Two alternative verbal descriptions, Model X and Model Y
CHEMISTRY · Multi-part · AP · Chemistry · Compound Structure and Properties · Compound Structure and Properties
Problem
Two alternative verbal descriptions, Model X and Model Y, are offered for the arrangement of ions in an idealized fragment of lithium oxide, Li₂O.
• Model X: “In every unit cell, oxide ions (O²⁻) occupy all face centers and lithium ions (Li⁺) occupy the eight corners. No other lattice points are filled.”
• Model Y: “The lattice is based on a cubic close-packed array of oxide ions with lithium ions filling all tetrahedral holes. The pattern repeats every two close-packed layers.”
Assume charge neutrality and space-filling considerations must be satisfied for a stable ionic solid.
(a) Develop three independent criteria that any particulate representation must satisfy in order to be considered a physically reasonable model for the Li₂O lattice.
(b) Apply each criterion from part (a) to Models X and Y, and construct a concise evaluative table that indicates whether each model satisfies (✓) or violates (✗) each criterion.
(c) On the basis of your analysis, identify which model (X or Y) is more plausible. Provide a comprehensive justification that synthesizes all three criteria.
(d) For the less plausible model, outline a minimal set of modifications that would bring the representation into compliance with all criteria while retaining the Li₂O stoichiometry.