The magnitude of the lattice enthalpy of a solid increases if-

Options

A. the ions are large
B. the ions are small
C. the ions are of equal size
D. Charges on the ions are small

Answer

To determine the conditions under which the magnitude of the lattice enthalpy of a solid increases, we need to analyze the factors that influence lattice energy.

### Step-by-Step Solution:

1. **Understanding Lattice Enthalpy**:
Lattice enthalpy (or lattice energy) is the energy released when gaseous ions combine to form an ionic solid. It is a measure of the strength of the forces between the ions in an ionic solid.

2. **Factors Affecting Lattice Enthalpy**:
The lattice enthalpy is influenced by two main factors:
- The **charge** of the ions.
- The **size** of the ions.

3. **Charge Density**:
Lattice energy is directly proportional to the charge density of the ions. Charge density can be defined as:
\[ \text{Charge Density} = \frac{\text{Charge}}{\text{Size}} \]
This means that a higher charge and a smaller size will lead to a higher charge density.

4. **Effect of Ion Size**:
- If the size of the ions decreases (i.e., the ions are smaller), the charge density increases, which increases the lattice enthalpy.
- Conversely, if the ions are larger, the charge density decreases, leading to a lower lattice enthalpy.

5. **Effect of Ion Charge**:
- If the charge of the ions increases (i.e., the ions have higher charges), this also increases the charge density, which in turn increases the lattice enthalpy.
- Lower charges on the ions will decrease the lattice enthalpy.

6. **Conclusion**:
Therefore, the magnitude of the lattice enthalpy of a solid increases if:
- The size of the ions decreases (smaller ions).
- The charge of the ions increases (higher charges).

### Final Answer:
The magnitude of the lattice enthalpy of a solid increases if the size of the ions decreases or the charge of the ions increases.

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