Molar Masses from Colligative Properties

In physical chemistry, we apply the term colligative to those properties that depend upon number of molecules present. The principal colligative properties are boiling point elevation, freezing point depression, vapour pressure lowering, and osmotic pressure. All such methods require extrapolation of experimental data back to infinite dilution. This arises due to the fact that the physical properties of any solute at a reasonable concentration in a solvent are 

For practical purposes, the colligative property that is most useful for measuring relative molar masses of polymers is osmotic pressure. As Table 6.2 shows, all other properties take such small values that their measurement is impractical. 

Colligative properties measure average relative molar masses, M, and in the case of osmotic pressure, II, the important relationship is  

From this we can develop a general expression for the relationship of these parameters to concentration. Thus  

In equation (6.6), F is a constant and g is a function that varies according to the extent of polymer-solvent interaction, and has values close to zero for poor solvents and values close to 0.25 for good solvents. 

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Determination of Molar Masses from Colligative Properties... 

Table 6.2 Colligative properties of a solution of polymer of molar mass 20 000 at a concentration o/O.Ol g (from F. W. Billmeyer, Textbook of Polymer Science , John Wiley Sons, New York, 1962)...

One of the laboratory requirements for the course, and also the topic of former test questions, is the determination of the molar mass of a substance from the freezing-point depression. Actually, any of the colligative properties can be used to determine the molar mass, but the only one that you are required to know is the freezing-point depression method. It is easier to illustrate the technique within the framework of a problem, so the discussion of this process will be done within a sample problem. 

Rudin s aim was to predict the size of dissolved polymer molecules and the colligative properties of polymer solutions (hydrodynamic volume, second virial coefficient, interaction parameter, osmotic pressure, etc) from viscometric data (average molar mass, intrinsic viscosity, etc.). 

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). 

Each colligative property relates concentration to some measurable quantity—the number of degrees the freezing point is lowered, the magnitude of osmotic pressure created, and so forth. From these measurements, we can determine the amount (mol) of solute particles and, for a known mass of solute, the molar mass of the solute as well. 

The determination of single molar mass averages from simple solution properties, such as colligative and viscosity methods, has not been a popular held of research in the past few years. The state of the art has been reviewed by Slade and by Billingham. Since the publication of ref. 2, two major manufacturers (Perkin-Elmer and Hewlett-Packard) have withdrawn from the market so that there is now a much reduced choice in equipment for membrane osmometry and for vapour pressure osmometry. Membrane osmometry as a technique has received virtually no attention during the review period, although its use has been reported in a number of papers. Oman has described studies of the osmotic coefficients of aqueous polyelectrolytes, and Oman and Batho describe theoretical models for... 

Although these expressions provide no information about the activity coefficient of a solute, they are useful for estimating the solute molar mass. For example, from a measurement of any of the colligative properties of a dilute solution and the appropriate theoretical relation, we can obtain an approximate value of the solute molality niB- (It is only approximate because, for a measurement of reasonable precision, the solution cannot be extremely dilute.) If we prepare the solution with a known amount a of solvent and a known mass of solute, we can calculate the amount of solute from b = nAMpjnB, then the solute molar mass is the solute mass divided by ns-... 

Colligative properties arise from the number, not the type, of solute particles. Compared to pure solvent, a solution has lower vapor pressure (RaoulLs law), elevated boiling point, and depressed freezing point, and it gives rise to osmotic pressure. Colligative properties are used to determine solute molar mass osmotic pressure gives the most precise measurements. 

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