Pressure Lowering

We have seen that a liquid exerts a characteristic vapor pressure [W Section 12.2]. When a nonvolatile solute (one that does not exert a vapor pressure) is dissolved in a liquid, the vapor pressure exerted by the liquid decreases. The difference between the vapor pressure of a pure solvent and that of the corresponding solution depends on the concentration of the solute in the solution. This relationship is expressed by Raoult s law, which states that the partial pressure of a solvent over a solution, Pu is given by the vapor pressure of the pure solvent. Pf, times the mole fraction of the solvent in the solution, X - 

Tn a solution containing only one solute. A = 1 where Xi the mole fraction of the solute. Equation 13.4 can therefore be rewritten as 

Frangois Marie Raoult (1839-1901). French chemist. Raoult s work was mainly in solution properties and electrochemisby. 

the decrease in vapor pressure, P, is directly proportional to the solute concentration expressed as a mole fraction. 

Think About It This problem can also be solved using Equation 13.5 to calculate the vapor-pressure lowering, AF 

6 Colligative Properties Vapor Pressure Lowering, Freezing Point Depression, Boiling Point Elevation, and Osmotic Pressure 

Have you ever wondered why you add salt to the ice in an ice-cream maker Or why salt is scattered on icy roads in cold climates Salt lowers the temperature at which a salt water solution freezes. A salt and water solution will remain liquid even below 0 °C. When salt is added to ice in the ice-cream maker, an ice/water/salt mixture forms that can reach a temperature of about -10 °C, at which point the cream freezes. On the winter road, the salt allows the ice to melt when the ambient temperature is below freezing. 

For example, when 1 mol of NaCl dissolves in water, it forms 1 mol of dissolved Na ions and 1 mol of dissolved CF ions. Therefore, the resulting solution has 2 mol of dissolved particles. The colligative properties of electrolyte solutions reflect this higher concentration of dissolved particles. In this section we examine colligative properties of nonelectrolyte solutions we then expand the concept to include electrolyte solutions in Section 12.7. 

A In winter, salt is often applied to roads so that the ice wiU melt at lower temperatures. 

Recall from Section 11.5 that the vapor pressure of a hquid is the pressure of the gas above the liquid when the two are in dynamic equihbrium (that is, when the rate of vaporization equals the rate of condensation). What is the effect of a nonvolatile nonelectrolyte solute on the vapor pressure of the liquid into which it dissolves The basic answer to this question is that the vapor pressure of the solution is lower than the vapor pressure of the pure solvent. We can understand why this happens in two different ways. 

You have learned that adding a nonvolatile solute to a solvent lowers the vapor pressure of that solvent. The amount by which the vapor pressure is lowered can be calculated by means of a relationship discovered by the French chemist Francois Marie Raoult (1830-1901) in 1886. According to Raoult s law, the vapor pressure of a solvent (P) is equal to the product of its vapor pressure when pure (P°) and its mole fraction (X) in the solution, or 

The solution shown at the right was made by adding 75.0 g of sucrose (C12H22On) to 500.0 g of water at a temperature of 20°C. Answer the following questions about this solution. 

Why do the sugar molecules in the solution lower the vapor pressure of the water  

What is the vapor pressure of the solution if the vapor pressure of pure water at 20°C is 17.54 mm Hg  

In addition to freezing-point lowering and boiling-point raising, vapor-pressure lowering and osmotic pressure are also colligative properties. As we examine each one, notice how solute concentration quantitatively affects the property. 

A liquid in a closed container establishes equilibrium with its vapor. = (Section 11.5) The vapor pressure is the pressure exerted by the vapor when it is at equilibrium with the liquid (that is, when the rate of vaporization equals the rate of condensation). A substance that has no measurable vapor pressure is nonvolatile, whereas one that exhibits a vapor pressure is volatile. 

A solution consisting of a volatile liquid solvent and a nonvolatile solute forms spontaneously because of the increase in entropy that accompanies their mixing. In effect, the solvent molecules are stabilized in their liquid state by this process and thus have a lower tendency to escape into the vapor state. Therefore, when a nonvolatile solute is present, the vapor pressure of the solvent is lower than the vapor pressure of the pure solvent, as illustrated in FIGURE 13.21. 

