Which of the following ionic compounds has the largest lattice energy (i.e., the lattice energy most favorable to a stable lattice)?
a) BaO
b) BeO
c) CsI
d) NaBr
e) BaS
The correct answer and explanation is :
The correct answer is b) BeO.
Explanation:
Lattice energy refers to the energy released when ions in the gas phase combine to form an ionic solid. The lattice energy is influenced by two key factors:
- Charge of the ions: The higher the charge on the ions, the greater the lattice energy. This is because the electrostatic force between ions increases with the magnitude of their charges.
- Size of the ions: Smaller ions have higher lattice energies because the distance between the ion centers is smaller, resulting in a stronger Coulomb attraction between the oppositely charged ions.
To determine which compound has the largest lattice energy, we need to evaluate these two factors for each ionic compound:
1. BaO:
- Ba²⁺ (charge 2) and O²⁻ (charge 2).
- Ba²⁺ is relatively large, and the ionic size of Ba²⁺ is considerably bigger than that of smaller ions like Be²⁺. The large size of Ba²⁺ reduces the lattice energy despite the high charge on both ions.
- Result: Lower lattice energy compared to BeO.
2. BeO:
- Be²⁺ (charge 2) and O²⁻ (charge 2).
- Be²⁺ is much smaller than Ba²⁺, and O²⁻ is the same size in both cases. The small size of Be²⁺ leads to a much stronger Coulomb attraction between Be²⁺ and O²⁻, resulting in a very high lattice energy.
- Result: BeO has the largest lattice energy.
3. CsI:
- Cs⁺ (charge 1) and I⁻ (charge 1).
- Both ions are relatively large (Cs⁺ is much larger than Be²⁺), and the charge on both ions is only ±1. This significantly reduces the lattice energy compared to compounds with higher charges.
- Result: Lower lattice energy.
4. NaBr:
- Na⁺ (charge 1) and Br⁻ (charge 1).
- Similar reasoning as CsI applies here, with the ions being large and the charges low.
- Result: Lower lattice energy.
5. BaS:
- Ba²⁺ (charge 2) and S²⁻ (charge 2).
- While both ions have a high charge, Ba²⁺ is large, which lowers the lattice energy compared to smaller ions.
- Result: Lower lattice energy than BeO.
Conclusion:
BeO has the smallest ionic radii for its divalent cation (Be²⁺), and both ions carry a high charge, leading to the largest lattice energy, which corresponds to a more stable lattice.
