Which of the following has highest lattice energy

Options

A. `LiF`
B. `NaF`
C. `KF`
D. `RbF.`

Explanation

To determine which of the given compounds has the highest lattice energy, we need to understand the factors that influence lattice energy. Lattice energy is the energy required to separate one mole of an ionic solid into its gaseous ions. It can be represented by the formula:

\[ \text{Lattice Energy} \propto \frac{Q^+ \times Q^-}{R^+ + R^-} \]

Where:
- \( Q^+ \) = charge of the cation
- \( Q^- \) = charge of the anion
- \( R^+ \) = radius of the cation
- \( R^- \) = radius of the anion

### Step-by-Step Solution:

1. **Identify the Charges**:
- All the cations provided in the options belong to the alkali metals group (Li⁺, Na⁺, K⁺, Rb⁺). Therefore, the charge \( Q^+ \) for all these cations is +1.
- The anion in all cases is fluorine (F⁻), which has a charge of -1. Thus, \( Q^- \) is -1 for all options.

2. **Consider the Anion Radius**:
- Since the anion is the same (F⁻) for all compounds, the radius \( R^- \) is constant across all options.

3. **Focus on Cation Radius**:
- The lattice energy is inversely proportional to the sum of the radii of the cation and anion. Therefore, we need to compare the radii of the cations (Li⁺, Na⁺, K⁺, Rb⁺).
- The ionic radii of the alkali metals increase as we move down the group:
- Li⁺ < Na⁺ < K⁺ < Rb⁺

4. **Determine the Smallest Cation**:
- Lithium ion (Li⁺) has the smallest radius among the given cations, which means it will have the highest lattice energy because a smaller radius leads to a stronger electrostatic attraction between the cation and anion.

5. **Conclusion**:
- Since Li⁺ has the smallest radius, the lattice energy of LiF (Lithium Fluoride) will be the highest among the given options.

### Final Answer:
The compound with the highest lattice energy is **LiF (Lithium Fluoride)**.

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