Vapor pressure phase diagrams

Energy and Phase Changes Heating Curves Vapor Pressure Phase Diagrams The Solid State... 

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/... 

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... 

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. 

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

Phase Behavior. One of the pioneering works detailing the phase behavior of ternary systems of carbon dioxide was presented ia the early 1950s (12) and consists of a compendium of the solubiHties of over 260 compounds ia Hquid (21—26°C) carbon dioxide. This work contains 268 phase diagrams for ternary systems. Although the data reported are for Hquid CO2 at its vapor pressure, they yield a first approximation to solubiHties that may be encountered ia the supercritical region. Various additional sources of data are also available (1,4,7,13). 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (soHd line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, C , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are CO2—/ -hexane and CO2—benzene. More compHcated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (Hquid—Hquid) immiscihility lines, and even three-phase (Hquid—Hquid—gas) immiscihility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include CO2—hexadecane and CO2—H2O Class IV, CO2—nitrobenzene Class V, ethane—/ -propanol and Class VI, H2O—/ -butanol. 

Phase relationships ia the system K O—B2O2—H2O have been described and a portion of the phase diagram is given ia Figure 8. The tetrahydrate, which can be dried at 65°C without loss of water of crystallisation, begias to dehydrate between 85 and 111°C, depending on the partial pressure of water vapor ia the atmosphere. This conversion is reversible and has a heat of dehydration of 86.6 kj/mol (20.7 kcal/mol) of H2O. Thermogravimetric curves iadicate that two moles of water are lost between 112 and 140°C, one more between 200 and 230°C and the last between 250 and 290°C (121). 

Carbon disulfide is completely miscible with many hydrocarbons, alcohols, and chlorinated hydrocarbons (9,13). Phosphoms (14) and sulfur are very soluble in carbon disulfide. Sulfur reaches a maximum solubiUty of 63% S at the 60°C atmospheric boiling point of the solution (15). SolubiUty data for carbon disulfide in Hquid sulfur at a CS2 partial pressure of 101 kPa (1 atm) and a phase diagram for the sulfur—carbon disulfide system have been published (16). Vapor—Hquid equiHbrium and freezing point data ate available for several binary mixtures containing carbon disulfide (9). 

FIG. 2-30 Entbalpy-concentration diagram for aqueous sulfuric acid at 1 atm. Reference states enthalpies of pure-bquid components at 32 F and vapor pressures are zero. NOTE It should be observed that the weight basis includes the vapor, which is particularly important in the two-phase region. The upper ends of the tie bnes in this region are assumed to be pure water. (Hougen and Watson, Chemical Process Principles, I, Wiley, New York, 1943. )... 

Solid-Fluid Equilibria The phase diagrams of binai y mixtures in which the heavier component (tne solute) is normally a solid at the critical temperature of the light component (the solvent) include solid-liquid-vapor (SLV) cui ves which may or may not intersect the LV critical cui ve. The solubility of the solid is vei y sensitive to pressure and temperature in compressible regions where the solvent s density and solubility parameter are highly variable. In contrast, plots of the log of the solubility versus density at constant temperature exhibit fairly simple linear behavior. 

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... 

Vapor—Liquid Systems. The vapor-liquid region of a pure substance is contained within the phase or saturation envelope on a P-V diagram (see Figure 2-80), A vapor, whether it exists alone or in a mixture of gases, is said to be saturated if its partial pressure (P.) equals its equilibrium vapor pressure (P, ) at the system temperature T. This temperature is called the saturation temperature or dew point T ... 

Point A on a phase diagram is the only one at which all three phases, liquid, solid, and vapor, are in equilibrium with each other. It is called the triple point. For water, the triplepoint temperature is 0.01°C. At this temperature, liquid water and ice have the same vapor pressure, 4.56 mm Hg. 

In the three areas of the phase diagram labeled solid, liquid, and vapor, only one phase is present. To understand this, consider what happens to an equilibrium mixture of two phases when the pressure or temperature is changed. Suppose we start at the point on AB... 

Case I. At sufficiently low pressures, the solubility curve does not intersect the coexistence curve. In this case, the gas solubility is too low for liquid-liquid immiscibility, since the coexistence curve describes only liquid-phase behavior. Stated in another way, the points on the coexistence curve are not allowed because the fugacity f2L on this curve exceeds the prescribed vapor-phase value f2v. The ternary phase diagram therefore consists of only the solubility curve, as shown in Fig. 28a where V stands for vapor phase. 

Case III. As the pressure increases still further, the solubility curve intersects larger liquid-liquid regions until the critical solution pressure of the system has been reached. Above this critical pressure, no vapor phase exists, and the phase diagram consists of only the coexistence curve, as shown in Fig. 28c. In Fig. 28, L, and L2 stand for the two liquid phases and F stands for a fluid phase. 

Figure 8.1 Phase diagram for CCF. Point (a) is the critical point and point (b) is the triple point. Line ab gives the vapor pressure of the liquid, line be gives the vapor pressure of the solid, and line bd gives the melting temperature as a function of pressure.

Tin also has a vapor phase, but its vapor pressures are so low that the vapor phase does not show on this diagram. 

At high pressures, solid II can be converted (slowly) to solid III. Solid III has a body-centered cubic crystal structure. Line bd is the equilibrium line between solid II and solid III, while line be is the melting line for solid III.P A triple point is present between solid II, solid III, and liquid at point b. Two other triple points are present in this system, but they are at too low a pressure to show on the phase diagram. One involves solid II, liquid, and vapor while the other has solid I, solid II, and vapor in equilibrium. 

In Figure 8.15, a two-phase (liquid + vapor) region is again enclosed by a liquid line and a vapor line. However, the lines have inverted from those in the pressure against mole fraction phase diagram, with the vapor line now on top and the liquid line on the bottom. At temperatures below the liquid line, only liquid is present while above the vapor line, only vapor is present. 

A boiling point phase diagram such as that shown in Figure 8.15 can be better understood by taking an example in which we start with a liquid mixture with temperature and mole fraction given by a point such as point a. Heating the liquid at a constant atmospheric pressure, in this case 101.3 kPa, causes the temperature to rise along the vertical dotted line until point b is reached. At this temperature, the vapor pressure of the mixture has become equal to... 

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