Three classmates each write a verbal description of what they believe is an accurate…
CHEMISTRY · Multi-part · AP · Chemistry · Compound Structure and Properties · Compound Structure and Properties
Problem
Three classmates each write a verbal description of what they believe is an accurate particulate-level diagram for calcium fluoride, CaF₂. The relevant portions of their descriptions are reproduced below.
• Diagram I (Clara): “Cations (Ca²⁺) occupy all the body-center positions of a set of identical cubes; anions (F⁻) occupy only the eight vertices of every cube.”
• Diagram II (Dan): “Cations occupy every other vertex along all three axes so that no two Ca²⁺ ions are edge-sharing; anions completely fill the centers of all tetrahedral voids.”
• Diagram III (Eli): “Cations and anions alternate at every lattice point of a face-centered cubic array.”
Assume each description refers to a macroscopic fragment large enough to display periodicity.
(a) Determine which one of the three diagrams (I, II, or III) provides the most accurate qualitative representation of the CaF₂ lattice. Justify your choice in terms of charge balance and the minimization of like-charge repulsions.
(b) For each of the two remaining diagrams, identify one specific structural flaw and propose a correction that would eliminate the flaw while preserving the CaF₂ empirical formula.
(c) Qualitatively predict how the structural flaws you identified in part (b) would affect the lattice energy of the hypothetical crystal compared with that of authentic CaF₂. Explain your reasoning.