Equilibrium vaporization curve

Suppose some of this vapor is removed and condensed to a liquid. The vapor in equilibrium with this new solution would be still richer in the more volatile component, and the process could be continued further (see Fig. 11.16). This progression underlies the technique of separating a mixture into its pure components by fractional distillation, a process in which the components are successively evaporated and recondensed. What we have described so far corresponds to a constant-temperature process, but actual distillation is conducted at constant total pressure. The vapor pressure-mole fraction plot is transformed into a boiling temperature-mole fraction plot (Fig. 11.17). Note that the component with the lower vapor pressure (component 2) has the higher boiling point, T. If the temperature of a solution of a certain composition is raised until it touches the liquid line in the plot, the vapor in equilibrium with the solution is richer in the more volatile component 1. Its composition lies at the intersection of the horizontal constant-temperature line and the equilibrium vapor curve. 

Top Temperature. The temperature at the top of the tower must be just high enough to allow complete vaporization of the overhead product. A lower temperature will condense a part of the desired overhead product and incorporate it in the first side-draw product, and a higher temperature will cause the inclusion of high-boiling materials which are not desired in the overhead product. If the top of the tower is at atmospheric pressure and no steam is used, the 100 per cent point of the equilibrium vaporization curve of the overhead product is the top temperature. Such a rimple case is seldom encountered, and hence the top temperature at 760 mm must be corrected for the tower pressure and for the partial-pressure effect of steam or gas. 

The initial condensation temperature for the gasoline (100 per cent point on equilibrium vaporization curve) is 296 F (Fig. 16-5). 

The vapor pressure (P ) of a pure liquid at a given temperature (T) is the pressure exerted by its vapor in equilibrium with the liquid phase in a closed system. All liquids and solids exhibit unique vapor pressure-temperature curves. For instance, in Figure 2-79, lines BA and AC represent the equilibrium vapor pressure curves of the solid and liquid phases, respectively. 

Curve AB is a portion of the vapor pressure-temperature curve of liquid water. At any temperature and pressure along this line, liquid water is in equilibrium with water vapor. At point A on the curve, these two phases are in equilibrium at 0°C and about 5 mm Hg (more exactly, 0.01°C and 4.56 mm Hg). At B, corresponding to 100°C, the pressure exerted by the vapor in equilibrium with liquid water is 1 atm this is the normal boiling point of water. The extension of line AB beyond point B gives the equilibrium vapor pressure of the liquid above the normal boiling point. The line ends at 374°C, the critical temperature of water, where the pressure is 218 atm. 

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/... 

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. 

In porous media, liquid-gas phase equilibrium depends upon the nature of the adsorbate and adsorbent, gas pressure and temperature [24]. Overlapping attractive potentials of the pore walls readily overcome the translational energy of the adsorbate, leading to enhanced adsorption of gas molecules at low pressures. In addition, condensation of gas in very small pores may occur at a lower pressure than that normally required on a plane surface, as expressed by the Kelvin equation, which relates the radius of a curved surface to the equilibrium vapor pressure [25],... 

Kelvin s equation determines the equilibrium vapor pressure over a curved meniscus of liquid ... 

Figure 8.27 Experimental values of standard partial molal heat capacity of sodium acetate (A) and ethylene (B) in water as a function of P(°C) at pressures corresponding to water-vapor equilibrium. Interpolating curves generated by the HKF model equations. Reprinted from E. L. Shock and H. C. Helgeson, Geochimica et Cosmochimica Acta, 54, 915-946, copyright 1990, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

Adsorption studies leading to measurements of pore size and pore-size distributions generally make use of the Kelvin equation which relates the equilibrium vapor pressure of a curved surface, such as that of a liquid in a capillary or pore, to the equilibrium pressure of the same liquid on a plane surface. Equation (8.1) is a convenient form of the Kelvin equation ... 

Equilibrium Vaporization. The cesium release results presented in this chapter may also be used to demonstrate our earlier conclusion that equilbirium vaporization represents the upper limit for the fractional fission-product release as a function of sodium vaporization. Figure 6 shows three cesium release curves. Curve A was calculated from the Rayleigh Equation in conjunction with the partial molar excess free energy of mixing of infinitely dilute cesium—sodium solutions reported... 

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. 

Figure 9.9 Left BET adsorption isotherms plotted as total number of moles adsorbed, n, divided by the number of moles in a complete monolayer, ri7non, versus the partial pressure, P, divided by the equilibrium vapor pressure, Po. Isotherms were calculated for different values of the parameter C. Right Adsorption isotherms of water on a sample of alumina (Baikowski CR 1) and silica (Aerosil 200) at 20°C (P0 = 2.7 kPa, redrawn from Ref. [379]). The BET curves were plotted using Eq. (9.37) with C = 28 (alumina) and C = 11 (silica). To convert from n/nmo to thickness, the factors 0.194 nm and 0.104 nm were used, which correspond to n-mon = 6.5 and 3.6 water molecules per nm2, respectively.

PK r0 Equilibrium vapor pressure of a vapor in contact with a liquid having a curved surface (Pa)... 

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... 

From Table 13-5 it can be seen that the variables subject to the designer s control are C -H 3 in number. The most common way to utilize these is to specify the feed rate, composition, and pressure (C -H 1 variables) plus the drum temperature T2 and pressure P2. This operation will give one point on the equilibrium-flash curve shown in Fig. 13-26. This curve shows the relation at constant pressure between the fraction V/F of the feed flashed and the drum temperature. The temperature at V/F = 0.0 when the first bubble of vapor is about to form (saturated liquid) is the bubble-point temperature of the feed mixture, and the value at V/F = 1.0 when the first droplet of liquid is about to form (saturated liquid) is the dew-point temperature. 

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