Liquid-vapor equilibrium line

If you plot the temperature and vapor pressure data given in Table 1, you reconstruct the liquid-vapor equilibrium line in the phase diagram of that liquid (Fig. 139). The equation of this line, and you might remember this from your freshman chemistry course, is the Clausius -Clapyron equation ... 

Fig. 3.2. A stylized phase diagram for a simple pure substance. The dashed line represents 1 atm pressure and the intersection with the solid-liquid equilibrium line represents the normal boiling point and the intersection with the liquid-vapor equilibrium line represents the normal boiling point.

The differentiation in this equation is carried out at constant pressure P. One must distinguish between this derivative and the derivative along the liquid-vapor equilibrium line. The relation between the two quantities is discussed in section 7.6. 

Figure 1.44 shows the values of AGf — (scan be either H2O or D2O) for water and heavy water in the entire range of the liquid state. Note that the values for D2O are systematically lower than those for H2O. As we increase the temperature along the liquid-vapor equilibrium line, the densities of the two phases become closer and closer. The values of AG — AG become smaller and smaller, and at the critical point they should approach zero. 

The starting point of this sequence is the reactive mixture xi on the chemical equilibrium line. This liquid mixture is in phase equilibrium with the vapor yl, which is totally condensed to x. Since this mixture is apart from the chemical equilibrium line, it reacts along the stoichiometric line to the equilibrium composition X2- As can be seen in figure 2.2, the difference of the slope between the stoichiometric and liquid-vapor equilibrium lines defines the orientation of the reactive distillation lines. This difference in behavior allows one to identify a point, at which both the phase equilibrium and stoichiometric lines are collinear and where liquid concentration remains unchanged. This special point (labelled A in figure 2.2) is conventionally referred to as reactive azeotrope and is surveyed in section 2.4. 

TABLE 7. Experimental Study of the Thermodynamic Properties of Freon-20 on the Liquid-Vapor Equilibrium Line (Saturation)... 

TABLE 8. Parameters of Fundamental Points on the Saturation Liquid-Vapor Equilibrium Line for Freon-20... 

Altunin V. V. Thermophysical properties of Freon-22 on the liquid-vapor equilibrium line.—Thermophysical Properties of Freons. Gosstandart SSSR, GSSSD, 1977, 1. 

Let us apply Equation (6.8) to the two-phase liquid-vapor equilibrium requirement for a pure substance, namely p = p T) only. This applies to the mixed-phase region under the dome in Figure 6.5. In that region along a p-constant line, we must also have T constant. Then for all state changes along this horizontal line, under the p—v dome, dg = 0 from Equation (6.8b). The pure end states must then have equal Gibbs functions ... 

Univariant equilibrium for which there is one degree of freedom, represents the equilibrium between two co-existing phases. Since there is only one degree of freedom, choosing a value for one external variable, e.g. temperature, determines the remaining variable in a dependent manner, and the locus of points represented on the phase diagram for univariant behavior must lie on a line or curve. Thus the curves on the unary phase diagram represent solid-liquid, solid-vapor, solid-solid, and liquid-vapor equilibrium. 

Liquid-Vapor Equilibrium. In order to quantify the vapor pressure-temperature relationship (bold line in Fig. 4.2) we start out by considering the liquid-vapor... 

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 ... 

To start with, let us consider a particular case of metastable states - a liquid superheated with respect to the liquid-vapor equilibrium temperature. For simplicity let us take a pure liquid at positive pressures, see Fig. 1. The region of superheated states is limited from below by the binodal Ts(p) and from above by the experimental line of attainable superheat, or, in other words, the line of spontaneous boiling-up T (p Cxp) of the liquid. An understandable limitation is imposed on the volume of superheated sample V and the time period Cxp of experiment. Naturally, the experimental time should be shorter than the life time t of the metastable state. 

