The incorrect order of solubility in water is:

Options

A. `Ca(OH)_(2)ltSr(OH)_(2)ltBe(OH)_(2)`
B. `Li_(2)CO_(3)ltNa_(2)CO_(3)ltK_(2)CO_(3)`
C. `CsNO_(3)ltRbNO_(3)ltKNO_(3)`
D. `BaS_(2)O_(3)ltMgS_(2)O_(3)ltCaS_(2)O_(3)`

Answer

To determine the incorrect order of solubility in water among the given options, we need to understand the relationship between lattice energy, hydration energy, and solubility of the s-block elements. Here’s a step-by-step solution:

### Step 1: Understand Lattice Energy and Hydration Energy
- **Lattice Energy (LE)**: This is the energy released when ions are combined to form a solid lattice. It is inversely proportional to solubility; higher lattice energy means lower solubility.
- **Hydration Energy (HE)**: This is the energy released when ions are surrounded by water molecules. It is directly proportional to solubility; higher hydration energy means higher solubility.

### Step 2: Analyze the Options
We will analyze each option based on the principles of lattice energy and hydration energy.

#### Option A: Ca²⁺, Sr²⁺, Be²⁺
- **Lattice Energy Order**: Be²⁺ > Ca²⁺ > Sr²⁺ (smaller ions have higher lattice energy)
- **Solubility Order**: Be²⁺ < Ca²⁺ < Sr²⁺ (because solubility is inversely related to lattice energy)
- **Conclusion**: This order is correct.

#### Option B: Li⁺, Na⁺, K⁺
- **Lattice Energy Order**: Li⁺ > Na⁺ > K⁺
- **Solubility Order**: Li⁺ < Na⁺ < K⁺ (again, solubility is inversely related to lattice energy)
- **Conclusion**: This order is also correct.

#### Option C: Cs⁺, Rb⁺, K⁺
- **Lattice Energy Order**: Cs⁺ > Rb⁺ > K⁺
- **Solubility Order**: Cs⁺ < Rb⁺ < K⁺ (consistent with the inverse relationship)
- **Conclusion**: This order is correct as well.

#### Option D: Ba²⁺, Mg²⁺, Ca²⁺
- **Lattice Energy Order**: Ba²⁺ < Ca²⁺ < Mg²⁺ (larger ions have lower lattice energy)
- **Solubility Order**: Ba²⁺ > Ca²⁺ > Mg²⁺ (this contradicts the expected order based on lattice energy)
- **Conclusion**: This order is incorrect.

### Final Answer
The incorrect order of solubility in water is **Option D: Ba²⁺, Mg²⁺, Ca²⁺**.