The most soluble hydroxide among the following is 

Options

A. `Be(OH)_(2)`
B. `Ca(OH)_(2)`
C. `Mg(OH)_(2)`
D. `Ba(OH)_(2)`

Answer

To determine the most soluble hydroxide among beryllium hydroxide (Be(OH)₂), calcium hydroxide (Ca(OH)₂), magnesium hydroxide (Mg(OH)₂), and barium hydroxide (Ba(OH)₂), we need to analyze the solubility based on lattice energy, hydration energy, and polarization power of the cations involved.

### Step-by-Step Solution:

1. **Understanding Lattice Energy and Hydration Energy**:
- Lattice energy is the energy required to separate one mole of an ionic solid into its gaseous ions. Higher lattice energy means lower solubility.
- Hydration energy is the energy released when gaseous ions are surrounded by water molecules. Higher hydration energy means higher solubility.

2. **Polarization Power**:
- Polarization power refers to the ability of a cation to distort the electron cloud of an anion. This is influenced by the charge and size of the cation.
- The polarization power is directly proportional to the charge of the cation and inversely proportional to its size.

3. **Cations of the Hydroxides**:
- The cations for the hydroxides in question are:
- Beryllium ion (Be²⁺)
- Magnesium ion (Mg²⁺)
- Calcium ion (Ca²⁺)
- Barium ion (Ba²⁺)

4. **Comparing Cation Sizes**:
- The size of cations increases down the group in the periodic table. Thus, the order of size from smallest to largest is:
- Be²⁺ < Mg²⁺ < Ca²⁺ < Ba²⁺

5. **Determining Polarization Power**:
- Since all cations have the same charge (+2), we can compare them based on size:
- Be²⁺ has the highest polarization power (smallest size).
- Ba²⁺ has the lowest polarization power (largest size).

6. **Solubility Order**:
- Since solubility is inversely proportional to polarization power, the order of solubility for the hydroxides will be:
- Beryllium hydroxide (Be(OH)₂) < Magnesium hydroxide (Mg(OH)₂) < Calcium hydroxide (Ca(OH)₂) < Barium hydroxide (Ba(OH)₂).
- However, beryllium hydroxide is unique as it is amphoteric and can dissolve in both acids and bases, which contributes to its higher effective solubility.

7. **Conclusion**:
- Based on the analysis, beryllium hydroxide (Be(OH)₂) is the most soluble hydroxide among the given options.

### Final Answer:
The most soluble hydroxide among the following is **Beryllium hydroxide (Be(OH)₂)**.