Vapor-liquid boundary

FIGURE 8.10 The liquid-vapor boundary curve is a plot of the vapor pressure of the liquid (in this case, water) as a function of temperature. The liquid and its vapor are in equilibrium at each point on the curve. At each point on the solid liquid boundary curve (for which the slope is slightly exaggerated), the solid and liquid are in equilibrium. 

A feature of the phase diagram in Fig. 8.12 is that the liquid-vapor boundary comes to an end at point C. To see what happens at that point, suppose that a vessel like the one shown in Fig. 8.13 contains liquid water and water vapor at 25°C and 24 Torr (the vapor pressure of water at 25°C). The two phases are in equilibrium, and the system lies at point A on the liquid-vapor curve in Fig. 8.12. Now let s raise the temperature, which moves the system from left to right along the phase boundary. At 100.°C, the vapor pressure is 760. Torr and, at 200.°C, it has reached 11.7 kTorr (15.4 atm, point B). The liquid and vapor are still in dynamic equilibrium, but now the vapor is very dense because it is at such a high pressure. 

B Carbon dioxide is liquid at 60 atm and 25° C. When it is released into a room at 1 atm and 25° C, as the pressure lowers, the system reaches the liquid-vapor boundary, at which pressure the liquid is changed to vapor. The vaporization absorbs sufficient heat to cool the C02 to below its sublimation temperature at 1 atm. As a result, fine particles of solid C02 snow are produced. 

The line intersects the liquid-vapor boundary at about 0.25 atm. A vacuum pump capable of reducing P below 0.25 atm can be used to vaporize and remove the NH3 while keeping the temperature below 220 K. 

Cracking of PS because of capillary forces can be circumvented if one avoids crossing the liquid-vapor boundary in the phase diagram of the solvent. This is the case for supercritical drying [Ca4] or freeze drying [Ami], as shown in the inset of Fig. 6.12. 

Liquid-vapor boundary vapor pressure change by temperature Clausius-Clapeyron equation... 

Figure 3. Pressure-temperature-density diagram for liquid water. LV represents the liquid-vapor boundary CP represents the critical point. The isochors are labeled by density in g/cm. ...

The liquid-vapor boundary line in the phase diagram of any substance always stops abruptly at a certain point. Why ... 

But the simple no-flow picture of equation 4 can no longer hold in view of equations 7a and 7b. At the liquid-vapor boundary, the viscous shear force must balance the force imposed by surface tension gradients, rjdu/dz = da/dx (z = h). This boundary condition leads to a linear flow profile toward the drying line,... 

Temperatures are given on the lTS-90 scale. Liquid-vapor boundaries are indicated by horizontal lines. 

Plotting the tluee points, and coiuiecting the boiling point to the critical point witli both a straiglit line and a cur ed line, we see that the point (20 C, 18 atm) lies on the liquid side of die phase boundary. Tlie gas will condense imder these conditions. Tlie curved line better represents the liquid/vapor boundary for a typical phase diagram. See Figures 11.40 and 11.41 of the text. 

The supercritical extraction methods avoid the liquid/vapor boundary line by bringing the solvent above its supercritical point and then removing it from the sol-gel matrix as a supercritical fluid. In this state there is no liquid-vapor interface and therefore no capillary stresses due to the receding meniscus. The supercritical extraction technique was first developed by Kistler [22] in the 1930s. There are several types of supercritical extraction methods in use. They include high temperature, low temperature, and rapid supercritical techniques, each of which is described in more detail below. 

Heating the liquid-filled gel under pressure to above the critical point where no liquid-vapor boundary exists and releasing the vapor, that is, the aerogcl process. ... 

R. C. Tolman, The superficial density of matter at a liquid-vapor boundary,/ Chem. Phys., 17,118 (1949). 

The plot of the vapor pressure against temperature is also the liquid-vapor boundary in a phase diagram. To appreciate that interpretation, suppose we have a liquid in a cylinder fitted with a piston. If at some temperature we apply a pressure greater than the vapor pressure of the liquid, the vapor is eliminated, the piston rests on the surface of the liquid, and the system moves to one of the points in the liquid region of the phase diagram. If instead we reduce the pressure on the system to a value below the vapor pressure at that temperature, the system moves to one of the points in the vapor region of the diagram. At the vapor pressure itself, vapor and liquid are in equihbrium, and the state of the system is represented by a point on the phase boundary. 

Thermodynamics provides us with a way of predicting the location of the phase boundaries and relating their location and shape to the thermodynamic properties of the system. For instance, the shape of the vapor pressme cmve (the liquid-vapor boundary) is related to the enthalpy of vaporization of the hquid. 

For the liquid-vapor boundary (the vapor pressure curve), both the enthalpy and volume of vaporization are invariably positive, so the vapor pressure invariably increases with temperature (dp is positive if dT is positive). However, we have to be cautious because although the enthalpy of vaporization is not very sensitive to temperature, the volume of vaporization depends strongly on the temperature (through the effect of temperature on the volume of a gas). If we suppose that the vapor behaves as a perfect gas, then we show in the following Justification that the relation between a change in temperature and a change in vapor pressure is given by the Qausius-Clapeyron equation ... 

The liquid-vapor boundary of the phase diagram for water has a positive slope, and we shall see in Section 3.4(d) that the slope of the liquid-vapor phase boundary is much less steep than the slope of the ice-water phase boundary. 

The temperature at which the surface disappears is the critical temperature, T. The vapor pressure at the critical temperature is called the critical pressure, p, and the critical temperature and criticcd pressure together identify the critical point of the substance (see Table 3.1). If we exert pressure on a sample that is above its criticcd temperature, we produce a denser fluid. However, no surface appears to sepjffate the two pjffts of the Scunple and a single uniform phase, a supercritical fluid, continues to fill the contmner. That is, we have to conclude that a liquid cannot be produced by the application of pressure to a substance if it is at or above its critical temperature. That is why the liquid-vapor boundary in a phase diagram terminates at the critical point (Fig. 3.11). A supercritical fluid is not a true liquid, but it behaves like a liquid in many respects—for example, it has a density similar to that of a liquid. 

Figpre 9.2 Pressure-temperatvire phase diagram for H2O. Intersection of the dashed horizontal line at 1 atm pressnre with the sohd-liquid phase bonndary (point 2) corresponds to the melting point at this pressure (T = 0°C). Similarly, point 3, the intersection with the liquid-vapor boundary, represents the boiling point (T = 100°C). 

A typical plot of surface tension against the logarithm of concentration is shown in Fig. 4.2. The plot provides valuable practical information as well as theoretical insight. Initially, at low surfactant concentrations, the surface tension decrease is gradual (section A-B). With increasing surfactant concentration, the surface tension decreases more steeply and the curve becomes linear, as the liquid-vapor boundary becomes saturated with the adsorbed surfactant at the point B. The plot is linear (section B-C) until an inflection point C is reached. The inflection point usually corresponds to the critical micelle concentration (cmc)... 

In ideal systems, the surface area covered by mixtures of surfactants adsorbed at the liquid-vapor boundary is the sum of the areas covered by the components ... 

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