Why solubility of alkaline earth metal hydroxides increases from `Be(OH)_(2)` to `Ba(OH)_(2)`?

Explanation

To understand why the solubility of alkaline earth metal hydroxides increases from beryllium hydroxide (Be(OH)₂) to barium hydroxide (Ba(OH)₂), we can break down the explanation into several key steps:

### Step 1: Understanding Lattice Energy and Hydration Energy
- **Lattice Energy** is the energy required to separate one mole of a solid ionic compound into its gaseous ions. It is influenced by the charge and size of the ions.
- **Hydration Energy** is the energy released when ions are surrounded by water molecules. It depends on the size and charge of the ions; smaller ions generally have higher hydration energies.

### Step 2: Trend in Lattice Energy
- As we move down the group from beryllium to barium, the size of the cations increases (Be²⁺ < Mg²⁺ < Ca²⁺ < Sr²⁺ < Ba²⁺).
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