm mol .  

Note that both the triple and critical points are uniquely defined in the phase diagram. They are fundamentally different kinds of points. The triple point, here of vapor-liquid-ice //, is characterized by the coexistence of three phases at equilibrium. On the other hand, when we approach the critical point along the vapor-liquid boundary line, the two phases become more and more similar — in the sense that the densities of the two phases become closer and closer. At the critical point, the densities of the vapor and the liquid phases become identical, and hence, we observe only a single phase. Beyond the critical point, i.e. increasing either the pressure, or the temperature, there exists only one phase which is referred to as a fluid. The fluid may be viewed as either a highly compressed gas or as an expanded liquid. 

If we move along the solid-liquid boundary, do we encounter a new critical point The answer is no. We might encounter other triple points (see below) but never another critical point. The reason is that there exists a fundamental difference between a solid phase (any solid, not necessarily ice), and either a liquid or gaseous phase. Both the liquid and the gas phases are randomly disordered systems the two phases differ in their densities. When we move along the vapor-liquid curve, the difference 

12 (a) For substances that have phase diagrams resembling the one shown here (which is common for most substances, with the important exception of water), the triple point and the critical point mark the range of temperatures over which the substance can exist as a hquid. The shaded areas show the regions of temperature in which a liquid cannot exist as a stable phase, (b) A liquid cannot exist as a stable phase if the pressure is below that of the triple point for normal or anomalous liquids. 

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Freeze drying is mostly done with water as solvent. Fig. 1.1 sows the phase diagram of water and the area in which this transfer from solid to vapor is possible. This step is difficult, even for pure water. If the product contains two or more components in true solutions or suspensions, the situation can become so complicated that simplified model substances have to be used. Such complex systems occur ubiquitously in biological substances. 

We now look at the phase diagram of water in Figure 5.6, which will help us follow the modem method of removing the water from coffee to yield anhydrous granules. A low temperature is desirable to avoid charring the coffee. Water vapour can be removed from the coffee solution at any temperature, because liquids are always surrounded by their respective vapour. The pressure of the vapour is the saturated vapour pressure, s.v.p. The water is removed faster when the applied pressure decreases. Again, a higher temperature increases the rate at which the vapour is removed. The fastest possible rate occurs when the solution boils at a temperature we call T oii). 

A summary of our results on the phase diagram of water is shown in Figure 8. We find that the molecular to non-molecular transition in water occurs in the neighborhood of the estimated ZND state of HMX. This transition shows that the detonation of typical energetic materials occurs in the neighborhood of the molecular to non-molecular transition. 

Figure 3 The phase diagram of water. Critical temperature and pressure of light water, H2O, are 374 C and 22.1 MPa.

Draw a phase diagram of water. What is called a phase, component, and degree of freedom How many phases and degrees of freedom are there at different points of the phase diagram of water What is known as the freezing (boiling) point of pure substances ... 

A vacuum pump is attached to a flask of water at 0°C and 2 atm and the pressure on the liquid is decreased to 5 Torr. (a) Explain what would be observed, by using the phase diagram of water in Fig. 

Freeze-dried foods are prepared by freezing the food and removing water by subliming the ice at low pressure. Look at the phase diagram of water in Figure 10.28, and tell the maximum pressure (in mm Hg) at which ice and water vapor are in equilibrium. 

A substance that can exist in more than one crystalline form is said to exhibit allotropy, and the different forms are called allotropes. Figure 9 is the high-pressure part of the phase diagram of water and shows that water has a number of allotropes. The crystalline forms of water in the allotropes that melt are... 

C. Vega et al., Can simple models describe the phase diagram of water J. Phys. Condens. Matter 17, S3283-S3288 (2005)... 

The ideas underlying elemental structures models are to establish microstructures experimentally, to compute free energies and chemical potentials from models based on these structures, and to use the chemical potentials to construct phase diagrams. Jonsson and Wennerstrom have used this approach to predict the phase diagrams of water, hydrocarbon, and ionic surfactant mixtures [18]. In their model, they assume the surfactant resides in sheetlike structures with heads on one side and tails on the other side of the sheet. They consider five structures spheres, inverted (reversed) spheres, cylinders, inverted cylinders, and layers (lamellar). These structures are indicated in Fig. 12. Nonpolar regions (tails and oil) are cross-hatched. For these elemental structures, Jonsson and Wennerstrom include in the free energy contributions from the electrical double layer on the water... 

This paper deals with the degradation of substances like PVC, Tetrabromobisphenol A, y-HCH and HCB in supercritical water. This process is called "Supercritical Water Oxidation", a process which gained a lot of interest in the past. The difference between subcritical and supercritical processes is easy to recognize in the phase diagram of water. The vapor pressure curve of water terminating at the critical point, i.e. at 374 °C and 221 bar. The relevant critical density is 0.32 g/cm3. This corresponds to approx. 1/3 of the density of normal liquid water. Above the critical point, a compression of water without condensation, i.e. without phase transition is possible. It is within this range that supercritical hydrolysis and oxidation are carried out. The vapor pressure curve is of special importance in subcritical hydrolysis as well as in wet oxidation. 

