A Kinetic Approach to the Theory of Conductance of Infinitely Dilute Solutions, Based on the ``Cage'' Model of Liquids

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Abstract
Attention is called to the disparity between the hydrodynamic model of an electrolytic solution and its physical counterpart. The ``cage'' theory of liquids is reviewed, and some of its equations developed with the purpose of bringing to the surface the underlying assumptions. A quantitative comparison is carried out between the behavior of an ion subject to Brownian motion and that of the placidly moving ion of the hydrodynamic theory. The conclusion is drawn that the tremendous difference between the two models casts doubt upon the validity of the hydrodynamic equations. The possibility is mentioned that the hydrodynamic theory, while giving fortuitously approximately correct values of ionic radii, may still be incorrect in its theoretical implications. Stress is laid on the desirability of a kinetic theory of electrolytic conductance. An approach to a kinetic theory is made, based on the cage model of liquids. In this method, the ionic migration is considered as the cumulative effect of a feeble, sporadic, but directed perturbation of the violent but random Brownian movement. The method leads to an experimentally substantiated relation between the diffusion and the conductivity of an electrolyte. It offers a plausible explanation of the high temperature coefficient of the slow‐moving ions. For the ions of an infinitely dilute aqueous solution of potassium chloride, the method yields the following data: Heat of activation for a cage‐to‐cage jump, 4230 calories; frequency of cage‐to‐cage jumps, 1.12×1011 sec.—1; frequency of oscillation within the cage, 8.3×1013 sec.—1; average number of oscillations in each cage, 740.