A Prelude to the Ionic-Cloud Theory

A spectacular advance in the understanding of the distribution of charges around an ion in solution was achieved in 1923 by Debye and Hiickel. It is as significant in the understanding of ionic solutions as the Maxwell theory of the distribution of velocities is in the understanding of gases. 

Before going into the details of their theory, a moment s reflection on the magnitude of the problem will promote appreciation of their achievement. Consider, for example, a 10 M (mol dm ) aqueous solution of sodium chloride. There will be 10 X 6.023 X10 sodium ions per cubic centimeter of solution and the same number of chloride ions, together, of course, with the corresponding number of water molecules. Nature takes these 2 x 6.023 x lO ions cm and arranges them so that there 

The genius of Debye and Hiiekel lay in their formulation of a very simple but powerful model for the time-averaged distribution of ions in very dilute solutions of electrolytes. From this distribution they were able to obtain the electrostatic potential contributed by the surrounding ions to the total electrostatic potential at the reference ion and hence the chemical-potential change arising from ion-ion interactions [Eq.(3.3)]. Attention will now be focused on their approach. 

the electrolytic solution is considered to consist of a central ion standing alone in a continuum. Thanks to the water molecules, this continuum acquires a dielectric constant (taken to be the value for bulk water). The charges of the discrete ions that populate the environment of the central ion are thought of as smoothed out and contribute to the continuum dielectric a net charge density (excess charge per unit volume). In this way, water enters the analysis in the guise of a dielectric constant e and the ions, except the specific one chosen as the central ion, in the form of an excess charge density Q (Fig. 3.7). 

Fig- 3.6. A schematic comparison of (a) the assembly of ions and solvent molecules that constitute a real electrolytic solution and (b) the Debye-Hiickel picture in which a reference ion is surrounded by net charge density q due to the surrounding ions and a dielectric continuum of the same dielectric constant s as the bulk solvent. 

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