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 understand the factors that influence lattice energy. Lattice energy is the energy required to separate one mole of a solid ionic compound into its gaseous ions. The lattice energy is influenced by two main factors: the charges of the ions and the distance between them (ionic radii).

### Step-by-Step Solution:

1. **Understanding Lattice Energy**:
- Lattice energy is defined as the energy required to separate one mole of an ionic solid into its gaseous ions. It can be represented by the equation:
\[ U \propto \frac{q_1 \cdot q_2}{r} \]
where \( U \) is the lattice energy, \( q_1 \) and \( q_2 \) are the charges of the cation and anion, respectively, and \( r \) is the distance between the ions (ionic radii).

2. **Analyzing Ionic Compounds**:
- Consider the following ionic compounds:
- NaF: \( Na^+ \) and \( F^- \) (charges: +1 and -1)
- AlF3: \( Al^{3+} \) and \( 3F^- \) (charges: +3 and -1)
- AlN: \( Al^{3+} \) and \( N^{3-} \) (charges: +3 and -3)
- MgF2: \( Mg^{2+} \) and \( 2F^- \) (charges: +2 and -1)

3. **Calculating Charge Products**:
- For each compound, calculate the product of the charges:
- NaF: \( 1 \times 1 = 1 \)
- AlF3: \( 3 \times 1 = 3 \)
- AlN: \( 3 \times 3 = 9 \)
- MgF2: \( 2 \times 1 = 2 \)

4. **Comparing Charge Products**:
- The charge product indicates the strength of the electrostatic attraction between the ions:
- NaF: 1
- AlF3: 3
- AlN: 9
- MgF2: 2

5. **Determining the Largest Lattice Energy**:
- Since lattice energy is directly proportional to the product of the charges, AlN has the highest charge product (9), indicating it will have the largest lattice energy.

6. **Conclusion**:
- Therefore, the ionic compound with the largest amount of lattice energy is **AlN**.