Vapor pressure lowering colligative property

The presence of a solute affects some of the physical properties of a solution, but the identity of the solute makes little difference in the colligative properties. Vapor-pressure lowering, freezing-point depression, boiling-point elevation, and osmotic pressure are four such properties. 

Calculate the molar mass of a nonvolatile solute from the changes it causes in the colligative properties (vapor-pressure lowering, boiling-point elevation, freezing-point lowering, or osmotic pressure) of its dilute solution (Section 11.5, Problems 41-56). 

Colligative Properties Vapor Pressure Lowering, Freezing Point Depression, Boiling Point Elevation, and Osmotic Pressure 567... 

Historically, chemists have used the group of colligative properties— vapor pressure lowering, freezing-point depression, boiling-point elevation, and osmotic pressure—for molecular mass determinations. In Example 14-9, we showed how this could be accomplished with osmotic pressure. Example 14-10 shows how freezing-point depression can be used to determine a molar mass and, with other information, a molecular formula. To help you understand how this is done, we present a three-step procedure in the form of answers to three separate questions. In other cases, you should be prepared to work out your own procedure. 

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 ... 

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. 

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)]... 

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 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... 

Francois Marie Raoult studied colligative properties in the 1870s. He developed Raoult s Law relating solute and solvent mole fraction to vapor pressure lowering. 

Suppo.se that a colligative property of the polymer solution is measured. These are properties that depend on the number of dissolved solute molecules and not on their sizes (see also Section 2.10). Osmotic pressure, vapor pressure lowering, and freezing point depression are some examples of colligative properties. If the value of the property measured is P, then by definition... 

Colligative properties reflect the chemical potential of the solvent in solution. Alternatively, a colligative property is a measure of the depression of the activity of the solvent in solution, compared to the pure state. Colligative properties include vapor pressure lowering, boiling point elevation, freezing point depression, and membrane osmometry. The latter property is considered here, since it is the most important of the group as far as synthetic polymers are concerned. 

Other colligative properties can similarly be shown to be related to the left-hand side of Eq. (2-62). Vapor pressure lowering is related, for example, through Raoult s law and Eq. (2-54). Reference should be made to standard introductory physical chemistry textbooks. 

Regular membrane osmometry is not suitable for measurements of below about 30,000 because of permeation of the solute through the membrane. Other colligative methods must be employed in this range, and vapor pressure lowering can be considered in this connection. The expanded virial form of Eq. (2-72) for this property is... 

The simplicity and generality of Equation 6.5-3 are surprising. According to the equation, if a solution contains 20 mole% solute, then the solvent partial pressure is 80% of the vapor pressure of pure solvent at the system temperature, regardless of the temperature, the pressure, and what the solute and solvent are. (Hence, vapor pressure lowering is a colligative property, by definition.) The only stipulations are that Raoult s law holds and the solute is nonvolatile, nonreactive, and nondissociative. 

The colligative properties we will be observing are freezing-point depression, boiling-point elevation, vapor-pressure lowering, and osmosis. Put on your safety glasses for all four demonstrations. 

The four colligative properties that are of importance are 1) the vapor pressure lowering 2) the elevation of boiling point 3) the freezing-point depression and 4) the osmotic pressure. An attempt is made below to describe qualitatively and quantitatively each colligative property of solutions, with an emphasis on their interrelationship and their application later in measurement and adjustment of the tonicity of solutions, with particular reference to parenteral formulations. Although theoretical derivations based on thermodynamics can be used to show how each of the colligative properties of solution arises and relate to each other, textbooks on physical chemistry for theoretical derivations are recommended. 

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