Phase diagrams vapor-pressure curves

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. 

An exceptional case of a very different type is provided by helium [15], for which the third law is valid despite the fact that He remains a liquid at 0 K. A phase diagram for helium is shown in Figure 11.5. In this case, in contrast to other substances, the solid-liquid equilibrium line at high pressures does not continue downward at low pressures until it meets the hquid-vapor pressure curve to intersect at a triple point. Rather, the sohd-hquid equilibrium line takes an unusual turn toward the horizontal as the temperature drops to near 2 K. This change is caused by a surprising... 

Temperature at the critical point (end of the vapor pressure curve in phase diagram) is termed critical temperature. At temperatures above critical temperature, a substance cannot be liquefied, no matter how great the pressure. Pressure at the critical point is called critical pressure. It is the minimum pressure required to condense gas to liquid at the critical temperature. A substance is still a fluid above the critical point, neither a gas nor a liquid, and is referred to as a supercritical fluid. The critical temperature and pressure are expressed in this text in -C and atm, respectively. 

KEY CONCEPT PROBLEM 11.17 The following phase diagram shows part of the vapor-pressure curves for a pure liquid (green curve) and a solution of the first liquid with a second volatile liquid (red curve). 

Figure 33 FT diagram showing the vapor-pressure curve for a pure substance and constant-volume lines in the single-phase regions.

The third plane identified in Fig. 12.1 is the vertical one perpendicular to the composition axis and indicated by MNQRSLM. When projected on a parallel plane, the lines from several such planes present a diagram such as that shown by Fig. 12.4. This is the PT diagram lines t/C, and KC2 are vapor-pressure curves for the pure species, identified by the same letters as in Fig. 12.1. Each interior loop represents the PT behavior of saturated liquid and of saturated vapor for a mixture of fixed composition the different loops are for different compositions. Clearly, the PT relation for saturated liquid is different from that for saturated vapor of the same composition. This is in contrast with the behavior of a pure species, for which the bubble line and the dew line coincide. At points A and B in Fig. 12.4 saturated-liquid and saturated-vapor lines intersect. At such points a saturated liquid of one composition and a saturated vapor of another composition have the same T and P, and the two phases are therefore in equilibrium. The tie lines connecting the coinciding points at A and at B are perpendicular to the PT plane, as illustrated by the tie line VX in Fig. 12.1. 

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. 

The critical point (end of a vapor pressure curve in a phase diagram) above this temperature, a gas cannot be liquefied. 

You know that a substance s state depends on temperature and that pressure affects state changes. To get a complete picture of how temperature, pressure, and states are related for a particular substance, you can look at a phase diagram. A phase diagram has three lines. One line is a vapor pressure curve for the liquid-gas equilibrium. A second line is for the liquid-solid equilibrium, and a third line is for the solid-gas equilibrium. All three lines meet at the triple point. The triple point is the only temperature and pressure at which three states of a substance can be in equilibrium. 

Figure 3.23 represents a two-component system with a fixed overall composition. You might wonder what a diagram would look like if we were to try to show systems of several compositions on one page. This has been done in Fig. 3.24. Here we have a composite p-T diagram, which is somewhat awkward to visualize, but represents the bubble-point and dew-point curves for various mixtures of ethane and heptane. These curves in essence are intersections of surfeces in the composition coordinate sliced out of a three-dimensional system and are stacked one in front of the other, although in two dimensions it appears that they intersect one another. The vapor-pressure curves for the two pure components are at the extreme sides of the diagrams as single curves (as you might expect). Each of the loops represents the two-phase area for a system of a specific composition. An infinite number of these surfaces are possible, of course. The dashed line indicates the envelope of the critical points for each possible composition. Although this line appears to be two-dimensional in Fig. 3.24, it actually is a three-dimensional line of which only the projection is shown in the figure.

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... 

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.

Let us clarify the nature of the fluid phases (liquid and gas) and of the critical point hy describing two different ways that a gas can he liquefied. A sample at point IVin the phase diagram of Figure 13-18b is in the vapor (gas) phase, below its critical temperature. Suppose we compress the sample at constant T from point IV to point Z. We can identify a definite pressure (the intersection of line IVZ with the vapor pressure curve AC) where the transition from gas to liquid takes place. If we go around the critical point by the path WXYZ, however, no such clear-cut transition takes place. By this second path, the density and other properties of the sample vary in a continuous manner there is no definite point at which we can say that the sample changes from gas to liquid. 

In P-T projections, the composition axis is collapsed into the pressure-temperature plane. The vapor pressure curve for component A is labeled LV(A) and that for component B is labeled LV(B). These curves terminate at the component critical points (L = V) designated as hollow circles. In Fig. 2, dew pressure and bubble pressure curves for an intermediate composition x intersect at a point on the (L = V) critical locus where the liquid and vapor phases become critically identical. Normally, dew and bubble pressure curves are not shown in projections. They are shown here so that the construction of the related P-x at fixed T, and T-x at fixed P, phase diagrams is clearly illustrated. Each critical point on the critical locus corresponds to a fixed composition. Points close to the critical point of component A are critical points for mixtures with high concentrations of A, whereas points closer to the critical point of... 

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. 

In Fig. 3.2, we show the pressure-temperature view of the phase diagram for binary mixtures of methane and ethane. The point Ci represents the critical point of pure methane, and the point C2 represents the critical point of pure ethane. The curve connecting the points A and Ci is the vapor pressure curve for pure methane the curve connecting points B and C2 is the vapor pressure curve for pure ethane. The dotted curve connecting the points C and C2 is the critical locus. The critical points of the mixtures, where the coexisting liquid and vapor phases become identical, lie on this critical locus. 

Skill 15.5 Analyzing vapor pressure curves and phase diagrams... 

The phase behavior of a pure substance may be depicted schematically on a pressure-temperature diagram as shown in Figure 1.1. The curve OC, the vapor pressure curve, separates the vapor and liquid phases. At any point on this curve, the two phases can coexist at equilibrium, both phases having the same temperature and pressure. Phase transition takes place as the curve is crossed along any path. Figure 1.1 shows two possible paths at constant pressure (path AB) and at constant temperature (path DE). At the critical point, C, the properties of the two phases are indistinguishable and no phase transition takes place. In the entire region above the critical temperature or above the critical pressure, only one phase can exist. 

A schematic of a pressure-temperature diagram for a fixed composition mixture is shown in Figure 2.1. The phase representation of a mixture on a P P diagram is bivariant rather than univariant as in the case of a pure-component vapor pressure curve. At temperature Tj and pressure Pj, represented by point A, the mixture is... 

Figure 8. P-T projections of main phase diagram types. The roman numbers correspond to the classification introduced by Scott and van Konynenburg the solid lines are critical curves the dashed lines are vapor pressure curves of pure components with critical points Ci and the dash dotted lines are three phase lineg C is critical end point.

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