Which of the following is most soluble in water?

Options

A. `CsClO_(4)`
B. `NaClO_(4)`
C. `KClO_(4)`
D. `LiClO_(4)`

Answer

To determine which of the given compounds is most soluble in water, we need to analyze the solubility factors, specifically hydration energy and lattice energy.

### Step-by-Step Solution:

1. **Identify the Compounds**: The compounds in question are lithium perchlorate (LiClO4), sodium perchlorate (NaClO4), potassium perchlorate (KClO4), and cesium perchlorate (CsClO4).

2. **Understand Solubility Factors**: Solubility in water is influenced by two main energies:
- **Hydration Energy**: The energy released when water molecules surround and interact with ions.
- **Lattice Energy**: The energy required to separate a compound into its gaseous ions.

3. **Analyze Hydration Energy**: Hydration energy is inversely proportional to the size of the ion. Smaller ions have higher hydration energy because they can attract water molecules more effectively.
- Li+ (lithium) is smaller than Na+, K+, and Cs+, so Li+ will have the highest hydration energy.

4. **Analyze Lattice Energy**: Lattice energy is directly related to the size of the ions. Larger ions result in lower lattice energy because the distance between the ions increases, reducing the electrostatic attraction.
- As we move from Li+ to Cs+, the size of the cations increases, leading to a decrease in lattice energy.

5. **Compare Hydration and Lattice Energy**:
- For LiClO4: High hydration energy (due to small Li+) and relatively lower lattice energy.
- For NaClO4: Moderate hydration energy and moderate lattice energy.
- For KClO4: Lower hydration energy and lower lattice energy.
- For CsClO4: Lowest hydration energy and lowest lattice energy.

6. **Conclusion**: Since lithium perchlorate (LiClO4) has the highest hydration energy relative to its lattice energy, it will be the most soluble in water compared to the other compounds.

### Final Answer:
**LiClO4 (lithium perchlorate) is the most soluble in water.**