Sodium chloride adopts a face-centered cubic (rock-salt) lattice in which each Na^+…
CHEMISTRY · Multi-part · AP · Chemistry · Compound Structure and Properties · Compound Structure and Properties
Problem
Sodium chloride adopts a face-centered cubic (rock-salt) lattice in which each Na^+ ion is octahedrally coordinated by Cl^– ions. A materials scientist prepares a series of crystalline samples in which 2.0 mol % of the Na^+ sites are replaced by Ca^{2+} ions while the positions of the chloride ions remain unchanged. Relevant ionic radii (six-coordinate) are provided below.
• Na^+ : 1.02 Å
• Ca^{2+} : 1.00 Å
• Cl^– : 1.81 Å
Assume that the average Na–Cl distance in pure NaCl is 2.82 Å.
Answer the following questions about the doped lattice. (Assume that the small substitution level does not alter the overall crystal structure.)
(a) Predict whether the substitution of Ca^{2+} for Na^+ will increase, decrease, or leave unchanged the magnitude of the lattice energy per ion pair relative to pure NaCl. Justify your prediction qualitatively.
(b) Explain, in terms of Coulombic attractions and the given ionic radii, why the direction of the change you predicted in part (a) is expected.
(c) The melting point of pure NaCl is 801 °C. Predict how the melting point of the Ca^{2+}-doped sample is expected to compare with this value. Provide a brief rationale.
(d) Discuss one possible source of lattice strain or distortion that may arise from the Ca^{2+} substitution and describe how it could affect mechanical brittleness.