Solute molar mass determination from

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... 

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. 

D—To calculate the molar mass, the mass of the solute and the moles of the solute are needed. The molality of the solution may be determined from the freezing-point depression, and the freezing-point depression constant (I and II). If the mass of the solvent is known, the moles of the solute may be calculated from the molality. These moles, along with the mass of the solute, can be used to determine the molar mass. 

The molar mass (M) of a solute can be determined from measurements of the sedimentation coefficient, s, and the diffusion coefficient, D (see Prob. 4.18), according to the Svedberg equation ... 

The molar mass of a solute can be determined from the observed boiling-point elevation, as shown in Example 17.2. 

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. 

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. 

The determination of single molar mass averages from simple solution properties, such as colligative and viscosity methods, has not been a popular held of research in the past few years. The state of the art has been reviewed by Slade and by Billingham. Since the publication of ref. 2, two major manufacturers (Perkin-Elmer and Hewlett-Packard) have withdrawn from the market so that there is now a much reduced choice in equipment for membrane osmometry and for vapour pressure osmometry. Membrane osmometry as a technique has received virtually no attention during the review period, although its use has been reported in a number of papers. Oman has described studies of the osmotic coefficients of aqueous polyelectrolytes, and Oman and Batho describe theoretical models for... 

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. 

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. 

Microgels are distinguished from linear and branched macromolecules by their fixed shape which limits the number of conformations of their network chains like in crosslinked polymers of macroscopic dimensions. The feature of microgels common with linear and branched macromolecules is their ability to form colloidal solutions. This property opens up a number of methods to analyze microgels such as viscometry and determination of molar mass which are not applicable to the characterization of other crosslinked polymers. 

We begin by determining the molar mass of Na2S04 10H2O. The amount of solute needed is computed from the concentration and volume of the solution. 

First determine the concentration of the solution from the osmotic pressure, then the amount of solute dissolved, and finally the molar mass of that solute. 

In this equation, u is the osmotic pressure in atmospheres, n is the number of moles of solute, R is the ideal gas constant (0.0821 Latm/K mol), T is the Kelvin temperature, V is the volume of the solution and i is the van t Hoff factor. If one knows the moles of solute and the volume in liters, n/V may be replaced by the molarity, M. It is possible to calculate the molar mass of a solute from osmotic pressure measurements. This is especially useful in the determination of the molar mass of large molecules such as proteins. 

From this relationship, we can see that each Na2S04 produces three ions. The production of three ions means that the van t Hoff factor, i, is 3. We need to know the molality of the solution to find our answer. To determine the molality, we will begin by determining the moles of sodium sulfate. Sodium sulfate has a molar mass of 142.04 g/mol. Thus, the number of moles of sodium sulfate present is ... 

Using the molar mass, calculate the moles of all weighed samples. The moles of substances are converted to molarities by dividing by the volume (in liters) of the solution. Molarities may also be determined from pipet or buret readings using the dilution equation. (If a buret is used, one of the volumes is calculated from the difference between the initial and final readings.) The dilution equation may be needed to calculate the concentration of each reactant immediately after all the solutions are mixed. 

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