The vapor pressure of a volatile solvent above a solution containing a nonvolatile solute is proportional to the solvent s concentration in the solution. This relationship is expressed quantitatively by Raoult s law, which states that the partial pressure exerted 

J Volatile solvent particles Nonvolatile solute particles 

A solution consisting of a volatile liquid solvent and a nonvolatile solute forms spontaneously because of the increase in entropy that accompanies their mixing. In 

I Volatile solvent particles I Nonvolatile solute particles 

Rate of vaporization reduced by presence of nonvolatile solute 

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Vapor pressure lowering. Equation (8.20) shows that for any component in a binary liquid solution aj = Pj/Pi°. For an ideal solution, this becomes... 

Complexes. In common with other dialkylamides, highly polar DMAC forms numerous crystalline solvates and complexes. The HCN—DMAC complex has been cited as an advantage ia usiag DMAC as a reaction medium for hydrocyanations. The complexes have vapor pressures lower than predicted and permit lower reaction pressures (19). 

Both technical- and reagent-grade phosphoms pentoxide is typically >99% P O q. Phosphoms pentoxide sublimes near 360°C at atmospheric pressure. Lower oxides, which may account for <0.3% (as P40 ) in technical-grade material, are present at <0.02% in reagent-grade phosphoms pentoxide. Lower oxides are detected by decolorization of a dilute potassium permanganate solution (Table 11). 

Dilute (1—3%), chloride-containing solutions of either HOCl, hypochlorite, or aqueous base, can be stripped in a column against a current of CI2, steam, and air at 95—100°C and the vapors condensed giving virtually chloride-free HOCl solutions of higher concentration in yields as high as 90% (122—124). Distillation of more concentrated solutions requires reduced pressure, lower temperature, and shorter residence times to offset the increased decomposition rates. 

Pressure affects flash point. A decrease in pressure lowers the flash point. With toluene, for example, at two-thirds of an atmosphere the vapor pressure must be only 0.74 kPa (5.6 mm Hg) to equal the LFL of 1.1 percent. (No significant difference in LFL will exist at two-thirds of an atmosphere compared to the published LFL of 1.1 percent at one atmosphere.) This vapor pressure occurs at —3°C, corresponding to a decrease in flash point of about 7.4°C from one atmosphere. Conversely, an increase in pressure raises the flash point. 

Just as at low pH, concentration mechanisms substantially increase attack. The two principal mechanisms of concentration are evaporation and condensation. Evaporation increases solute concentrations of compounds with vapor pressures lower than water (such as caustic compounds). Condensation increases concentration of aggressive gases such as ammonia. 

The boiling point of a liquid varies with the atmospheric pressure to which it is exposed. A liquid boils when its vapour pressure is the same as the external pressure on its surface, its normal boiling point being the temperature at which its vapour pressure is equal to that of a standard atmosphere (760mm Hg). Lowering the external pressure lowers the boiling point. For most substances, boiling point and vapour pressure are related by an equation of the form. 

Vacuum distillation. This expression is commonly used to denote a distillation under reduced pressure lower than that of the normal atmosphere. Because the boiling point of a substance depends on the pressure, it is often possible by sufficiently lowering the pressure to distil materials at a temperature low enough to avoid partial or complete decomposition, even if they are unstable when boiled at atmospheric pressure. 

There is usually some descent (subsidence) of air above surface high-pressure systems. This air warms dry adiabatically as it descends, decreasing the relative humidity and dissipating any clouds in the layer. A subsidence inversion forms as a result of this sinking. Since the descending air compresses as it encounters the increased pressures lower in the atmo-... 

Increasing the steam temperature at a given steam pressure lowers the steam output of the steam turbine slightly. This occurs because of two contradictory effects first the increase in enthalpy drop, which increases the output and second the decrease in flow, which causes a loss in steam turbine output. The second effect is more predominant, which accounts for the lower steam turbine amount. Lowering the temperature of the steam also increases the moisture content. 

Finally, we may note that every solution exerts a vapor pressure less than that of the pure solvent at the same temperature. Corresponding to this vapor-pressure lowering is an equivalent boiling-point raising. Dissolved substances lower the vapor pressure of the solvent. Such reduction increases with the concentration of solute. Since a solution boils when its vapor pressure reaehes that of its surroundings, it must be heated to a temperature above the boiling point of the pure... 

Following a reduction of vessel pressure, the disc returns under the action of the spring but reseats at a pressure lower than set pressure by an amount termed the blowdown (4 to 8% of set pressure). The blowdown may be adjusted within certain limits, by various means recommended by the valve vendor or manufacturer, to provide a longer or shorter blowdown. 

