Molar mass osmometry

The van t Ho ff equation is used to determine the molar mass of a solute from osmotic pressure measurements. This technique, which is called osmometry, involves the determination of the osmotic pressure of a solution prepared by making up a known volume of solution of a known mass of solute with an unknown molar mass. Osmometry is very sensitive, even at low concentrations, and is commonly used to determine very large molar masses, such as those of polymers. 

EXAMPLE 8.10 Sample exercise Using osmometry to determine molar mass... 

SOLUTION Polymers commonly have very high molar masses (of the order of kilograms per mole). Use the procedure for osmometry in Toolbox 8.2. Because polyethylene is a nonelectrolyte, i = 1. Use R in the units that match the data in this case, liters and atmospheres. 

Osmosis is the flow of solvent through a semipermeable membrane into a solution the osmotic pressure is proportional to the molar concentration of the solute. Osmometry is used to determine the molar masses of compounds with large molecules, such as polymers reverse osmosis is used in water purification. 

J 10 Use osmometry to find the molar mass of a solute (Toolbox 8.2 and Example 8.10). 

CH,CH(CN)—. (c) What would be the vapor pressure of the solution if the vapor pressure of pure water at 25°C is 0.0313 atm (Assume that the density of the solution is 1.00 g-ern .) (d) Which approach (osmometry or the lowering of vapor pressure) would you prefer for the determination of very high molar masses such as those of acrylic resins Why ... 

Practically, polymers with molar masses between 2 x 104 and 2 x 106 g/mol can be characterized by membrane osmometry, but measurements of Mn <104 g/mol have also been reported with fast instruments and suitable membranes [16]. The lower limit is set by insufficient retention of short polymer chains. Above M 2 x 106 g/mol, the osmotic pressure, which is proportional to Mr1, is too low for a reasonable signal-to-noise ratio. An advantage of the low molar mass cut-off is that impurities with a very low molar mass can permeate through the membrane and, hence, do not contribute to the measured osmotic pressure. Their equilibration time may, however, be different from that of the solute, leading to complex time-dependent signals. 

Vapour pressure osmometry is the second experimental technique based on colligative properties with importance for molar mass determination. The vapour pressure of the solvent above a (polymer) solution is determined by the requirement that the chemical potential of the solvent in the vapour and in the liquid phase must be identical. For ideal solutions the change of the vapour pressure p of the solvent due to the presence of the solute with molar volume V/1 is given by... 

Experimental considerations Sample preparation and data evaluation are similar to membrane osmometry. Since there is no lower cut-off as in membrane osmometry, the method is very sensitive to low molar mass impurities like residual solvent and monomers. As a consequence, the method is more suitable for oligomers and short polymers with molar masses up to (M)n 50kg/mol. Today, vapour pressure osmometry faces strong competition from mass spectrometry techniques such as matrix-assisted laser desorption ionisation mass spectrometry (MALDI-MS) [20,21]. Nevertheless, vapour pressure osmometry still has advantages in cases where fragmentation issues or molar mass-dependent desorption and ionization probabilities come into play. 

Membrane osmometry measurements were carried out with the capillary osmometer shown in Figure 3. Owing to the short equilibration time of the instrument and the low cut-off molar mass of the membrane, solute permeation through the membrane, which would show up as a drift of the baseline, did not cause problems even for the lowest molar mass fraction. M was obtained from... 

Note 1 An infinite number of molar-mass averages can in principle be defined, but only a few types of averages are directly accessible experimentally. The most important averages are defined by simple moments of the distribution functions and are obtained by methods applied to systems in thermodynamic equilibrium, such as osmometry, light scattering and sedimentation equilibrium. Hydrodynamic methods, as a rule, yield more complex molar-mass averages. 

Its related value was originally denoted as X- Numerous % values in terms of volume fractions are collected in Ref. [37]. Unfortunately the scatter in % values found in the literature is large as they reflect also both the polymer source (e.g., narrow molar mass fractions or anionically prepared samples) and the method of measurement, for example, light scattering, osmometry, or inverse gas chromatography. The interaction parameters g (%) for the polymer-good solvent systems assume values between 0 and 0.5 [37]. 

Changes in molar mass of irradiated polymers were measured by viscosity, gel permeation chromatography, osmometry and light scattering. G (scission) and G (cross-link) values can be derived from gel contents if cross-linking predominates (3) and a GPC technique requiring only 50 mg of polymer, which could be in the form of powder, was developed for this purpose (4). 

Amur, K.S., Harlapur, S.F., Aminabhavi, T.M. (1997). A novel analytical method to estimate molar mass and virial coefficients of polymer from osmometry. Polymer, 38, 6417-6420. 

Explain how osmometry is used to measure molar mass. What are the advantages of osmometry over measurements of boiling points and freezing points of solutions ... 

In a solution containing both unimer and micelles, Ma, which is by definition more sensitive to low molar mass particles, is always less than the weight-average molecular weight, Mv. Further details on osmometry can be found in the review by Adams (1989), whilst examples of its application to micellar block copolymer solutions are given in Chapter 3. 

Further important information about these products comes from measurements of their molar masses. Of the available methods, vapour pressure osmometry (VPO) and gel permeation chromatography (GPC) are the most widely used, but, because of its sensitivity to low-molar-mass components, VPO tends to yield results which are too low. In contrast, GPC provides a detailed picture of the molar mass distribution. 

Molecular weights are determined by end-group analysis (Mn), membrane osmometry (Mn), viscometry (Mv), size exclusion chromatography (Mm), light scattering photometry, and sedimentation (Mw). Any molar mass computed by these methods must be evaluated critically, in view of a dependence on methodology. 

Molar mass versus generation low-angle laser light scattering (LALLS) chemical ionization, fast atom bombardment, laser desorption and electrospray mass spectroscopy vapor phase osmometry electrophoresis. 

The sample amount can be easily determined from the injection volume and the sample concentration, and no information from a concentration detector is required. With this approach, the Mn value of any polymer sample can be determined by SEC using only a viscosity detector. Other molar mass averages, however, cannot be determined. The advantage of the Goldwasser Mn method is that it can access much wider molar mass ranges than other existing methods like osmometry or end-group methods. 

Difficulties for obtaining exact molecular weights also occur when taking the metal free products of TCB and some metal disulfides After GPC diagrams the molar masses correspond to 10 (Table 11). But from membrane osmometry, values near 2 10 were obtained. It was assumed that stiff Pc-structure will lead to a large effective hydrodynamic value which may explain the high GPC data. 

Osmometry is a technique used to determine the molar mass of a solute if the mass concentration is measured. 

The experimental measurement of these averages has largely been performed on polymers in solution (Hunt and James, 1999). Since M depends on the measurement of the number of polymer chains present in a given mass, colligative properties such as vapour-pressure depression AP (measured by vapour-phase osmometry) and osmotic pressure (measured by membrane osmometry) relative to the pure solvent, can in principle provide the molar mass through an equation of the form... 

The complications mentioned imply that the average conformation can mostly not be calculated from first principles. However, many of the parameters mentioned can be determined, such as molar mass and composition. The radius of gyration rg can be obtained from light scattering experiments, [1 from osmometry. If molecules of varying (average) molar... 

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