A phase diagram of a pure substance is a plot of one system variable against another that shows the conditions at which the substance exists as a solid, a liquid, and a gas. The most common of these diagrams plots pressure on the vertical axis versus temperature on the horizontal axis. The boundaries between the single-phase regions represent the pressures and temperatures at which two phases may coexist. The phase diagrams of water and carbon dioxide are shown in Figure 6.1-1. 

At high pressure, there are many kinds of ice polymorphs and the phase diagram of water is complicated. In ice VlII and XI, protons are ordered while most of ice phases have proton disordered forms. In ambient condition, satisfied is the ice rule water exists as an H2O molecule and a proton sits between two adjacent oxygens. In ice Ih, the number of configurations arising from the proton-disordering is approximately (3/2) " for Nw molecule system[16. This is also true for ice Ic and some other ices except for proton-ordered forms. 

Fig. 2.3.1. Sketch of the phase diagram of water (not drawn to scale).

Point A on the phase diagram of water is the triple point for water. The triple point is the point on a phase diagram that represents the temperature and pressure at which three phases of a substance can coexist. All six phase changes can occur at the triple point freezing and melting evaporation and condensation sublimation and deposition. Point B is called the critical point. This point indicates the critical pressure and critical temperature above which water cannot exist as a liquid. If water vapor is at the critical temperature, an increase in pressure will not change the vapor into a liquid. 

The methods which are basically available for dehydration will be explained by employing the phase diagram of water (Fig. 2.60). The starting point shall be within the liquid phase. 

Figure 13-18 Some interpretations of phase diagrams, (a) The phase diagram of water. Phase relationships at various points in this diagram are described in the text, (b) Two paths by which a gas can be liquefied. (1) Below the critical temperature. Compressing the sample at constant temperature is represented by the vertical line WZ. Where this line crosses the vapor pressure curve AC, the gas liquefies at that set of conditions, two distinct phases, gas and liquid, are present in equilibrium with each other. These two phases have different properties, for example, different densities. Raising the pressure further results in a completely liquid sample at point Z. (2) Above the critical temperature. Suppose that we instead first warm the gas at constant pressure from W to X, a temperature above its critical temperamre. Then, holding the temperamre constant, we increase the pressure to point Y. Along this path, the sample increases smoothly in density, with no sharp transition between phases. From Y, we then decrease the temperature to reach final point Z, where the sample is clearly a liquid.

Caupin, F. (2005) Liquid-vapor interface, cavitation, and the phase diagram of water, Phys. Rev. Ell, 051605... 

The overall relationships among the solid, liquid, and vapor phases are best represented in a single graph known as a phase diagram. A phase diagram summarizes the conditions at which a substance exists as a solid, liquid, or gas. In this section we will briefly discuss the phase diagrams of water and carbon dioxide. 

Figure 11.40(a) shows the phase diagram of water. The graph is divided into three regions, each of which represents a pure phase. The line separating any two regions indicates conditions under which these two phases can exist in equilibrium. For example, the curve between the liquid and vapor phases shows the variation of vapor pressure with temperature. (Compare this curve with Figure 11.35.) The other two curves similarly indicate conditions for equilibrium between ice and liquid water and between ice and water vapor. (Note that the solid-liquid boundary line has a negative slope.) The point at which all three curves meet is called the triple point, which is the only condition under which all three phases can be in equilibrium with one another. For water, this point is at 0.01°C and 0.006 atm.

Fig. 12-1. Surface temperatures expected on the three planets Venus, Earth, and Mars as a function of the water vapor pressure. An increase in the vapor pressure increases the retention of infrared radiation in the atmosphere, raising the temperature via the greenhouse effect. Overlaid is the phase diagram of water. On Earth and Mars the starting (radiation equilibrium) temperatures are low enough for water to condense out when the temperature intersects the condensation curve. On Venus, the temperature rises more rapidly and runs away. [Adapted from Walker (1977), originally modeled by Rasool and DeBergh (1970).]...

The curve TK is not an infinite curve, it is terminated by the point K corresponding to the so-called critical state. The temperature and pressure corresponding to this state are called the critical temperature t and critical pressure p. In the critical states the densities of both states are equal and any differences between both phases — liquid and vapour — disappear, and they form one state only (the fluid zone ). At very high pressures the phase diagram of water becomes more complicated (Fig. 3.6). At such... 

Table 3.1. Triple-point relations for the phase diagram of water, H O...

In Fig. 7.1, the phase diagram of water is presented schematically. We emphasize that we are dealing with a single compound, or as addressed in thermodynamics, we are dealing with a system composed of one component. At low pressures, there is a region where water exists only as gas. At low pressures and low temperatures, water appears as ice. Between ice and gas, there is the liquid region. Every two regions are separated by border lines. 

The phase diagram of water as shown in Fig. 7.1 is not complete. It has been found out that at higher pressures there are further modifications of ice besides of... 

As you can see in the phase diagram of water shown above, there are three regions in the graph representing solid, liquid, and gas phases. The segment BC divides the solid and the liquid phases of water. This segment represents the equilibrium region between the solid and the liquid phases. Because water is... 

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