4 - Colligative Properties

Abstract

The colligative properties of a solution are defined as the properties which are determined by the number or the mole fraction of components (solutes and solvent) in the solution and are independent of the nature of the solutes and their molecular weights. If any physical quantities belonging to the colligative property (i.e. the colligative quantity) can be measured under thermodynamic equilibrium and also if the total weight of solute dissolved in a given solution is known, the molecular weight of the nonvolatile solute (or in the case of a nonuniform solute, the average molecular weight) can be determined. Unfortunately, both the osmotic pressure of the real solution and the vapor pressure of the vapor phase in equilibrium with the real solution are significantly influenced, in the finite concentration range of the solute, by the solute-solvent interaction and are not unique functions of the number of solute molecules existing in the solution. In general the activity of the solvent can be directly evaluated from the osmotic pressure or the partial vapor pressure. In fact, an extraordinarily large discrepancy from a simple proportionality of the osmotic pressure or the vapor pressure to the solute mole fraction was observed in the late 1920s to early 1930s in polymer solutions and these experimental facts motivated theoretical study by Flory, Huggins et al., based on the lattice model, of the thermodynamics of polymer solutions. Conversely, measurement of the extent of the deviation of polymer solutions from the proportionality relations between osmotic pressure or vapor pressure and solute mole fraction enables us to elucidate the thermodynamic interaction between a polymer chain and a solvent molecule (see equations 50 and 51) and to study the dissolved state of polymer molecules. The osmotic pressure and vapor pressure of the solution can be approximately regarded as colligative in the extremely low polymer concentration range for polymer-good solvent systems, and over the whole range of concentration when the polymer is dissolved in a solvent in which the second and the higher virial coefficients (equations 57–58) are zero. In the above cases, we can determine unambiguously the molecular weight of the polymer from its colligative properties. In fact, in the 1930s the determination of molecular weight of polymers using the colligative properties of the solutions was widely attempted, mainly by Staudinger and his collaborators,1 for cellulose derivatives and synthetic polymer solutions, giving a direct verification of ‘macromolecular compounds’. The importance of the use of colligative properties to determine the molecular weights of polymers and to estimate the polymer-solvent interactions remains unchanged to the present day.