Resumen de Calculating Soft-Sphere Ionic Radii for Solid-State Arrangements from Solution Measurements
Megan N. Aardema, Jamison Koeman, Douglas A. Vander Griend
Despite extensive conceptualization of ions as hard spheres in most textbooks, solid-state structures are more accurately modeled as overlapping soft spheres that better reflect the size of the ions. The corresponding soft-sphere ionic radii of alkali and halide ions can be empirically established from the partial molar volume of the ions in aqueous solution. Partial molar volumes for 15 alkali halide solutes are calculated from the slope of solution density (g/L) versus the solution molarity (mol/L) at the infinite dilution limit. The set of resulting ion sizes for the lithium, sodium, potassium, rubidium, cesium, chloride, bromide, and iodide is both self-consistent, being composed of quantities that are mathematically additive, and physically meaningful. Upon setting the volume of Li(I) to 5.2 mL/mol, the solid-state structures of all 15 alkali halides, whether rock salt or CsCl, can be constructed to accurately model ion overlap as well as hole volume, though the size ordering of the ions is different than the ordering found for hard spheres. This new conceptual and empirical bridge between the solution and solid phases should help advance the teaching of these commonly disparate subjects by reinforcing aspects of both while drawing new connections between them.
