III. Ionic size in relation to the physical properties of aqueous solutions

Abstract

The electrical conductivity of a solution depends upon the rates of transference of the ionised portions of the solute in opposite directions under the influence of the applied electro-motive force. These rates of transference under a given potential gradient are conditioned by the viscosity of the medium and the sizes and possibly the shapes of the ions. Increase of viscosity of the solution and increase in the sizes of the migrating ions both tend to diminish the rates of transference of the ions, and thus to lower the conductivity. If the ion enters into combination with one or more molecules of water, its size is necessarily increased, and the motion of the water­ logged ion becomes more sluggish as the amount of water in combination increases. To separate the elements which determine the conductivity of an electrolytic solution, and to analyse the joint effect of variations in ionisation, viscosity and water com­bination is a matter of great difficulty, but of much importance to the theory of solution. In a former paper (Bousfield on “Ionic Sizes in Relation to the Conductivity of Electrolytes”) was proposed a method for effecting such an analysis based upon the expression evaluated by Stokes for the terminal velocity of a small sphere moving in a viscous medium. A consideration of the influence of the water in combination with the ion upon its mobility was used to obtain a correction of the coefficient of ionisation, which made Van’t Hoff’s law (in a slightly modified form) an accurate expression of the relation between ionisation and dilution, down to twice decinormal solutions of KCl. This method of procedure gave for the radius of the hydrated ion an expression of the form r = r α ( 1 + B h -2/3 ) -1 , which indicated that the average radius of the ion steadily increased with dilution, owing to increasing hydration of the ion, up to “infinite dilution.” Whether the resulting expression for r did in fact represent the average radius of the ion was tested by a consideration of the density law which would thence result. The volumes of the ions would be proportional to r 3 , and it was found that a rational density formula could be constructed upon this basis which accurately corresponded with the observed densities of the solutions.