Mass colligative properties

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... 

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... 

Determination of Molar Masses from Colligative Properties... 

Colligative properties, particularly freezing point depression, can be used to determine molar masses of a wide variety of nonelectrolytes. The approach used is illustrated in Example 10.9. 

A laboratory experiment on colligative properties directs students to determine the molar mass of an unknown solid. Each student receives 1.00 g of solute, 225 mL of solvent and information that may be pertinent to the unknown. 

Molar masses can also be determined using other colligative properties. Osmotic pressure measurements are often used, particularly for solutes of high molar mass, where the concentration is likely to be quite low. The advantage of using osmotic pressure is that the effect is relatively large. Consider, for example, a 0.0010 M aqueous solution, for which... 

Use colligative properties to determine molar mass of a solute. 

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 ). 

Two measures of concentration that are useful for the study of colligative properties, because they indicate the relative numbers of solute and solvent molecules, are mole fraction and molality. We first met the mole fraction, x, in Section 4.8, where we saw that it is the ratio of the number of moles of a species to the total number of moles of all the species present in a mixture. The molality of a solute is the amount of solute species (in moles) in a solution divided by the mass of the solvent (in kilograms) ... 

HOWTO USE COLLIGATIVE PROPERTIES TO DETERMINE MOLAR MASS... 

The lowering of freezing point and the generation of osmotic pressure both depend on the total concentration of solute particles. Therefore, by using the colligative property to determine the amount of solute present, and knowing its mass, we can infer its molar mass. 

Colligative properties can be sources of insight into not only the properties of solutions, but also the properties of the solute. For example, acetic acid, CH.COOH, behaves differently in two different solvents, (a) The freezing point of a 5.00% by mass aqueous acetic acid solution is — l.72°C. What is the molar mass of the solute Explain any discrepancy between the experimental and the expected molar mass, (b) The freezing-point depression associated with a 5.00% by mass solution of acetic acid in benzene is 2.32°C. Whar is the experimental molar mass of the solute in benzene What can you conclude about the nature of acetic acid in benzene ... 

For practical purposes, the colligative property that is most useful for measuring relative molar masses of polymers is osmotic pressure. As Table 6.2 shows, all other properties take such small values that their measurement is impractical. 

Colligative properties measure average relative molar masses, M, and in the case of osmotic pressure, II, the important relationship is ... 

Table 6.2 Colligative properties of a solution of polymer of molar mass 20 000 at a concentration o/O.Ol g (from F. W. Billmeyer, Textbook of Polymer Science , John Wiley Sons, New York, 1962)...

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... 

An unknown hydrocarbon is burned in the presence of oxygen in order to determine its empirical formula. Another sample of the hydrocarbon is subjected to colligative property tests in order to determine its molecular mass. 

The osmotic pressure is a colligative property and mathematically can be represented as 71 = (nRTIV) i, where It is the osmotic pressure in atmospheres n is the number of moles of solute R is the ideal gas constant 0.0821 L atm/Kmol T is the Kelvin temperature Vis the volume of the solution and i is the van t Hoff factor. Measurements of the osmotic pressure can be used to calculate the molar mass of a solute. This is especially useful in determining the molar mass of large molecules such as proteins. 

If you instead add the same number of moles of calcium chloride (2.71 mol) to the water, the calcium chloride would dissociate into three particles per mole in solution. This gives you 2.71 molx3 = 8.13 mol of solute in solution. As with the sodium chloride solution, divide the number of moles by the mass of solvent (1.2 kg) to get 6.8 m, and multiply by the of water (0.512°C/m) to get a of 3.5°C. This is a difference of more than 1 degree The difference arises because colligative properties such as boiling point elevation depend on only the number of particles in solution. 

Depression of Freezing Temperature. One of the colligative properties of solutions of nonvolatile solutes is that the freezing temperature is lower than that of the pure solvent. The depression of the freezing temperature is approximately proportional to the mass ratio of solute to solvent—that is,... 

Colligative properties have many practical uses, including the melting of snow by salt, the desalination of seawater by reverse osmosis, the separation and purification of volatile liquids by fractional distillation, and the determination of molecular mass by osmotic pressure measurement. 

Which of the four colligative properties is most often used for molecular mass determination, and why ... 

Osmotic pressure, which is a colligative property, depends simply on the number of solute molecules present and so yields a number-average relative molecular mass ... 

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