Solution molar mass determination

In carrying out a molar mass determination by freezing point depression, we must choose a solvent in which the solute is readily soluble. Usually, several such solvents are available. Of these, we tend to pick one that has the largest kf. This makes ATf large and thus reduces the percent error in the freezing point measurement From this point of view, cyclohexane or other organic solvents are better choices than water, because their kf values are larger. 

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... 

Introduction and Orientation, Matter and Energy, Elements and Atoms, Compounds, The Nomenclature of Compounds, Moles and Molar Masses, Determination of Chemical Formulas, Mixtures and Solutions, Chemical Equations, Aqueous Solutions and Precipitation, Acids and Bases, Redox Reactions, Reaction Stoichiometry, Limiting Reactants... 

X V iution), the determination of the molar mass of a solute requires a measurement of mass, volume, temperature, and osmotic pressure. Osmotic pressures are generally large and can be determined quite accurately, thus yielding accurate molar masses. Boiling-point elevations and freezing-point depressions are usually small and not very accurate, so molar mass determinations based on those measures often are not accurate. 

A solution of 1.00 g of anhydrous aluminum chloride, AICI3, in 50.0 g of water freezes at — 1.11°C. Does the molar mass determined from this freezing... 

Colligative properties are related to the number of dissolved solute particles, not their chemical nature. Compared with the pure solvent, a solution of a nonvolatile nonelectrolyte has a lower vapor pressure (Raoult s law), an elevated boiling point, a depressed freezing point, and an osmotic pressure. Colligative properties can be used to determine the solute molar mass. When solute and solvent are volatile, the vapor pressure of each is lowered by the presence of the other. The vapor pressure of the more volatile component is always higher. Electrolyte solutions exhibit nonideal behavior because ionic interactions reduce the effective concentration of the ions. 

What we have described is an idealized picture, and the bands of solute will not remain thin but will spread out as they move down the column for the reasons described above. The error, for example, in using the molar mass determination described in conjunction with Eq. (4.7.2) is primarily a result of the band breadth during elution. By way of illustration, we ask the question, what would be the actual shape of an eluted band of solute if dispersion were to... 

In a molar mass determination, if Wj is the mass of solute dissolved in the volume, V, then n = W2RT/M2V, or... 

Thermal FFF (ThFFF) is driven by a temperature gradient where the channel is positioned between two highly heat conductive metal blocks that allow introduction of rapid and controlled temperature gradients. Particles and molecules in suspension or solution are generally driven towards the cold wall by thermal diffusion. No commercial particle size instrument based on this technique is currently marketed. However, FF Fractionation, Inc. does produce a Model T-KX) ThFFF suitable for molar mass determinations. 

The basic principles for the transport of macromolecules in dilute solution will be discussed in this section these principles will be utilized for molar mass determinations in Section 9. In addition, the viscosities of melts and concentrated solutions will also be treated, but the determination of molar masses by relative viscosities will not be treated here, but in Section 9. It is also more appropriate to treat heat conduction with the thermal properties of polymers in Section 10. 

Molar mass determination methods can be classed as absolute, equivalent, or relative. Absolute methods allow the molar mass to be directly calculated from the measured quantities without the need for assumptions concerning the physical and/or chemical structure of the polymers. In contrast, equivalent methods require a knowledge of the chemical structure of the macromolecules. Relative methods depend on the chemical and physical structure of the solute as well as on the solute-solvent interaction these methods require calibration against another molecular mass determination method. 

According to the derivation. Equation (9-45) is valid for infinitely dilute solutions. It is the basis of molar mass determinations by the light-scattering method. The molar mass Mi obtained here is the mass-average molar mass Mw), as shown in the following derivation ... 

A relationship is shown to exist in viscometry experiments between particle size or molecular size and the viscosity of dispersions of inorganic colloids or the viscosity of macromolecular solutions. It is therefore possible to determine the molar mass from the viscosity of dilute macromolecular solutions. Since this experiment can be rapidly performed with simple equipment, it is, in practice, the most important molar mass determination method. However, the method is not an absolute one, since the viscosity depends on other molecular properties (for example, on the shape of the molecule), as well as on the molecular weight. 

As pointed out above, dynamic vapor-hquid equilibrium measurement mediods are not very suitable for concentrated polymer solutions, especially due to their heavy foaming behavior. For dilute polymer solutions, however, diere is continuing apphcation of ebulhomelry as an absolute method for the direct determination of die number-average molecular mass M . Dedicated differential ebulliometers allow the determination of values up to an order of 100,000 g/mol. Ebulliometry as a mediod for molar mass determination was recently reviewed by Cooper, Glover, and Mays and Hadjichristidis. ... 

For Flory Huggins like models it can be shown that the mass average molar mass determines the shape and position of the spinodal. For the hole theory other moments of the molar mass distribution become important also. The exact influence of the molar mass distribution on the complete phase diagram of polymer solutions is a topic of current research. The description of the spinodal conditions are almost quantitative without the introduction of empirical parameters. The cell free volume is very important for this quantitative success. 

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. 

PRACTICE EXAMPLE B What would be the osmotic pressure of a solution containing 2.12 g of human serum albumin in 75.00 mL of water at 37.0 °C Use the molar mass determined in Example 14-9. 

Molar mass determination by freezing-point depression or boiling-point elevation has its limitations. Equations (14.5) and (14.6) apply only to dilute solutions of nonelectrolytes, usually much less than 1 mol kg . This requires the use of special thermometers so that temperatures can be measured very precisely, say to 0.001 °C. Because boiling points depend on barometric pressure, precise measurements require that pressure be held constant. As a consequence, boiling-point elevation is not much used. The precision of the freezing-point depression method can be improved by using a solvent... 

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