Vapor colligative properties

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. 

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. 

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... 

Osmotic pressure, like vapor pressure lowering, is a colligative property. For any nonelectrolyte, ir is directly proportional to molarity, M. The equation relating these two quantities is very similar to the ideal gas law ... 

The easiest of the colligative properties to visualize is the effect of solute molecules on the vapor pressure exerted by a liquid. In a closed system, the solvent and its vapor reach dynamic equilibrium at a partial pressure of solvent equal to the vapor pressure. At this pressure, the rate of condensation of solvent vapor equals the rate of evaporation from the liquid. 

The dissolution of a solute into a solvent perturbs the colligative properties of the solvent, affecting the freezing point, boiling point, vapor pressure, and osmotic pressure. The dissolution of solutes into a volatile solvent system will affect the vapor pressure of that solvent, and an ideal solution is one for which the degree of vapor pressure change is proportional to the concentration of solute. It was established by Raoult in 1888 that the effect on vapor pressure would be proportional to the mole fraction of solute, and independent of temperature. This behavior is illustrated in Fig. 10A, where individual vapor pressure curves are... 

Colligative properties are those properties of solutions that depend on the number of solute particles present and not their identity. Colligative properties include vapor pressure lowering, freezing point depression, boiling point elevation, and osmotic pressure. Colloids are homogeneous mixtures, in which the solute particles are intermediate in size between suspensions and true solutions. We can distinguish colloids from true solutions by the Tyndall effect. 

If a liquid is placed in a sealed container, molecules will evaporate from the surface of the liquid and eventually establish a gas phase over the liquid that is in equilibrium with the liquid phase. The pressure generated by this gas is the vapor pressure of the liquid. Vapor pressure is temperature-dependent the higher the temperature, the higher the vapor pressure. If the liquid is made a solvent by adding a nonvolatile solute, the vapor pressure of the resulting solution is always less than that of the pure liquid. The vapor pressure has been lowered by the addition of the solute the amount of lowering is proportional to the number of solute particles added and is thus a colligative property. 

Know how to use the appropriate colligative properties equation to calculate the amount of vapor-pressure lowering, freezing-point lowering, van t Hoff factor, etc. 

Activity data for electrolytes usually are obtained by one or more of three independent experimental methods measurement of the potentials of electrochemical cells, measurement of the solubility, and measurement of the properties of the solvent, such as vapor pressure, freezing point depression, boiling point elevation, and osmotic pressure. All these solvent properties may be subsumed under the rubric colligative properties. 

As we saw in Section 17.5, the activity coefficient of a nonelectrolyte solute can be calculated from the activity coefficient of the solvent, which, in turn, can be obtained from the measurement of colligative properties such as vapor pressure lowering, freezing point depression, or osmotic pressure. We used the Gibbs-Duhem equation in the form [Equation (17.33)]... 

The state of aggregation of RLi in various solvents has been investigated by a variety of methods. In 1967, West and Waack used a differential vapor pressure technique to study solution colligative properties of RLi . Deviations from ideality indicated that in THF at 25 °C, MeLi and BuLi are tetrameric, PhLi dimeric and benzyllithium monomeric. MeLi was also suggested to be tetrameric in diethyl ether. 

The alternative value, which describes the polymer-solvent interaction is the second virial coefficient, A2 from the power series expressing the colligative properties of polymer solutions such as vapor pressure, conventional light scattering, osmotic pressure, etc. The second virial coefficient in [mL moH] assumes the small positive values for coiled macromolecules dissolved in the thermodynamically good solvents. Similar to %, also the tabulated A2 values for the same polymer-solvent systems are often rather different [37]. There exists a direct dependence between A2 and % values [37]. 

There are several basic physical-chemical principles involved in the ability of aerosol particles to act as CCN and hence lead to cloud formation. These are the Kelvin effect (increased vapor pressure over a curved surface) and the lowering of vapor pressure of a solvent by a nonvolatile solute (one of the colligative properties). In Box 14.2, we briefly review these and then apply them to the development of the well-known Kohler curves that determine which particles will grow into cloud droplets by condensation of water vapor and which will not. 

Phase equilibrium (2 component), liquid-vapor, solid-liquid, colligative properties, FP depression, osmotic pressure... 

This relationship constitutes the basic definition of the activity. If the solution behaves ideally, a, =x, and Equation (18) define Raoult s law. Those four solution properties that we know as the colligative properties are all based on Equation (12) in each, solvent in solution is in equilibrium with pure solvent in another phase and has the same chemical potential in both phases. This can be solvent vapor in equilibrium with solvent in solution (as in vapor pressure lowering and boiling point elevation) or solvent in solution in equilibrium with pure, solid solvent (as in freezing point depression). Equation (12) also applies to osmotic equilibrium as shown in Figure 3.2. 

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. 

Hydroxyl number and molecular weight are normally determined by end-group analysis, by titration with acetic, phthalic, or pyromellitic anhydride (264). For lower molecular weights (higher hydroxyl numbers), 19F- and 13C-nmr methods have been developed (265). Molecular weight determinations based on colligative properties, eg, vapor-phase osmometry, or on molecular size, eg, size exclusion chromatography, are less useful because they do not measure the hydroxyl content. 

Values for many properties can be determined using reference substances, including density, surface tension, viscosity, partition coefficient, solubility, diffusion coefficient, vapor pressure, latent heat, critical properties, entropies of vaporization, heats of solution, colligative properties, and activity coefficients. Table 1 lists the equations needed for determining these properties. 

The final colligative property, osmotic pressure,24-29 is different from the others and is illustrated in Figure 2.2. In the case of vapor-pressure lowering and boiling-point elevation, a natural boundary separates the liquid and gas phases that are in equilibrium. A similar boundary exists between the solid and liquid phases in equilibrium with each other in melting-point-depression measurements. However, to establish a similar equilibrium between a solution and the pure solvent requires their separation by a semi-permeable membrane, as illustrated in the figure. Such membranes, typically cellulosic, permit transport of solvent but not solute. Furthermore, the flow of solvent is from the solvent compartment into the solution compartment. The simplest explanation of this is the increased entropy or disorder that accompanies the mixing of the transported solvent molecules with the polymer on the solution side of the membrane. Flow of liquid up the capillary on the left causes the solution to be at a hydrostatic pressure... 

Effect of Pressure on Solubility 203 Effect of Temperature on Solubility 204 Colligative Properties of Solutions 205 Vapor Pressure 205 Boiling Point 207 Freezing Point 208 Osmotic Pressure 209 Colloids 212 Review Questions 213... 

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