A water-soluble phosphine derivative of diazepam allows for more convenient parenteral tranquilizer therapy and avoids some complications due to blood pressure lowering caused by the propylene glycol medium otherwise required for administration. Fosazepam (82) is prepared from benzodiazepine by sodium hydride-mediated alkylation with chioromethyldimethyl phosphine... 

A solution or dispersion consisting of 20.1 g (0.1 mol) of 7-chloro-p-fluorobutyrophenone, 19.8 g (0.2 mol) of 4-methylpiperidine end 0.1 g of potassium iodide in 150 ml toluene is heated in a seeled gless tube for 15 hours at 100°C to 110°C. The potassium iodide and the 4-methylpiperidine hydrochloride formed in the reaction are separated by filtration and the solvent removed from the filtrate by evaporation In vacuum on a steam bath. The residue is distilled and the fraction obtained at 120°C to 125 0 and at a pressure lower than 0.1 mm Hg is collected. The basa Is dissolved in ether and the 4-fluoro-7-(4-methylpiperidino)-butyro-phenone precipitated as the hydrochloride. The reaction product is purified by recrystallization in ethanol/ether. 

Safety-relief valves are available for relieving or set pressures as low as 2, 10, and 20 psig, as well as higher pressures. Lower pressures are available on special order. Usually a more accurate relief is obtained from the higher pressures. 

M depends not on the molecular sizes of the particles but on the number of particles. Measuring colligative properties such as boiling point elevation, freezing point depression, and vapor pressure lowering can determine the number of particles in a sample. 

If any equipment having a design pressure lower than the maximum output pressure of the compressor is used, or if an increase of pressure above normal operating pressure will cause a malfunction, it shall be protected against overpressure by suitable means. 

Pressure reducing valves provide a steady pressure into a part of the system that operates at a pressure lower that normal system pressure. A reducing valve can normally be set for any desired downstream pressure within its design limits. Once the valve is set, the reduced pressure will be maintained regardless of changes in the supply pressure and system load variations. 

The properties of a solution differ considerably from those of the pure solvent Those solution properties that depend primarily on the concentration of solute particles rather than their nature are called colligative properties. Such properties include vapor pressure lowering, osmotic pressure, boiling point elevation, and freezing point depression. This section considers the relations between colligative properties and solute concentration, with nonelectrolytes that exist in solution as molecules. 

Vapor pressure lowering is a true colligative property that is, it is independent of the nature of the solute but directly proportional to its concentration. For example, the vapor pressure of water above a 0.10 M solution of either glucose or sucrose at 0°C is the same, about 0.008 mm Hg less than that of pure water. In 0.30 M solution, the vapor pressure lowering is almost exactly three times as great, 0.025 mm Hg. 

To obtain a direct expression for vapor pressure lowering, note that Xt = 1 — X2, where X2 is the mole fraction of solute. Substituting l — X2 for X in Raoulfs law,... 

The quantity (P° — Pi) is the vapor pressure lowering (AP). It is the difference between the solvent vapor pressure in the pure solvent and in solution. 

A solution contains 82.0 g of glucose, QH Oe, in 322 g of water. Calculate the vapor pressure lowering at 25°C (vapor pressure of pure water =... 

Strategy First (1), calculate the number of moles of glucose (MM = 180.16 g/mol) and water (MM = 18.02 g/mol). That information allows you to find (2) the mole fraction of glucose. Finally (3), use Raoult s law to find the vapor pressure lowering. 

Reality Check You expect the vapor pressure lowering to be small (0.589 mm Hg)... 

Boiling point elevation is a direct result of vapor pressure lowering. At any given temperature, a solution of a nonvolatile solute has a vapor pressure lower than that of the pure solvent. Hence a higher temperature must be reached before the solution boils, that is, before its vapor pressure becomes equal to the external pressure. Figure 10.8 (p. 270) illustrates this reasoning graphically. 

Boiling point elevation and freezing point lowering, like vapor pressure lowerings are colligative properties. They are directly proportional to solute concentration, generally expressed as molality, m. The relevant equations are... 

Effects of vapor pressure lowering. Because a nonvolatile solute lowers the vepor pressure of a solvent, the boiling point of a solution will be higher and the freezing point lower than the corresponding values for the pure solvent Water solutions freeze below 0°C at point A and boil above 100°C at point B. 

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