Ionic Size in Solutions

In order to apply the models which are introduced in this chapter, one needs an estimate of the size of the ions which make up the electrolyte. This is most easily done for monoatomic ions, since they are spherical, so that ionic size is known by determining the ionic radius. Furthermore, accurate interparticle distances are available from X-ray diffraction studies of ionic crystals, and more importantly, from X-ray and neutron diffraction studies of aqueous electrolyte solutions [1]. 

One of the most widely known and used set of ionic radii are those estimated by Pauling [2] on the basis of interionic distances in ionic crystals. He noted that repulsive effects between ions of the same charge depend on the relative size of the cation and anion in the crystal, and also took into consideration the coordination number of the ion with oppositely charged neighbors in the crystal lattice. The results obtained for the alkali metal and halide ions for the case that the coordination number is six (rock salt structure) are summarized in table 3.1. 

As the collection of X-ray diffraction data became more extensive, it was possible to describe the electron density distribution in ionic crystals in more detail. Using these data one can divide up the internuclear distance in the crystal on the basis of the minimum in the electron density between the two oppositely charged ions [3, 4]. For example, in the case of NaCl for which the internuclear distance is 281 pm, the minimum in the electron density leads to radii of 117 pm for Na and 164pm for CP. Radii derived on this basis are larger for cations and smaller for anions than those of Pauling. 

Shannon and PrewiLL [5] considered a very large collecLion of crysLallographic data for metal oxides and metal fluorides. Included in these data were transition metal compounds in which the bonding between cation and anion is both electrostatic and covalent in character. They noted that the eflective radius for a given ion depends on its coordination number in the crystal. In addition, for transition metal ions the radius depends on whether the d electrons in the ion are in a high or low spin state. By assigning a radius of 126 pm to the ion and 119 pm to the F ion when they are surrounded by six counter ions, they found that the eflective radii of the alkali metal ions and halide ions are very close to those obtained from electron density maps for the corresponding crystals. Their results for these ions are also summarized in table 3.1. 

Studies of pure water have resulted in the conclusion that water has a diameter of 284 pm in a spherical representation [G3]. Thus, if the electrolyte solution is represented as a collection of hard spheres, the distance between the center of a 

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