Learning Objectives Understand the geometric basis of radius ratio rules. Understand the chemical basis of structure maps and why they are better predictors of crystal structures than radius ratios. Use the Born-Mayer and Kapustinskii equations to calculate lattice energies of known and hypothetical compounds. Construct Born-Haber cycles using lattice energies and calculate unknown quantities in the cycles. Predict the stabilities of low and high oxidation states using lattice energies. Understand the quantum mechanical origin of the extra "resonance" stability of metals. Predict trends in the solubility and thermal stability of inorganic compounds using lattice energies. In Chapter 8, we learned all about crystal structures of ionic compounds . A good question to ask is, what makes a compound choose a particular structure? In addressing this question, we will learn about the forces that hold crystals together and the relative energies of different structures. This will in turn help us understand in a more quantitative way some of the heuristic concepts we have learned about in earlier chapters, such as hard-soft acid-base theory. 10.1: Ionic Radii and Radius Ratios 10.2: Structure Maps 10.3: Energetics of Crystalline Solids- The Ionic Model 10.4: Born-Haber Cycles for NaCl and Silver Halides Now that we have an equation for the lattice energy of an ionic crystal, we can ask the question of how accurate it is. Remember, we made several approximations in arriving at this formula. We assumed that the lattice was completely ionic, we ignored the van der Waals attractive energy of the ions, and we assumed that there was no covalent contribution to the bonding. 10.5: Kapustinskii Equation Kapustinskii noticed that difference in ionic radii between the monovalent vs. divalent radii largely compensates for the differences in A/n between monovalent (NaCl, CsCl) and divalent (rutile, CaF2) structures. He thus arrived at a lattice energy formula using an average Madelung constant, corrected to monovalent radii. 10.6: Discovery of Noble Gas Compounds 10.7: Stabilization of High and Low Oxidation States 10.8: Alkalides and Electrides Another interesting consequence of lattice energies involves the formation of certain salts containing Na- and e- anions. These compounds are known as alkalides and electrides, respectively. Most of these compounds have been discovered by Prof. James Dye at Michigan State University. 10.9: Resonance Energy of Metals The valence electrons in Na metal are in orbitals that are delocalized over the entire crystal. However in the Na+ e- "salt" form, the electrons are localized on specific anion sites. This localization imparts an additional kinetic energy (via the "particle in a box" effect) that adds to the total energy. 10.10: Prelude to Ionic and Covalent Solids - Energetics 10.11: The Strange Case of the Alkali Oxides 10.12: Lattice Energies and Solubility 10.13: Discussion Questions 10.14: Problems 10.15: References