Concentrated Solutions

It is easy to see that this can only be the case with substances which are very similar in nature. Thus if we have a liquid made up of molecules of a kind W, say water (fig. 4), and we replace half of them by molecules of another kind A, e.g., alcohol, it is evident that the attractive forces acting on a single molecule W can only be the same in the pure liquid (a) and in the solution (b) if the attraction between a molecule W and a molecule A is the same as that between two molecules W. This can only be the case when the two substances are very closely related. If the molecules of a substance are held in the solution by forces greater than those acting in the pure liquid, the vapour pressure will be less than that given by Raoult's law; if the forces are less, the vapour pressure will be greater.

In a theory of solutions first put forward in 1916, J. H. Hildebrand has taken the in ternal pressure as a convenient measure of the attractive forces between molecule and molecule in a liquid. The internal pressure can be regarded as the cohesive force acting across a surface I sq.cm. in area in the interior of a liquid. If the internal pressures of two liquids are the same it may be possible to replace molecules of one by molecules of the other without changing the cohesion. If the internal pressures are different, it is unlikely that the cohesive forces acting on a molecule in the solution can be the same as in its pure liquid. Hildebrand has shown that liquids having nearly identical internal pressures do in fact form ideal solutions, while deviations from it are the greater the greater the difference of internal pressures. Table IV. gives the relative internal pressures of some typical substances (taking that of naphthalene as a standard).

Activities.

In order to express the behaviour of non-ideal solutions, G. N. Lewis and M. Randall in 1907 introduced a quan tity which they called the activity. In ideal solutions the partial vapour pressure of a component is proportional to its molar frac tion ; in non-ideal solutions the quantity to which it is propor tional is called its activity, a , so that we have: (I) in ideal solutions, p= poN; (2) in non-ideal solutions p=p0a.

The ratio of the partial pressure of a component in a given solu tion to its vapour pressure as pure liquid (i.e., p/p0), which in ideal solutions is equal to the molar fraction, is thus in general equal to the activity. The ratio of the activity to the correspond ing molar fraction is called the activity coefficient. In ideal solu tions the activity coefficient is therefore equal to unity; its differ ence from unity indicates the extent of the deviation from the Partially Miscible Liquids.—When the deviation from Raoult's law is very great two liquids may no longer form homo geneous solutions when mixed in all proportions. There may be a limit to the extent to which each liquid dissolves the other, and if the proportions are not within these limits two liquid layers are formed.

The mutual solubility of two such liquids at different tempera tures may be represented by a graph. Thus in fig. 5 the left hand branch represents the solu bility of water in phenol, the right-hand branch that of phenol in water. In this case the mutual solubility of the two liquids in creases as the temperature rises and the two curves meet at a temperature of 68.8° C, which is known as the critical solubility temperature. Above this the liquids are miscible in all proportions.

It is usually the case that deviations from Raoult's law de

crease, and the mutual solubility increases, as in fig. 5, with rise of temperature. But a few cases have been observed in which the reverse happens. Thus the mu tual solubilities of triethylamine and water increase as the temper ature is lowered, and there is a lower critical solubility tempera ture below which the two liquids are miscible in all proportions. Solutions of nicotine and water have the extraordinary property of having two critical solubility temperatures, an upper and a lower one. Thus above 21o° and below 6o° C the two liquids are miscible in all proportions; at in termediate temperatures they are only partially miscible. The mutual solubilities are thus repre sented by a closed curve. (See CHEMISTRY : PHYSICAL.)