Lattice energy : Lattice energy is the amount of energy released when one mole of ionic compound is formed from its gaseous ions
`underset((g))(Na^(+)) + underset((g))(Cl^(-)) to NaCl(s) + Deltax kJ`
Lattice energy also depend on the 3-D arrangement of ion .
In the given compounds least Lattice energy is present in

Options

A. AgF
B. AgBr
C. AgCl
D. NaCl

Answer

To determine which compound has the least lattice energy among the given options (NaCl, AgF, AgCl, AgBr), we need to analyze the factors that affect lattice energy.

### Step 1: Understand Lattice Energy
Lattice energy is the energy released when one mole of an ionic compound is formed from its gaseous ions. It is influenced by:
- The charges of the ions: Higher charges lead to greater lattice energy.
- The size of the ions: Larger ions result in lower lattice energy due to increased distance between them.

### Step 2: Analyze the Given Compounds
The compounds provided are:
1. NaCl
2. AgF
3. AgCl
4. AgBr

### Step 3: Compare the Ionic Sizes
- **NaCl**: Sodium (Na⁺) is a smaller cation compared to silver (Ag⁺).
- **AgF**: Fluoride (F⁻) is a small anion.
- **AgCl**: Chloride (Cl⁻) is larger than fluoride.
- **AgBr**: Bromide (Br⁻) is larger than chloride.

### Step 4: Determine the Charge Product
The charge product (cation charge × anion charge) is the same for all compounds since:
- Na⁺ and Cl⁻ both have a charge of ±1.
- Ag⁺ has a charge of +1 for all compounds, and F⁻, Cl⁻, and Br⁻ have charges of -1.

### Step 5: Assess the Lattice Energy Trend
- **NaCl** has a relatively high lattice energy due to the smaller size of Na⁺ compared to Ag⁺.
- **AgF** has a high lattice energy because F⁻ is small.
- **AgCl** has lower lattice energy than AgF because Cl⁻ is larger than F⁻.
- **AgBr** has the lowest lattice energy because Br⁻ is larger than Cl⁻.

### Conclusion
Based on the analysis, the compound with the least lattice energy is **AgBr**.

### Final Answer
The compound with the least lattice energy is **AgBr**.

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