Osmometry

Osmometry is the determination of molar mass by the measurement of osmotic pressure. Biological macromolecules dissolve to produce solutions that are far from ideal, but we can still calculate the osmotic pressure by assuming that the van t Hoff equation is only the first term of a lengthier expression  

The empirical parameter B in this expression is called the osmotic virial coefficient. To use eqn 3.24a, we rearrange it into a form that gives a straight line by dividing both sides by [B]  

As we illustrate in the following example, the molar mass of the solute B can be found by measuring the osmotic pressure at a series of mass concentrations and making a plot of /7/[B] against [B] (Fig. 3.36). 

Example 3.4 ) Determining the molar mass of an enzyme from measurements of the osmotic pressure 

The osmotic pressures of solutions of an enzyme in water at 298 K are given below. Find the molar mass of the enzyme. 

Membrane osmometry is by far the most important of the colligative properties for the measurement of the molecular weight of relatively high molecular 

There are several drawbacks to this approach. Diffusion of solvent dilutes the solution and it can often take many hours to achieve equilibrium. While this is undesirable, it becomes more significant as the longer the time it takes to achieve equilibrium, the more likely it is that solute molecules will find their way across the membrane into the pure solvent. As will be seen later, even 1% of solute finding its way across the membrane in the wrong direction can introduce a substantial error in the measured value of the molecular weight. Modern osmometers aim to prevent the diffusion of any solvent across the membrane by applying an appropriate pressure to the solution compartment of the osmometer. The instruments depend on the rapid detection of solvent 

The thermodynamic treatment of osmosis starts by considering the fact that, at equilibrium, the chemical potential of the solvent must be the same on each side of the membrane. If the chemical potential on the pure solvent side of the membrane experiences a pressure p and has a chemical potential p.° p) at equilibrium, this will be equal to that for the solvent on the solution side which is lowered by the presence of the solute (mole fraction X3), but raised because the total pressure is (p + n), i.e. 

Since the chemical potential of a pure solvent //° is reduced to + /ITlnx when a solute is present (x 1 hence Inx is negative), so 

For dilute solutions, Inx may be replaced by ln(I — x ) b-If the molar volume of the solvent is considered to be constant, then integration gives 

In membrane osmometry, use is made of the fact that the chemical potentials of water ( ju0) and of dispersion ( i, ), separated by a membrane permeable to water only, are unequal except at equilibrium, and that tt (a function of Ap) is directly proportional to Mn. Accurate measurements are confined to a practical upper limit of 105—106 Da (Garmon, 1975 Dautzenberg et al., 1994). 

Donnan distribution, leading to abnormally high tt, is a most serious source of error for Mn of polyanions measured by osmometry. The Donnan effect is allegedly overcome by very dilute concentrations that never exceed 25 g L 1 for the polyanion and i = 0.3 mol L-1 for the solvent (Wagner, 1949). A 25-g L-1 polysaccharide concentration is in the semidilute-to-concentrated domain, outside the theoretical dilution limit of osmometry where a power-law dependence of tt/c, on ct is expected. 

Equations (7.5)—(7.11) illustrate the effect of Donnan distribution on osmometry. Recalling Eq. (4.29) (,nVj = ntRT ), assuming an equivalent weight 

If the counterion is Na+, letting q be the equivalent of Na+CP diffusing to the polyanion (P3 ) from an outer volume at y molar concentration, and be the equivalent of H+ not diffusing outward, the equilibrium condition is 

Notwithstanding the problems associated with the Donnan distribution, a pectin Mn was obtained from e = 10-2 g mL-1 dispersion in 0.05-M sodium chloride and reported to have approximated Mn by reducing end-group analysis (Fishman et al., 1986). 

A measure of any of the colligative properties involves counting solute (polymer) molecules in a given amount of solvent. The most common technique for polymers is membrane osmometry. The technique is based on the use of a semipermeable membrane through which solvent molecules freely pass, but through which the large polymer molecules are unable 

In the vapor phase osmometry (VPO) technique, drops of solvent and solution are placed in an insulated chamber close to thermistor probes. Since the solvent molecules evaporate more rapidly from the solvent than from the polymer solution, a temperature difference results that is related to the molarity of the polymer (M), which can be determined if the heat of vaporization per gram of solvent (A) is known using the following relationship  

FIGURE 3.10 Plots of osmotic pressure tt divided by RTC used to determine 1 IM in osmometry. 

The choice of method depends primarily on the information required, and secondarily on the field of study, the amount of substance available, the time required, and, when necessary, on the effort required to purify the samples. Determinations are generally made at various concentrations. Then the apparent molar mass is calculated with the aid of an ideal theoretical relationship—that is, a relationship that only applies strictly at infinite dilution. This apparent molar mass must then be extrapolated to zero concentration to obtain the true molar mass. Apparent and true molar masses may differ considerably. Coil-shaped macromolecules of number-average molar mass of 10 g/ mol can, for example, have an apparent number-average molar mass in good solvents of 555 000 g/mol at a concentration of 0.01 g/ ml and 110 000 g/mol only, on the other hand, when the concentration is 0.1 g/ml. 

