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 compound has the highest value of \( K_{sp} \) (solubility product), we need to analyze the given compounds: barium hydroxide, magnesium hydroxide, and calcium hydroxide.

### Step-by-Step Solution:

1. **Understanding \( K_{sp} \)**:
- The solubility product \( K_{sp} \) is a constant that reflects the solubility of a sparingly soluble ionic compound in water. It is defined as the product of the concentrations of the ions in a saturated solution, each raised to the power of their coefficients in the balanced equation.

2. **Dissociation of Compounds**:
- Let's write the dissociation equations for each compound:
- **Barium Hydroxide**:
\[ Ba(OH)_2 \rightleftharpoons Ba^{2+} + 2OH^{-} \]
\( K_{sp} = [Ba^{2+}][OH^{-}]^2 \)

- **Magnesium Hydroxide**:
\[ Mg(OH)_2 \rightleftharpoons Mg^{2+} + 2OH^{-} \]
\( K_{sp} = [Mg^{2+}][OH^{-}]^2 \)

- **Calcium Hydroxide**:
\[ Ca(OH)_2 \rightleftharpoons Ca^{2+} + 2OH^{-} \]
\( K_{sp} = [Ca^{2+}][OH^{-}]^2 \)

3. **Comparing Solubility**:
- The solubility of hydroxides generally decreases as we move down the group in the periodic table. This means:
- Barium hydroxide (Ba(OH)₂) is more soluble than calcium hydroxide (Ca(OH)₂), which in turn is more soluble than magnesium hydroxide (Mg(OH)₂).
- Therefore, the order of solubility is:
\[ Ba(OH)_2 > Ca(OH)_2 > Mg(OH)_2 \]

4. **Determining \( K_{sp} \)**:
- Since \( K_{sp} \) is directly related to the solubility, the compound with the highest solubility will have the highest \( K_{sp} \).
- Thus, since barium hydroxide is the most soluble, it will have the highest \( K_{sp} \).

5. **Conclusion**:
- The compound with the highest value of \( K_{sp} \) is **Barium Hydroxide**.

### Final Answer:
**Barium Hydroxide** has the highest value of \( K_{sp} \).