Which substance do you expect to have the greatest lattice energy: MgF2, CaF2, or ZrO2?
The Correct Answer and Explanation is:
Correct Answer: ZrO₂ (Zirconium dioxide)
Explanation:
Lattice energy is the amount of energy released when ions in the gaseous state form an ionic solid. It is influenced by two main factors according to Coulomb’s Law:
- Charge of the ions
- Distance between the ions (ionic radii)
Mathematically, lattice energy is approximately proportional to:Lattice Energy∝q1⋅q2r\text{Lattice Energy} \propto \frac{{q_1 \cdot q_2}}{{r}}Lattice Energy∝rq1⋅q2
Where:
- q1q_1q1 and q2q_2q2 are the charges on the cation and anion
- rrr is the distance between the centers of the ions (which relates to the size of the ions)
Now, consider the compounds:
- MgF₂:
Magnesium ion: Mg²⁺
Fluoride ion: F⁻
Charges: +2 and −1 - CaF₂:
Calcium ion: Ca²⁺
Fluoride ion: F⁻
Charges: +2 and −1
(Ca²⁺ is larger than Mg²⁺, so the ions are farther apart than in MgF₂) - ZrO₂:
Zirconium ion: Zr⁴⁺
Oxide ion: O²⁻
Charges: +4 and −2
The product of charges is much larger (+4 × −2 = −8), compared to MgF₂ or CaF₂ (each has −2)
Even though Zr⁴⁺ is larger than Mg²⁺ or Ca²⁺, the charge effect dominates because the electrostatic attraction is much stronger due to the high ionic charges. The oxide ion also carries a −2 charge, contributing further to the attraction.
Summary:
ZrO₂ has the highest lattice energy due to the greater ionic charges (Zr⁴⁺ and O²⁻). The large electrostatic force between these ions more than compensates for any increase in ionic size. This results in a very strong lattice and thus the greatest lattice energy among the three compounds.
