Which set of compounds in the following pair of ionic compounds has the higher lattice energy ?
(i) `KCl or MgO " " (ii) LiF or LiBr " " (iii) Mg_(3)N_(2) or NaCl`

Options

A. `KCl, LiBr , Mg_(2)N_(2)`
B. `MgO, LiBr, Mg_(3)N_(2)`
C. `MgO, LiF, NaCl`
D. `MgO, LiF, Mg_(3)N_(2)`

Answer

To determine which set of compounds has the higher lattice energy, we need to analyze each pair of ionic compounds based on the charges of the ions and their ionic radii. Lattice energy is influenced by the charges of the ions and the distance between them, as described by the formula:

\[ \text{Lattice Energy} \propto \frac{(q_1 \cdot q_2)}{r} \]

where \( q_1 \) and \( q_2 \) are the charges of the cation and anion, and \( r \) is the distance between the ions (ionic radius).

### Step-by-Step Solution:

1. **Comparing KCl and MgO:**
- KCl consists of \( K^+ \) and \( Cl^- \) ions. The charges are \( +1 \) and \( -1 \), respectively.
- MgO consists of \( Mg^{2+} \) and \( O^{2-} \) ions. The charges are \( +2 \) and \( -2 \), respectively.
- The product of charges for KCl: \( 1 \times 1 = 1 \)
- The product of charges for MgO: \( 2 \times 2 = 4 \)
- Since MgO has a higher product of charges, it will have a higher lattice energy than KCl.

**Conclusion:** MgO has higher lattice energy than KCl.

2. **Comparing LiF and LiBr:**
- LiF consists of \( Li^+ \) and \( F^- \) ions. The charges are \( +1 \) and \( -1 \), respectively.
- LiBr consists of \( Li^+ \) and \( Br^- \) ions. The charges are \( +1 \) and \( -1 \), respectively.
- The product of charges for both LiF and LiBr is the same: \( 1 \times 1 = 1 \).
- However, the ionic radius of Br is larger than that of F. Since lattice energy is inversely proportional to the distance (size), LiF will have a higher lattice energy than LiBr.

**Conclusion:** LiF has higher lattice energy than LiBr.

3. **Comparing Mg3N2 and NaCl:**
- Mg3N2 consists of \( Mg^{2+} \) and \( N^{3-} \) ions. The charges are \( +2 \) and \( -3 \), respectively.
- NaCl consists of \( Na^+ \) and \( Cl^- \) ions. The charges are \( +1 \) and \( -1 \), respectively.
- The product of charges for Mg3N2: \( 2 \times 3 = 6 \)
- The product of charges for NaCl: \( 1 \times 1 = 1 \)
- Since Mg3N2 has a much higher product of charges, it will have a higher lattice energy than NaCl.

**Conclusion:** Mg3N2 has higher lattice energy than NaCl.

### Final Summary:
- (i) MgO has higher lattice energy than KCl.
- (ii) LiF has higher lattice energy than LiBr.
- (iii) Mg3N2 has higher lattice energy than NaCl.