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 .
Which of the following has the highest Lattice energy ?

Options

A. MgO
B. NaCl
C. CaO
D. KCl

Answer

To determine which ionic compound has the highest lattice energy among the given options (NaCl, KCl, MgO, CaO), we can follow these steps:

### Step 1: Understand the Concept of 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 and the distance between them (ionic radii).

### Step 2: Analyze the Factors Affecting Lattice Energy
1. **Charge of Ions**: Lattice energy is directly proportional to the product of the charges of the cation and anion. Higher charges lead to stronger attractions and thus higher lattice energy.
2. **Ionic Radii**: Lattice energy is inversely proportional to the sum of the radii of the cation and anion. Smaller ions can get closer together, leading to stronger attractions.

### Step 3: Compare the Given Compounds
- **NaCl**: Contains Na⁺ (charge +1) and Cl⁻ (charge -1).
- **KCl**: Contains K⁺ (charge +1) and Cl⁻ (charge -1).
- **MgO**: Contains Mg²⁺ (charge +2) and O²⁻ (charge -2).
- **CaO**: Contains Ca²⁺ (charge +2) and O²⁻ (charge -2).

### Step 4: Evaluate the Ionic Sizes
- Na⁺ is smaller than K⁺, and Cl⁻ is the same in both NaCl and KCl.
- Mg²⁺ and Ca²⁺ are both larger than Na⁺ but have higher charges, which increases their lattice energy.
- O²⁻ is the same in both MgO and CaO.

### Step 5: Determine the Lattice Energy Trend
1. **Between NaCl and KCl**: NaCl has a higher lattice energy than KCl because Na⁺ is smaller than K⁺, leading to a stronger attraction.
2. **Between MgO and CaO**: MgO has a higher lattice energy than CaO because Mg²⁺ is smaller than Ca²⁺, leading to a stronger attraction.
3. **Comparing NaCl, KCl, MgO, and CaO**:
- MgO has the highest lattice energy due to its higher charges (+2 and -2) and smaller ionic size compared to CaO.
- NaCl has a higher lattice energy than KCl due to the smaller size of Na⁺ compared to K⁺.

### Conclusion
Based on the analysis, **MgO** has the highest lattice energy among the given options.

### Final Answer
The compound with the highest lattice energy is **MgO**.

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