Molecular weight from colligative property measurements

We have seen in Chapter 3 that measurements of the colligative properties are of great value in obtaining molecular weights. The colligative properties of solutions depend largely on the relative amounts of solvent and solute present, and only to a small extent on the nature of the solute species. We can derive the relationship between the colligative properties from thermodynamics. 

Membrane osmometry n. The pressure difference between a solution and the pure solvent is measured for the case where the solvent is separated from the solution by a semipermeable membrane, isothermally the measurement yields Ap (change in pressure) which corresponds to M number average molecular weight - a colligative property of polymer solutions ... 

The number average molecular weight is required. This is obtained directly from measurements of a colligative property, such as the osmotic pressure, of dilute polymer solutions (see Chap. VII). It is often more convenient to establish an empirical correlation between the osmotic molecular weight and the dilute solution viscosity, i.e., the so-called intrinsic viscosity, and then to estimate molecular weights from measurements of the latter quantity on the products of polymerization. 

Traditional methods for measuring molecular weight date from the dawn of modem physical chemistry in the 19th century. These relied on so-called colligative property measurements (see box opposite), such as boiling point elevation and freezing... 

The next example shows applications of Equations 6.5-2 through 6.5-5 to the determination of a vapor pressure and phase-transition temperatures for a known solution concentration, and to the calculation of a solution composition and solute molecular weight from a measured colligative property. 

Of the preponderance of small ions, the colligative properties of polyelectrolytes in ionising solvents measure counterion activities rather than Molecular weight. In the presence of added salt, however, correct Molecular weights of polyelectrolytes can be measured by membrane osmometry, since the small ions can move across the membrane. The second virial coefficient differs from that previously defined, since it is determined by both ionic and non-ionic polymer-solvent interactions. 

Membrane osmometry is the most sensitive and accurate colligative property technique. Consider, for example, a polystyrene with M around 200,000. Trial-and-error experience has shown that molecular weight measurements with similar samples are best made by starting with solutions in good solvents (like toluene in this case) at concentrations around lOg/liter and making successive dilutions from this value. The initial polymer concentration is then [(lO iter) (mol/200,000 g)] = 5 X At room temperature RT is of theorder of 23... 

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