The activity of a strong electrolyte is taken as the (geometrical) mean of the activities of its ions and in very dilute solutions is also equal to the concentration. Activities can be determined by a variety of methods, from measurements of the freezing points, boiling points and related properties of solutions, and in the case of slightly soluble salts, from their solubilities. These measure ments all depend on the equilibrium of the solution with either the solvent in the solid or vapour state or, in the case of solubilities, with the solid solute. They all depend on the tendency of either solvent or solute to leave the solution. Thus the vapour pressure measures the tendency of the solvent to leave the solution and enter the coexistent vapour ; a change in the freezing point meas ures the corresponding change in the tendency of the solvent to separate out as the solid, and a change in solubility measures the change in the tendency of the solute to deposit from the solution. These are all measures of what G. N. Lewis has called the "escap ing tendency" of either solvent or solute from the solution. The escaping tendencies of solute and solvent are inter-related and a change in the one can be calculated, by thermodynamical methods, from the corresponding change in the other. In ideal solutions the escaping tendencies of the components are related in a simple way to their molar fractions (or molecular concentrations, suit ably expressed). The activities are the quantities which measure the escaping tendencies in actual solutions.
If we divide the activity of an electrolyte by its concentration (usually the molal concentration is used) we get the activity co efficient. The activity coefficients of many strong electrolytes in
aqueous solution have been determined by G. N. Lewis, G. A. Linhart, A. A. Noyes, H. S. Harned and others. American physical chemists have been particularly active in this field. Table VIII. gives some representative values.
The effect of concentration on the activity coefficients of a few typical electrolytes is shown in fig. 7. As the concentration in creases the activity coefficients at first decrease. Usually they reach a minimum and then rise, becoming greater than unity in concentrated solutions. This behaviour is decisive against Arr henius' theory. An activity coefficient less than unity might pos sibly be interpreted as a degree of dissociation, but some other explanation must be found for activity coefficients which are greater than unity. The magnitude of the effect is shown by the fact that the activity coefficient of hydrochloric acid in a solution in which its molal concentration is i6, is 43.2. This cannot pos sibly be interpreted as a "degree of dissociation." The Ionic Strength.—In dilute solutions the change of the activity coefficient with concentration is very uniform. In solu tions of salts of the same type the activity coefficients are prac tically identical up to a molal concentration of 0.i. In mixed solu tions containing two or more salts of the same type, it is found that the activity coefficient depends only on the total ion concen tration when the latter is small. In studying mixtures containing ions of different types (i.e., having different electric charges), G. N. Lewis and M. Randall found that the effect of a bivalent ion on the activity coefficients of the salts in the solution was f our times that of a univalent ion, or that the effect is proportional to the square of the ionic charge. They therefore introduced a quantity which they termed the ionic strength of the solution ; this is obtained by multiplying each ion concentration by the square of its valency (or electric charge in electronic units) and dividing the sum by two. They were then able to state the rule that in dilute solutions the activity coefficient of a particular strong elec trolyte is the same in all solutions of the same ionic strength.
At concentrations greater than about 0.i molal each electrolyte begins to exhibit an individual behaviour, both in solutions of it alone and in mixed solutions.