For materials that are only partially miscible with each other, it is conventional to refer to the concentration of one material in another at a specific temperature and pressure as the solubility of that material. It is a terminology most often used about the solubility of gases in liquids and solids in liquids and this is the context in which we address the topic here but, in principle, it is not confined to this case.
Gases are sparingly soluble in liquids so that the solutions formed are always dilute. Figure 1 shows the mole fraction of a number of gases in water as a function of the pressure, which emphasises this fact. It is an empirical observation, supported by simple theory, that for dilute solutions the vapor pressure of the solute is linearly related to its mole fraction in the solution, so that
which is known as Henry's Law and KA is the Henry's Law coefficient. Of course, if the vapor pressure of the solvent is very much less than that of total pressure, an approximation to Henry's Law is
where p is the total pressure. This behavior is confirmed by the figure.
Generally, Henry's Law coefficients increase with increasing temperature so that gases are less soluble in liquids at high temperature. A review of experimental methods has been given by Battino and Clever (1966).
The addition of a relatively involatile solute to a solvent lowers the freezing point of the solvent and raises its boiling point. Generally, the depression of the freezing point is written
where m is the molality of the solute and K1 the so-called cryoscopic constant. The molality of a solution is the number of moles of a solute in a solution containing 1 kg of solvent and is a particularly convenient practical measure of solution concentration. The corresponding constant for the boiling point is called the ebullioscopic constant. Measurement of these constants is employed as a means of determining the molar mass of species in solution [Murrell and Boucher (1982)]. These two properties are known, together with the osmotic pressure, as colligative properties. They depend upon specific properties of the solvent but on only the molality (or mole fraction) of the solute.
Battino, R. and Clever, H. L. (1966) Chem. Rev., 66, 395.
Hildebrand, J. H. and Scott, R. L. (1950) The Solubility of Non-Electrolytes, Reinhold, New York.
Hildebrand, J. H., Prausnitz, J. M., and Scott, R. L. (1970) Regular and Related Solutions, Van Nostrand, New York.
Murrel, J. N. and Boucher, E. A. (1982) Properties of Liquids and Solutions, Wiley, New York.
Rowlinson, J. S. and Swinton, F. L. (1982) Liquids and Liquid Mixtures, 3rd edn., Butterworths, London.