Colligative Molecular Weights

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. 

The molecular weight of a substance is, for a large number of calculations, far more convenient than unit mass. This depends on the fact that a large number of properties are independent of the nature of the substance, and depend only on the number of molecular weights present ( molar, or colligative, properties) (cf. Chap. XI. on 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. 

Molecular weight Determination by Colligative Property Measurements... 

Methods for the determination of Molecular weight based on colligative property are vapour-pressure lowering, boiling point elevation (ebulliometry), freezing-point depression (cryoscopy), and the Osmotic pressure (osmometry). 

Osmotic pressure is one of the colligative properties of solutions containing both low-Molecular weight compounds and high polymers. The major difficulty faced in the study of the behaviour of low Molecular weight compounds in solution by the Osmotic pressure measurement method is the selection of a suitable semi-permeable membrane. 

The vapour pressure osmometer method is more acceptable of all the methods involving measurement of colligative properties because of the sensitivity of the detector. For ideal solvent-solvents with a low heat of vaporisation, the differential thermistors of the VPO can detect differences in temperature of the order of 0.001°C this sensitivity determines the Molecular weight of the samples upto 20,000. 

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. 

As noted earlier, certain techniques such as colligative methods, light-scattering photometry, special mass spectrometry (MS) techniques, and ultracentrifugation allow the calculation of specific or absolute molecular weights. Under certain conditions some of these also allow the calculation of the MWD. 

What type of molecular weight average, or M , is based on colligative properties ... 

What are colligative methods for measuring molecular weight and what kind of molecular weight do... 

Given the sensitivity of colligative methods to the presence of low molecular weight impurities, particular care was taken to isolate lignin samples free of such foreign contaminants. Thus, for example, the extraction... 

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. 

In addition to its major use in determining the number-average molecular weight (Ma) of polymers, osmometry has also been used to determine M of block copolymer micelles. The method involves determining the osmotic pressure (77) across a membrane that is permeable to solvent only. Because osmotic pressure is a colligative property, it depends on the number of particles, and hence yields Ma. It also depends on the interactions between particles, and thus... 

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