Depression of the vapor pressure

Though not a general adsorption equilibrium model the Kelvin equation does provide the relationship between the depression of the vapor pressure of a condensable sorbate and the radius (r) of the pores into which it is condensing. This equation is useful for characterization of pore size distribution by N2 adsorption at or near its dew point. The same equation can also describe the onset of capillary condensation the enhancement of sorption capacity in meso- and macro-pores of formed zeolite adsorbents. 

The vapor pressures of all solutions of nonvolatile solutes in a solvent are less than that of the pure solvent. If we prepare solutions of different solutes in a given solvent by adding equal numbers of solute molecules to a fixed amount of solvent, as we do in preparing solutions of equal molality, we find that the depression of the vapor pressure is the same in every case in dilute solutions of nonvolatile nonelectrolytes. 

The depression of the vapor pressure. Solutions have a lower vapor pressure than the pure solvent, both compared at the same temperature. 

An analytical approach to the phenomen with regard to cryogenic pumps was taken by Jacobs, et al. Here a theoretical analysis of the depression of the vapor pressure was derived as a function of vapor volume and an analysis of the heat output due to friction was also considered. Included in this report was a considerable amount of test data on water, liquid nitrogen and liquid hydrogen which further emphasizes... 

RaouWs Experiments on the Depression of the Vapor Pressure of a Liquid... 

The depression of the activity may be measured in various ways. The most obvious would involve a measurement of the vapor pressure lowering, but this method is superseded by others both in accuracy and in simplicity of execution. The boiling point elevation and freezing point depression methods relegated vapor pressure measurement... 

The colligative properties of solutions are those properties that depend upon the number of dissolved molecules or ions, irrespective of their kind. They are the lowering of the vapor pressure, the depression of the freezing point, the elevation of the boiling point, and the osmotic pressure. These properties may be used in determining molecular weights of dissolved substances. 

Figure 3.16 is a phase diagram of the vapor pressure vs. the temperature in a water-nonvolatile solute system and illustrates the freezing point depression and the... 

The heat of vaporization and the heat of fusion of water are 540 and 80 cal/g respectively, (a) For a solution of 1.2 g of urea in 100 g of water, estimate (i) the boiling point elevation, (ii) the freezing point depression, (iii) the vapor pressure lowering at 100°C. Assume ideal-solution and ideal-gas behavior and assume urea to be nonvolatile. (b) Discuss the foregoing properties of a solution of 1.2 g of a nonvolatile solute of molecular weight 10 in 100 g of water. 

The first of these is so small that it would be hard to measure precisely. Even this small lowering of the vapor pressure is sufficient to raise the boiling point by an amount that could be measured, although with difficulty. The freezing point depression is greater, but still could not be measured very precisely without a special apparatus. The osmotic pressure, on the other hand, is so large that it could be measured much more precisely. Thus, osmotic pressure is often the most easily measured of the four colligative properties, especially when very dilute solutions are used. 

The next major step was the enunciation of Raoult s law (Raoult 1887, 1888). In 1887, Francois Raoult published his investigations on the vapor pressure of the solvent in dilute solutions. He studied five solutes in water and 14 solutes in each of 11 organic solvents and found that the diminution of the vapor pressure of the solvent upon addition of a given (small) amount of solute was proportionally the same for all cases. The proportionality factor is the mole fraction of the solute. This may be expressed in the currently accepted notation as p° -pi p°X2 this is known as Raoult s law. Raoult had previously discovered the laws of freezing point depression and boiling point elevation (Raoult 1878, 1882), three of the so-called colligative properties of dilute solutions. 

Francois-Marie Raoult (1830-1901) A French chemist who discovered the depression of the freezing point of liquids by the presence of dissolved substances and found that the diminution of the vapor pressure of a solvent, caused by a substance dissolved In it, is proportional to the molecular weight of the substance dissolved. He also worked on phenomena of the voltaic cell. 

Because polyelectrolytes are nonvolatile, the most important thermodynamic property for vapor + liquid phase equilibrium considerations is the vapor pressure of water above the aqueous solution. Instead of the vapor pressure, some directly related other properties are used, e.g., the activity of water a, the osmotic pressure 71, and the osmotic coefficient < . These properties are defined and discussed in Sect. 4. Membrane osmometry, vapor pressure osmometry, and isopiestic experiments are common methods for measuring the osmotic pressure and/or the osmotic coefficient. A few authors also reported experimental results for the activity coefficient y i of the counterions (usually determined using ion-selective electrodes) and for the freezing-point depression of water AT p. The activity coefficient is the ratio of activity to COTicentration ... 

Consider a sealed flask with a movable piston that contains 5.25 L of 02 saturated with water vapor at 25°C. The piston is depressed at constant temperature so that the gas is compressed to a volume of 2.00 L. (Use the table in Appendix 1 for the vapor pressure of water at various temperatures.)... 

FIGURE 8.28 The vapor pressure of a solvent is lowered by a nonvolatile solute. The barometer tube on the left has a small volume of pure water floating on the mercury. That on the right has a small volume of 10 m NaCI(aq) and a lower vapor pressure. Note that the column on the right is depressed less by the vapor in the space above the mercury than the one on the left, showing that the vapor pressure is lower when solute is present. 

Ethylene glycol is not as active in depression of the freezing point as methanol, but it has a very low vapor pressure evaporation loss in a coolant system is due more to the evaporation of water than to the evaporazation of ethylene glycol. Furthermore, the flammability problem is literally eliminated. 1 1 mixtures of ethylene glycol and water do not exhibit a flash point at all. 

Alkad A process for improving the safety of alkylation processes using hydrofluoric acid as the catalyst. A proprietary additive curtails the emission of the acid aerosol that forms in the event of a leak. Based on observation of G. Olah in the early 1990s that liquid polyhydrogen fluoride complexes (of amines such as pyridine) depress the vapor pressure of HF above alkylation mixtures. Developed by UOP and Texaco and operated at Texaco s refinery at El Dorado, TX, since 1994. A competing process is ReVAP, developed by Phillips and Mobil. 

---