A student attempts to depict the crystal lattice of sodium chloride in three dimensions
CHEMISTRY · Multi-part · AP · Chemistry · Compound Structure and Properties · Compound Structure and Properties
Problem
A student attempts to depict the crystal lattice of sodium chloride in three dimensions. In the student’s written description of the sketch, every lattice point on a simple cubic array is labelled either “Na⁺” or “Cl⁻.” The student reports the following details.
• All vertices of every cube are Na⁺ ions.
• All face‐centres of every cube are Na⁺ ions.
• All edge‐centres of every cube are Cl⁻ ions.
• Ions at adjacent lattice positions are shown separated by equal distances.
Assume the student intends to model a macroscopic fragment of a perfect NaCl crystal (rock-salt structure).
(a) Identify two specific ways in which the student’s description is inconsistent with the actual three-dimensional arrangement of ions in solid NaCl.
(b) For each inconsistency you identified in part (a), explain—using Coulomb’s law—why the depicted arrangement would be energetically unfavorable compared with the actual NaCl lattice.
(c) Redraw or describe a corrected arrangement for one unit cell that resolves both inconsistencies while preserving the overall NaCl stoichiometry.