Solutions of Electrolytes

Interionic Attraction Theory.

That the electric forces between ions must have an important influence on the properties of salt solutions was pointed out by van Laar (z900), Sutherland (1902) and Bjerrum (1909). The first successful calculation of these forces was made in 1913 by S. R. Milner. Unfortunately his calculations were mathematically very complex, since he evaluated the electric forces between a given ion and every other ion present in the solution and summed the effect for all the ions.

His results could only with difficulty be applied to actual cases. J. Chandra Ghosh in 1918 attempted a partial solution of the problem, and in 1923 P. Debye and E. Hiickel found a compar atively simple method of calculating the effect. Since ions with electric charges of opposite sign attract each other and the attrac tion is greater the closer the ions approach, it is more difficult to remove a given ion from a strong solution than from a more dilute one. Thus the electric forces cause a decrease in the "escaping tendencies" of the ions, and the more concentrated the solution the greater is the effect.

Debye and Hiickel based their calculations on the fact that a particular ion tends to attract into its vicinity ions of unlike sign and to repel those of like sign, so that on the average it is sur rounded by more ions of unlike sign than of like sign. Making use of the Boltzmann equation, which gives the distribution of molecules in a region under the action of electric and other forces, and the Poisson equation (see ELECTROSTATICS), which defines how the forces vary in a known distribution of electric charges, they were able to calculate the work done in removing an ion, on account of the electric forces exerted on it by the surrounding ions. This is the quantity which determines the deviation from Raoult's law. In dilute solutions, in which the diameter of the ions is small in comparison with their distance apart, they found that the cal culation gave the result that the activity coefficient of a strong electrolyte is given by the formula log f = ziz2B where f is the activity coefficient andµ the ionic strength of the solution; z, and z, are the charges (in electronic units) on the two ions of the substance and B is a constant which is approximately for aqueous solutions at o° C. Not only does this formula agree with the ionic strength rule, already stated, that the activity co efficient of a strong electrolyte is determined by the ionic strength of the solution, but it is in numerical agreement with the values in dilute solutions.

Debye and Hiickel attempted to account for the individual behaviours of salts in more concentrated solutions by taking account of (I) the diameters of the ions, (2) the effect of the dis solved electrolytes on the dielectric constant of the solution. Al

though they were able to account qualitatively for the general form of the activity coefficient curve, they were not completely successful in calculating the activity coefficients from the known properties of the substances.

An important factor to be taken into account is the effect of the electric forces round the ions on the molecules of the solvent. Water, like all substances which dissolve strong electrolytes, has strongly "polar" molecules, i.e., its molecules are attracted towards regions in which electric forces are greatest. Thus water mole cules tend to congregate round ions, forming "water sheaths," which in strong solutions keep them apart, thus acting in the opposite sense to their attractive forces. It is probable that the rise in the activity coefficient in strong solutions is due to this effect.

Hydration of Ions.

It had previously been found in many phenomena that, in aqueous solutions, ions behaved as if they were associated with a certain amount of water, but in spite of many attempts no reliable estimate was made of the degree of hydration or amount of water associated with each ion. In 1919 K. Fajans showed that, knowing the lattice energies (see CRYSTALLOGRAPHY) of solid salts, it was possible to determine the energies of hydra tion of the ions. This quantity is the amount of energy liberated when a free ion in the gaseous state is introduced into water. Table IX. gives the energies of hydration of ions (in kilo gram calories per gram-atom) obtained by W. M. Latimer (1926).

As Max Born first pointed out in 1920, the energies of hydration of ions agree closely with the changes of electrical energy to be expected according to electrical theory, when a charged sphere the size of which is equal to that of the ion is moved from a vacuum into a medium having the dielectric constant of water. (The figures for given in parentheses are calculated in this way.) It thus appears that the energy effects on the solutions of ions are electrical in origin, and this gives powerful support to the idea that the "water of hydration" of ions is held by purely electrical forces and is not chemically combined with the ion. (For colloidal solutions, see COLLOIDS.) BiBuocRapHY.—Comprehensive accounts of solutions are to be found in most treatises on physical chemistry. Specialized works are: A. Findlay, Osmotic Pressure (1919) ; C. A. Kraus, The Properties of Electrically Conducting Systems (1922), deals exhaustively with electrolytic solutions; J. H. Hildebrand, Solubility (American Chemical Society monographs) , treats the subject mainly from the point of view of the author's own theory ; D. A. Clibbens, The Principles of the Phase Theory (1923), deals with the solubility relations of mixtures of salts. (J. A. V. B.)