Vapor pressure lowerings, saturation

Referring to Figure 8, temperature Tc is the chamber temperature and Ts is the surface temperature at the salt solution/vapor interface. The temperature of the chamber is well defined and is an experimental variable, whereas Ts must be higher than Tc due to condensation of vapor on the saturated solution surface. We can determine Ts by applying the Clausius-Clapeyron equation to the problem. Assume that the vapor pressures of the surface and chamber are equal (no pressure gradients), indicating that the temperature must be raised at the surface (to adjust the vapor pressure lowering of the saturated solution) to Pc (at Tc) = Ps (at Tc). However, there is a difference in relative humidity between the surface and the chamber, where RHC is the relative humidity in the chamber and RH0 is the relative humidity of the saturated salt solution, and we obtain... 

The Solvent Activity Calculation. A series of measurements on a Great Salt Lake (GSL) brine concentration sequence showed that the saturation vapor pressure lowering over a GSL brine at or near the labile saturation point should be about 9.5 millibars at 25°C. Application of the model to comparable GSL brine resulted... 

Table II. Saturation Vapor Pressure Lowerings for a Series of...

Measured values interpolated from graphically presented data giving vapor pressure lowering at 25°C as a function of brine density (31), e g is the saturated vapor pressure of the brine in millibars at 25°C. 

The equilibrium vapor pressure of a solution droplet containing a fixed mass of solute varies with droplet size in a way very different from that of a droplet of the pure solvent (Fig. 9.6). A droplet of pure solvent is always unstable at vapor pressures below saturation a solution droplet may be stable because of the vapor pressure lowering of the solute. The vapor pressure of the solvent can be expressed by the relation... 

This analysis can be applied to a small dry salt particle exposed to increasing relative humidity. The particle remains solid until, if it is hygroscopic, a characteristic relative humidity less than 100% at which it absorbs water and dissolves, forming a saturated solution. The relative humidities at which this occurs for saturated solutions of various salts are shown in Table 9.3. These values will vary with crystal size because of the Kelvin effect. For sodium chloride,. solution takes place at a relative humidity of 75% at which the diameter about doubles. With increasing relative humidity, the equilibrium relationship between drop size and vapor pressure is determined by the interaction of the Kelvin effect and vapor pressure lowering. 

Vapor-pressure osmometry is, from its name, compared with membrane osmometry by considering the vapor phase to act like the semipermeable membrane, however, from its principles it is based on vapor pressure lowering or boiling temperature elevation. Sinee the direct measure of vapor pressure lowering of dilute polymer solutions is impractieal because of the extreme sensitivity that is required, VPO is in widespread use for oligomer solutions (Mn less than 20,000 g/mol) by employing the thermoeleetrie method as developed by Hill in 1930. In the thermoelectric method, two matched temperature-sensitive thermistors are placed in a chamber that is thermostated to the measuring temperature and where the atmosphere is saturated with solvent vapor. If drops of pure solvent are placed on both thermistors, the thermistors will be at the same temperature (zero point ealibration). If a solution drop is placed on one thermistor, a temperature differenee AT oeeurs whieh is caused by condensation of solvent vapor onto the solution drop. From equilibrium thermodynamics follows that this temperature increase has its theoretical limit when the vapor pressure of... 

Adsorption may occur from the vapor phase rather than from the solution phase. Thus Fig. Ill-16 shows the surface tension lowering when water was exposed for various hydrocarbon vapors is the saturation pressure, that is, the vapor pressure of the pure liquid hydrocarbon. The activity of the hydrocarbon is given by its vapor pressure, and the Gibbs equation takes the form... 

Health and Safety Factors. Because of their high vapor pressures (methyl vinyl ether is a gas at ambient conditions), the lower vinyl ethers represent a severe fire hazard and must be handled accordingly. Contact with acids can initiate violent polymerization and must be avoided. Although vinyl ethers form peroxides more slowly than saturated ethers, distillation residues must be handled with caution. 