Category VI phase behavior, shown in Fig. 10.3-3/, occurs with components that are so dissimilar that component 2 has a melting or triple point (Mj) that is well above the critical temperature of component 1. In this case there are two regions of solid-liquid-vapor equilibrium (SLVE). One starts at the triple point of pure component 2 (M ) and intersects the liquid-vapor critical line at the upper critical end point U. The second solid-liquid-vapor critical line starts below the melting point Mt and intersects the vapor-liquid critical line starting at component 1 at the lower critical end point L. Between the lower and upper critical points only solid-vapor (or solid-fluid) equilibrium exists. 

Fig. 11.1 (a) Craitact-mode AFM deflection images of PS in water. The presence of nanobubbles is obsCTved. Occasionally the bubbles are removed by the effect of the tip only a portion of the nanobubble appears in the image white arrows), (b) Schematic representation of a nanobubble in a water/polymer interface. The contact angle 0 is determined by the equilibrium between the horizontal forces in the triple solid-liquid-vapor contact line liquid-vapor 71.v, solid-liquid 75.1, and solid-vapor 75. interfacial tensions. The vertical component of the liquid-vapor interfacial tension, 71. sin(0), is equilibrated by a deformation of the substrate, as described in the text... 

Three-component mixtures represent the simplest type of multicomponent mixtures. The majority of multicomponent mixture peculiarities become apparent in three-component mixtures. This is why the three-component mixtures are best studied. Liquid-vapor equilibrium in the concentration triangle C3 is represented by a vector connecting a point of hquid composition with a point of equilibrium vapor composition x y. This vector is called a liquid-vapor tie-line. The opposite vector y X (vapor-liquid) is called a vapor-liquid tie-line. The tie-hnes field in the concentration triangle characterizes phase equihbrium in each of its points. 

From Eq. (1.11), it results that in each point of a residue curve a liquid-vapor tie-line is tangent to this Une. The residue curves are convenient for the description of phase equilibrium because as these hues are continuous and noncrossing. 

FigureZ. PhasedlagramofwaterproposedbySpeedy [18] plotted using the lAPWSEoS [25,26]. The solid curves are equilibrium lines, the dotted curve is the liquid-vapor spinodal, and the dashed curve the LDM. The circles show the experimental determination of the LDM at negative pressure [27]. When the spinodal and the LDM meet, the spinodal pressure reaches a minimum, and (for this EoS) retraces to positive pressure at low temperature. However, note that this would imply an improbable crossing between the spinodal and the metastable liquid-vapor equilibrium (see text for details).

FIGURE 6.5 The triple point and the critical point for H2O. The liquid-gas equilibrium line is the only one that ends at a certain set of conditions for all substances. For H2O, the line ends at 374°C and 215 bar. At higher temperatures or vapor pressures, there is no distinction between a liquid and a gas phase. 

Conditions for Phase Equilibrium shows a plot of the vapor-pressure curve, it can be viewed from a slightly different viewpoint the points on each curve represent all the temperature-pressure combinations at which two phases (solid -h gas, or liquid -h gas, depending on the curve) can be at equilibrium. Liquid and gaseous water, for example, can be at equilibrium only at a temperature and pressure represented by a point which is on the liquid-gas equilibrium line. 

Foot et al. [22] have determined experimentally the high-pressure phase behavior of the binary systems (butane adamantane) and (butane -I- diamantane). The phase behavior of these binary systems is shown schematically in Figure 1.7. Because the phase diagrams of pure adamantane and diamantane show a solid-solid (si + S2) transition line the curve representing the (solid diamondoids -I- liquid + vapor) equilibrium will split into two branches. One branch corresponds to the (si -f 1 -f v) equilibrium and the other branch corresponds to the (. 2 1 ) equilibrium. Both branches intersect at the (si S2) equilibrium line of the pure diamondoids. The... 

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

Prepared by reading the h and H values from the Jennings and Shannon Aqua-Ammonia Tables [35] at 260 psia and various wt % s of ammonia in the liquid. The tie lines connect the vapor compositions with the equilibrium liquid values. Figure 8-44. 

For assumed values of x (mol fraction of component under consideration in liquid) from bottoms to overhead, read values of y (vapor under operating conditions corresponding to x) and values of y (vapor in equilibrium with x) from the equilibrium line. 

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