Osmotic pressure measurements of solutions of a polymer in a solvent can be employed to determine the molecular weight of the polymer. After approximately one hour the osmotic pressure of solutions of poly-a-methylstyrene in toluene becomes practically constant. From this osmotic pressure and the concentration of the polymer in solution it is possible to calculate the number-average molecular weight of the polymer from the following relationship  

Osmometry has been used to measure the molecular weight of a wide range of polymers including PVC [147], PET [148-150], Nylon [149], PS [148], and linear polyesters [150], including polytetramethylene terephthalate, polypentamethylene terephthalate, polyhexamethylene terephthalate and polytetramethylene isophthalate. 

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The measurement techniques most frequently used are derived from Raoult s and Van t Hoff s laws applied to cryometry, ebulliometry, osmometry, etc. They are not very accurate with errors on the order of ten per cent. Consequently, the molecular weight is often replaced by correlated properties. The mean average temperature or viscosity can thus replace molecular weight in methods derived from ndM. 

In the study described in the last problem, caprolactam was polymerized for 24 hr at 225°C in sealed tubes containing various amounts of water. M and were measured for the resulting mixture by osmometry and light scattering, respectively, and the following results were obtained ... 

In these unit conversions on H, we have used the facts that 1 atm = 760 Torr and the ratio of densities PHg/ soin - /Psoin t onverts from Torr to millimeters of solution. These numerical examples show that experiments in which Apj, ATf, or ATj, are measured are perfectly feasible for solutes of molecular weight 100, but call for unattainable sensitivity for polymeric solutes of M = 10 . By contrast, osmometry produces so much larger an effect that this method is awkward (at least for 1% concentration) for a low molecular weight solute, but is entirely feasible with the polymer. 

Our primary objective in this section is the discussion of practical osmometry, particularly with the goal of determining the molecular weight of a polymeric solute. We shall be concerned, therefore, with the design and operation of osmometers, with the question of units, and with circumventing the problem of nonideality. The key to these points is contained in the last section, but the details deserve additional comment. 

First, we consider the experimental aspects of osmometry. The semiperme-able membrane is the basis for an osmotic pressure experiment and is probably its most troublesome feature in practice. The membrane material must display the required selectivity in permeability-passing solvent and retaining solute-but a membrane that works for one system may not work for another. A wide variety of materials have been used as membranes, with cellophane, poly (vinyl alcohol), polyurethanes, and various animal membranes as typical examples. The membrane must be thin enough for the solvent to pass at a reasonable rate, yet sturdy enough to withstand the pressure difference which can be... 

These results show more clearly than Fq. (8.126)-of which they are special cases-the effect of charge and indifferent electrolyte concentration on the osmotic pressure of the solution. In terms of the determination of molecular weight of a polyelectrolyte by osmometry. ... 

Hydroxyl number and molecular weight are normally determined by end-group analysis, by titration with acetic, phthaUc, or pyromellitic anhydride (264). Eor lower molecular weights (higher hydroxyl numbers), E- and C-nmr methods have been developed (265). Molecular weight deterrninations based on coUigative properties, eg, vapor-phase osmometry, or on molecular size, eg, size exclusion chromatography, are less useful because they do not measure the hydroxyl content. 

Among the techniques employed to estimate the average molecular weight distribution of polymers are end-group analysis, dilute solution viscosity, reduction in vapor pressure, ebuUiometry, cryoscopy, vapor pressure osmometry, fractionation, hplc, phase distribution chromatography, field flow fractionation, and gel-permeation chromatography (gpc). For routine analysis of SBR polymers, gpc is widely accepted. Table 1 lists a number of physical properties of SBR (random) compared to natural mbber, solution polybutadiene, and SB block copolymer. 

Table 6 indicates mol wt vs K value obtained by this technique. Table 7 Hsts obtained by osmometry methods. The specifications for Technical and Pharmaceutical grades are given in Tables 8 and 9.

The molecular stmcture of the copolymers is also important. Molecular-weight measurements (osmometry, gpc) and functional group analysis are useful. Block copolymers require supermolecular (morphological) stmctural information as well. A listing of typical copolymer characterization tools and methods is shown in Table 6. 

The principal methods for deterrnination of the deuterium content of hydrogen and water are based upon measurements of density, mass, or infrared spectra. Other methods are based on proton magnetic resonance techniques (77,78), F nuclear magnetic resonance (79), interferometry (80), osmometry (81), nuclear reaction (82), combustion (83), and falling drop methods (84). 

In which the ratio m/n is close to 3. The silane was produced by free radical copolymerization of vinyltriethoxysilane with N-vinylpyrrolidone. Its number-average molecular weight evaluated by vapour-phase osmometry was 3500. Porous silica microballs with a mean pore diameter of 225 A, a specific surface area (Ssp) of 130 m2/g and a pore volume of 0.8 cm3/g were modified by the silane dissolved in dry toluene. After washings and drying, 0.55% by weight of nitrogen and 4.65% of carbon remained on the microballs. Chromatographic tests carried out with a series of proteins have proved the size-exclusion mechanism of their separation. 

Kaye and Chou39 also studied the effect of base stacking on the conformation of PA using osmometry, intrinsic viscosity, and light-scattering. The ideal behavior (under the 0 conditions) of PA existed at neutral pH (= 7.4) and at 26 and 40 °C from the osmotic measurements. 

The molecular weights of PAs are often not very high (M > 20,000) in this range M can be determined by endgroup analysis or, less frequently, by osmometry, Mw can be determined by light scattering. Both M and Mw can indirectly be determined by HPLC. 

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