Fig. 1. Vapor pressure and relative humidity over CaCl solutions and solids. The straight horizontal lines ia the right-hand portion represent two soHd phases and a gas phase for vertical line iatersections. In addition, a soHd phase, saturated solution, and a vapor phase occur ia the regions between the vertical lines. The lower left-hand corner shows the ice solution line. The region ia between, with skewed isothermal lines, represents unsaturated solutions ...

Fig. 8. The (p, T) projection of a system in which the saturated vapor pressure curves cut the critical line at lower and upper critical end points,...

Ewald22 studied this system at 150° and 155°K. These temperatures are above the critical temperature of pure nitrogen, 126°K, but he found that they are below the lower critical end point of the mixture. The saturated vapor pressure of the system was 50 atm at 150°K and 57 atm at 155°K. The mole fraction of xenon in the saturated gas (X in Figs. 5 and 9) was 0.035 and 0.045 at these temperatures, respectively. 

Systems in which the saturated vapor pressure curve cuts a three-phase line of liquid + liquid + gas at a second quaternary point (solid + liquid + liquid + gas). Such systems have the first (or normal) quaternary point (solid + solid + liquid + gas) at lower temperatures and pressures (Fig. 13). Examples, ethane +... 

If applied pressure P is increased from condition 1 to 2, then a(pyjpj) = V (Pi — PSi/RT, where molar volume is V, the gas constant is R and temperature is T. From this, e.g., for water, a 1000-fold increase in P only approximately doubles saturated vapor pressure p. For hydrocarbons, p could be doubled by a lower pressure increase, in the order of 150 times or so however for moderate pressures, a tenfold increase in P even here only increases p by some 5%. Hence, for most practical situations, vapor pressure of a liquid can be considered as independent of applied pressure. Vapor-free liquid may need chemical potential represented differently (possibly by work done). 

The eoexistence of laumontite and wairakite is common in zone (1). If the saturated water vapor pressure is equal to 0.3 of total pressure (Zeng and Liou, 1982), the temperature for equilibrium reaetion (1—23) and saturated water vapor pressure are estimated to be 170°C and 230 bar, respectively (Liou, 1971b). Zeng and Liou (1982) have shown that yugawaralite is stable at less than 230°C and a total pressure of 500 bar, under the condition of quartz saturation. However, if the activity of Si02 is not unity, the boundary for reactions (1-24) and (1-25) may shift to lower temperatures. Liou (1971a) studied the equilibrium for reaetion (1-26) and showed that the equilibrium... 

When the instantaneous local pressure becomes negative in liquid irradiated by ultrasound, bubbles are generated because gas such as air dissolved in the liquid can no longer be dissolved in the liquid under negative pressure, which is called acoustic cavitation [5, 6]. For a static condition, vapor bubbles are generated when the static pressure is lower than the saturated vapor pressure, which is called boiling. In many cases of acoustic cavitation, the instantaneous local pressure should be negative because the duration of low pressure is short. 

The desorption isotherm approach is the second generally accepted method for determining the distribution of pore sizes. In principle either a desorption or adsorption isotherm would suffice but, in practice, the desorption isotherm is much more widely used when hysteresis effects are observed. The basis of this approach is the fact that capillary condensation occurs in narrow pores at pressures less than the saturation vapor pressure of the adsorbate. The smaller the radius of the capillary, the greater is the lowering of the vapor pressure. Hence, in very small pores, vapor will condense to liquid at pressures considerably below the normal vapor pressure. Mathematical details of the analysis have been presented by Cranston and Inkley (16) and need not concern us here. 

Saturation properties such as solubility in water and vapor pressure can be measured directly for solids and liquids. For certain purposes it is useful to estimate the solubility that a solid substance would have if it were liquid at a temperature below the melting point. For example, naphthalene melts at 80°C and at 25°C the solid has a solubility in water of 33 g/m3 and a vapor pressure of 10.9 Pa. If naphthalene was a liquid at 25°C it is estimated that its solubility would be 115 g/m3 and its vapor pressure 38.1 Pa, both a factor of 3.5 greater. This ratio of solid to liquid solubilities or vapor pressures is referred to as the fugacity ratio. It is 1.0 at the melting point and falls, in this case at lower temperatures to 0.286 at 25°C. 

---