Masses from Colligative Properties

In physical chemistry, we apply the term coUigative to those properties that depend upon number of molecules present. The principal coUigative properties are boiling point elevation, freezing point depression, vapour pressure lowering, and osmotic pressure. All such methods require extrapolation of experimental data back, to infinite dilution. This arises due to the fact that the physical properties of any solute at a reasonable concentration in a solvent are determined not by the mole fraction of solute, but by the so-called activity of the solute. This takes a value less than the actual mole fraction, and is related to it by the activity coefficient  

For practical purposes, the coUigative 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. 

Boiling point elevation Freezing point depression Osmotic pressure Vapour pressure lowering 

CoUigative properties measure average relative molar masses, M , and in the case of osmotic pressure, 11, the important relationship is  

From this we can develop a general expression for the relationship of these parameters to concentration. Thus  

---

Determination of Molar Masses from Colligative Properties... 

When the state of a substance in solution is unknown the effective molecular mass determined from colligative properties may provide valuable information. 

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)...

One of the laboratory requirements for the course, and also the topic of former test questions, is the determination of the molar mass of a substance from the freezing-point depression. Actually, any of the colligative properties can be used to determine the molar mass, but the only one that you are required to know is the freezing-point depression method. It is easier to illustrate the technique within the framework of a problem, so the discussion of this process will be done within a sample problem. 

Rudin s aim was to predict the size of dissolved polymer molecules and the colligative properties of polymer solutions (hydrodynamic volume, second virial coefficient, interaction parameter, osmotic pressure, etc) from viscometric data (average molar mass, intrinsic viscosity, etc.). 

Calculate the molar mass of a nonvolatile solute from the changes it causes in the colligative properties (vapor-pressure lowering, boiling-point elevation, freezing-point lowering, or osmotic pressure) of its dilute solution (Section 11.5, Problems 41-56). 

For a molecular compound, the full molecular formula can be established from the empirical formula and the molecular mass (RMM). Various physical properties, including the vapour density of a gas, and so-called colligative properties (such as freezing point depression) in solution, can be used to determine the RMM. However the most important technique in modem research is mass spectrometry (MS) where molecular ions are accelerated in an electric field, and then pass through a magnetic field where their paths are bent to an extent that depends on the mass/charge ratio. The traditional MS method requires a volatile sample, ionized by electron bombardment, but methods are now available that overcome the limitations of that method. Direct desorption from solids by a laser beam or by fast atom bombardment (FAB) allow measurement of involatile compounds. Solutions may also be sprayed directly into the spectrometer inlet and the spectrum measured after the solvent has evaporated. 

Each colligative property relates concentration to some measurable quantity—the number of degrees the freezing point is lowered, the magnitude of osmotic pressure created, and so forth. From these measurements, we can determine the amount (mol) of solute particles and, for a known mass of solute, the molar mass of the solute as well. 

The essential feature of these four properties is that they depend only on the number of solute molecules present- -not on the chemical and physical characteristics. Consequently, there is an exact relationship between each of the colligative properties and any other one if one property is measured, the others can be calculated. From the measurement of a colligative property we can calculate the number of moles of solute present if we also know the mass of the substance. 

Although these expressions provide no information about the activity coefficient of a solute, they are useful for estimating the solute molar mass. For example, from a measurement of any of the colligative properties of a dilute solution and the appropriate theoretical relation, we can obtain an approximate value of the solute molality niB- (It is only approximate because, for a measurement of reasonable precision, the solution cannot be extremely dilute.) If we prepare the solution with a known amount a of solvent and a known mass of solute, we can calculate the amount of solute from b = nAMpjnB, then the solute molar mass is the solute mass divided by ns-... 

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. 

---