Colligation

Completely ah initio predictions can be more accurate than any experimental result currently available. This is only true of properties that depend on the behavior of isolated molecules. Colligative properties, which are due to the interaction between molecules, can be computed more reliably with methods based on thermodynamics, statistical mechanics, structure-activity relationships, or completely empirical group additivity methods. 

Osmotic pressure is one of four closely related properties of solutions that are collectively known as colligative properties. In all four, a difference in the behavior of the solution and the pure solvent is related to the thermodynamic activity of the solvent in the solution. In ideal solutions the activity equals the mole fraction, and the mole fractions of the solvent (subscript 1) and the solute (subscript 2) add up to unity in two-component systems. Therefore the colligative properties can easily be related to the mole fraction of the solute in an ideal solution. The following review of the other three colligative properties indicates the similarity which underlies the analysis of all the colligative properties ... 

One way to describe this situation is to say that the colligative properties provide a method for counting the number of solute molecules in a solution. In these ideal solutions this is done without regard to the chemical identity of the species. Therefore if the solute consists of several different components which we index i, then nj = S nj j is the number of moles counted. Of course, the total mass of solute in this case is given by mj = Sjnj jMj j, so the molecular weight obtained for such a mixture is given by... 

As noted above, all of the colligative properties are very similar in their thermodynamics if not their experimental behavior. This similarity also extends to an application like molecular weight determination and the kind of average obtained for nonhomogeneous samples. All of these statements are also true of osmotic pressure. In the remainder of this section we describe osmotic pressure experiments in general and examine the thermodynamic origin of this behavior. 

Before doing this, however, it is informative to compare the sensitivity of the four colligative properties in the determination of molecular weight. In the following example this is done by making the appropriate numerical calculations. 

As Morawetz puts the matter, an acceptance of the validity of the laws governing colligative properties (i.e., properties such as osmotic pressure) for polymer solutions had no bearing on the question whether the osmotically active particle is a molecule or a molecular aggregate . The colloid chemists, as we have seen, in regard to polymer solutions came to favour the second alternative, and hence created the standoff with the proponents of macromolecular status outlined above. 

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. 

The relationships among colligative properties and solute concentration are best regarded as limiting laws. They are approached more closely as the solution becomes more dilute. In practice, the relationships discussed in this section are valid, for nonelectrolytes, to within a few percent at concentrations as high as 1 Af. At higher concentrations, solute-solute interactions lead to larger deviations. 

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 ... 

Determination of Molar Masses from Colligative Properties... 

Colligative properties, particularly freezing point depression, can be used to determine molar masses of a wide variety of nonelectrolytes. The approach used is illustrated in Example 10.9. 

A laboratory experiment on colligative properties directs students to determine the molar mass of an unknown solid. Each student receives 1.00 g of solute, 225 mL of solvent and information that may be pertinent to the unknown. 

Molar masses can also be determined using other colligative properties. Osmotic pressure measurements are often used, particularly for solutes of high molar mass, where the concentration is likely to be quite low. The advantage of using osmotic pressure is that the effect is relatively large. Consider, for example, a 0.0010 M aqueous solution, for which... 

As noted earlier, colligative properties of solutions are directly proportional to the concentration of solute particles. On this basis, it is reasonable to suppose that, at a given concentration, an electrolyte should have a greater effect on these properties than does a nonelectrolyte. When one mole of a nonelectrolyte such as glucose dissolves in water, one mole of solute molecules is obtained. On the other hand, one mole of the electrolyte NaCl yields two moles of ions (1 mol of Na+, 1 mol of Cl-). With CaCl three moles of ions are produced per mole of solute (1 mol of Ca2+, 2 mol of Cl-). 

This behavior is generally typical of electrolytes. Their colligative properties deviate considerably from ideal values, even at concentrations below 1 m. There are at least a couple of reasons for this effect... 

Because of electrostatic attraction, an ion in solution tends to surround itself with more ions of opposite than of like charge (Figure 10.12). The existence of this ionic atmosphere, first proposed by Peter Debye (1884-1966), a Dutch physical chemist in 1923, prevents ions from acting as completely independent solute particles. The result is to make an ion somewhat less effective than a nonelectrolyte molecule in its influence on colligative properties. 

Freezing point lowering (or other colligative properties) can be used to determine the extent of dissociation of a weak electrolyte in water. The procedure followed is illustrated in Example 10.11. 

Use colligative properties to determine molar mass of a solute. 

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