Which of the following has highest value of `K_(sp)` ?

Options

A. `Be(OH)_2`
B. `Mg(OH)_2`
C. `Ca(OH)_2`
D. `Ba(OH)_2`

Answer

To determine which of the given hydroxides has the highest value of Ksp, we need to analyze the solubility product constant (Ksp) for each hydroxide. The Ksp is influenced by the solubility of the compound, which is affected by lattice energy and hydration energy.

### Step-by-Step Solution:

1. **Identify the Compounds**:
We are dealing with hydroxides of alkali earth metals (Group 2). Let's assume the compounds are:
- A) Mg(OH)₂
- B) Ca(OH)₂
- C) Sr(OH)₂
- D) Ba(OH)₂

2. **Understand Ksp**:
The solubility product (Ksp) of a compound can be expressed as:
\[ Ksp = [M^{2+}][OH^-]^2 \]
For a hydroxide M(OH)₂, if the solubility is S, then:
- [M²⁺] = S
- [OH⁻] = 2S
Therefore, the Ksp can be calculated as:
\[ Ksp = S \cdot (2S)^2 = 4S^3 \]

3. **Consider Lattice Energy and Hydration Energy**:
- Lattice energy decreases as we move down the group due to increasing ionic size.
- Hydration energy generally increases down the group but not as significantly as the decrease in lattice energy.

4. **Analyze Solubility**:
- As we move from Mg(OH)₂ to Ba(OH)₂, the lattice energy decreases, making the compounds more soluble.
- Mg(OH)₂ has the highest lattice energy, making it less soluble.
- Ba(OH)₂ has the lowest lattice energy, making it more soluble.

5. **Conclusion**:
Since Ksp is directly related to solubility, the compound with the highest solubility will have the highest Ksp. Thus, Ba(OH)₂, being the most soluble, will have the highest Ksp value.

### Final Answer:
The hydroxide with the highest value of Ksp is **Ba(OH)₂**.