Vapor curve

The liquid -vapor equilibria, along the vaporization curve is expressed as ... 

Many empidcal expressions have been proposed to represent the temperature dependence of the vapor—hquid saturation pressure, as shown by the vaporization curve of Figure 2. The most popular is the Antoine equation ... 

It is possible (with lower initial Led temperature, higher initial loading, or higher regeneration temperature or pressure) for the transition paths to contact the saturated vapor curve in Fig. 16-22 rather than intersect beneath it. For this case, liquid benzene condenses in the Led, and the effluent vapor is saturated during part of regeneration [Friday and LeVan, AIChE]., 30, 679 (1984)]. 

The reason for this simple relationship is that the concept of minimum reflux implies an infinite number of stages and thus no change in composition from stage to stage for an infinite number of stages each way from the pinch point (the point where the McCabe-Thiele operating lines intersect at the vapor curve for a well-behaved system, this is the feed zone). The liquid refluxed to the feed tray from the tray above is thus the same composition as the flash liquid. 

Figure 6.2. Pressure-vapor curve and superheat limit locus for propane (Reid 1979).

To use a thermodynamic graph, locate the fluid s initial state on the graph. (For a saturated fluid, this point lies either on the saturated liquid or on the saturated vapor curve, at a pressure py) Read the enthalpy hy volume v, and entropy from the graph. If thermodynamic tables are used, interpolate these values from the tables. Calculate the specific internal energy in the initial state , with Eq. (6.3.23). 

Referring to Figure 8-2, Henry s Law would usually be expected to apply on the vaporization curve for about the first 1 in. of length, starting with zero, because this is the dilute end, while Raoult s Law applies to the upper end of the curve. 

Increasing the temperature increases the vapor pressures and moves the liquid and vapor curves to higher pressure. This effect can best be seen by referring to Figure 8.14, which is a schematic three-dimensional representation for a binary system that obeys Raoult s law, of the relationship between pressure, plotted as the ordinate, mole fraction plotted as abscissa, and temperature plotted as the third dimension perpendicular to the page. The liquid and vapor lines shown in Figure 8.13 in two dimensions (with Tconstant)... 

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. 

A Moving from point R to P we begin with H20(g) at high temperature (>100°C). When the temperature reaches the point on the vaporization curve, OC, water condenses at constant temperature (100°C). Once all of the water is in the liquid state, the temperature drops. When the temperature reaches the point on the fusion curve, OD, ice begins to form at constant temperature (0°C). Once all of the water has been converted to H20(s), the temperature of the sample decreases slightly until point P is reached. 

Fig. 2.42 Condensation capacity of the condenser (surface area avaiiabie to condensation 1 rrf) as a function of intake pressure pp, of the water vapor. Curve a Cooling water temperature 12°C. Curve b Temperature 25 X. Consumption in both cases 1 mVh at 3 bar overpressure.

The vap. press, curve of solid iodine is indicated by PO, Fig. 16 that of liquid iodine by 00 and the effect of press, on the m.p. of iodine by ON. At the triple point 0 these curves meet. Fig. 18 shows a similar curve for water. The curve PO thus represents the sublimation curve or hoar-frost line OC. the boiling or vaporization curve, i.e. the effect of press, on the b.p. of the liquid. The same phenomenon occurs with water, iodine, etc., and the principle involved is the same as indicated in the law represented by Clapeyron-Clausius equations with respect to the lowering of the m.p. by an increase of press. Consequently, if the vap. press, of iodine be less than that of th,e triple point, the solid does not melt, but rather sublimes directly without melting at the triple point at 114-15° (89 8 mm.) and A. von Richter at 116 1° (90 mm.). According to R. W. Wood, if the condensation of iodine vapour occurs above —60°, a black granular deposit is formed, but below that temp, a deep red film is produced. 

Figure 2.9 Phase diagram for C02, showing solid-gas (S + G, sublimation ), solid-liquid (S + L, fusion ), and liquid-gas (L + G, vaporization ) coexistence lines as PT boundaries of stable solid, liquid, or gaseous phases. The triple point (triangle), critical point (x), and selected 280K isotherm of Fig. 2.8 (circle) are marked for identification. Note that the fusion curve tilts slightly forward (with slope 75 atm K-1) and that the sublimation and vaporization curves meet with slightly discontinuous slopes (angle < 180°) at the triple point. The dotted and dashed half-circle shows two possible paths between a liquid (cross-hair square) and a gas (cross-hair circle) state, one discontinuous (dashed) crossing the coexistence line, the other continuous (dotted) encircling the critical point (see text).

For a concentration value xB, the ordinate value (P or T) is to be read in each case from the vapor curve if xB = xBip is the vapor concentration, or from the liquid curve if xB = xBq is the liquid composition. In either case (7.42) or (7.43), a hole in the phase diagram results from use of a nonin tensive composition variable xB, whereas no such hole results if, as in (7.41a), only intensive plotting variables are chosen. 

The limiting linear behavior of the ideal P-xeq liquid diagram was previously described in Section 7.3.1. The corresponding P-xeap vapor curve can be added to give the full P-xB diagram for an ideal solution as follows ... 

At such a maximum (dotted line) the compositions of coexisting liquid and vapor phases necessarily coincide, and the two-phase hole closes as liquid and vapor curves meet at this point. Examples of such maxima occur frequently, for example, in alcohol-water mixtures, as in the C2H50H/H20 system at vh2o = 0.20. 

The vapor curve KLMNP gives the composition of the vapor as a function of the temperature T, and the liquid curve KKMSP gives the composition of die liquid as a function of die temperature. These two curves have a common point M. The state represented by M is that in which the two states, vapor and liquid, have the same composition xaB on die mole fraction scale. Because of die special properties associated with systems in this state, the Point M is called an azeotropic point and the system is said to form an azeotrope. In an azeotropic system, one phase may be transformed to the other at constant temperature, pressure and composition without affecting the equilibrium state. This property justifies the name azeotropy, which means a system diat boils unchanged. 

When a solution freezes, the solid is usually pure solvent. Thus the solid-vapor equilibrium (sublimation) P-T curve is unaffected by the presence of solute. The intersection of this curve and the liquid-vapor curve is the triple point (nearly the same temperature as the freezing point, which is measured at atmospheric pressure). Since a solute lowers the solvent vapor pressure, the triple point is shifted to lower temperature, as shown in Figure 11-2. Detailed calculations show that the decrease in freezing point for a dilute solution is proportional to the total molal concentration of solutes... 

---