Which ionic compound has the largest amount of lattice energy ?

Options

A. NaF
B. `AlF_(3)`
C. `AlN`
D. `MgF_(2)`

Explanation

To determine which ionic compound has the largest amount of lattice energy, we need to analyze the given compounds based on their ionic charges and sizes. Lattice energy is the energy released when gaseous ions combine to form an ionic solid, and it is influenced by the charges of the ions and the distance between them.

### Step-by-Step Solution:

1. **Understand Lattice Energy**:
Lattice energy is defined as the energy released when one mole of an ionic compound is formed from its gaseous ions. It is directly proportional to the product of the charges of the cation and anion and inversely proportional to the distance between them.

\[ \text{Lattice Energy} \propto \frac{q_1 \cdot q_2}{r} \]
where \( q_1 \) and \( q_2 \) are the charges of the cation and anion, and \( r \) is the distance between the ions.

2. **Evaluate the Given Compounds**:
The compounds to consider are:
- Sodium Fluoride (NaF): Na⁺ (charge +1), F⁻ (charge -1)
- Aluminum Trifluoride (AlF₃): Al³⁺ (charge +3), F⁻ (charge -1)
- Aluminum Nitride (AlN): Al³⁺ (charge +3), N³⁻ (charge -3)
- Magnesium Fluoride (MgF₂): Mg²⁺ (charge +2), F⁻ (charge -1)

3. **Calculate Effective Charges**:
- For NaF: \( q_1 \cdot q_2 = 1 \cdot 1 = 1 \)
- For AlF₃: \( q_1 \cdot q_2 = 3 \cdot 1 = 3 \)
- For AlN: \( q_1 \cdot q_2 = 3 \cdot 3 = 9 \)
- For MgF₂: \( q_1 \cdot q_2 = 2 \cdot 1 = 2 \)

4. **Consider Ionic Sizes**:
Smaller ionic sizes lead to a smaller distance \( r \), which increases lattice energy. Generally, the ionic radii of Al³⁺ and N³⁻ are smaller than those of Na⁺, Mg²⁺, and F⁻.

5. **Compare the Compounds**:
- NaF has the lowest charge product (1).
- MgF₂ has a moderate charge product (2).
- AlF₃ has a higher charge product (3).
- AlN has the highest charge product (9) and smaller ionic sizes.

6. **Conclusion**:
Since AlN has the highest product of charges (9) and smaller ionic sizes, it will have the largest lattice energy among the given compounds.

### Final Answer:
**Aluminum Nitride (AlN) has the largest amount of lattice energy.**