Which of the following sequence is correct for solubility in `H_(2)O`?
(1) `BeSO_(4)gtMgSO_(4)gtCaSO_(4)gtBaSO_(4)`
(2) `Be(OH)_(2)gtMg(OH)_(2)gtCa(OH)gtBa(OH)_(2)`
(3) `Li_(2)CO_(3)lt NaOH lt KOHltRbOH`
(4) `LicO_(3)ltNa_(2)CO_(3)ltK_(2)CO_(3)ltRCO_(3)`

Options

A. `1,3,4`
B. `1,2,4`
C. `2,4,`
D. `1,3,4`

Explanation

To determine the correct sequence for solubility in water for the given compounds, we need to analyze each option based on the principles of hydration energy and lattice energy.

### Step-by-Step Solution:

1. **Understanding Hydration Energy and Lattice Energy:**
- Hydration energy is the energy released when ions are surrounded by water molecules. It generally decreases down a group in the periodic table.
- Lattice energy is the energy required to separate ions in a solid ionic compound. It generally decreases down a group for larger ions.

2. **Analyzing Option (1): `BeSO4 > MgSO4 > CaSO4 > BaSO4`**
- As we move down the group from Be to Ba, the size of the cation increases, leading to a decrease in hydration energy.
- Therefore, the solubility of sulfates decreases down the group.
- **Conclusion:** This sequence is correct.

3. **Analyzing Option (2): `Be(OH)2 > Mg(OH)2 > Ca(OH)2 > Ba(OH)2`**
- For hydroxides, the trend is opposite. As we move down the group, the lattice energy decreases more significantly than hydration energy, leading to an increase in solubility.
- **Conclusion:** This sequence is incorrect.

4. **Analyzing Option (3): `Li2CO3 < NaOH < KOH < RbOH`**
- For alkali metal hydroxides, the solubility increases down the group due to decreasing lattice energy and increasing hydration energy.
- **Conclusion:** This sequence is correct.

5. **Analyzing Option (4): `Li2CO3 < Na2CO3 < K2CO3 < Rb2CO3`**
- Carbonates generally show an increase in solubility down the group, despite being larger anions, due to increased ionic character and stability.
- **Conclusion:** This sequence is correct.

### Final Answer:
The correct sequences for solubility in water are:
- (1) `BeSO4 > MgSO4 > CaSO4 > BaSO4` (Correct)
- (3) `Li2CO3 < NaOH < KOH < RbOH` (Correct)
- (4) `Li2CO3 < Na2CO3 < K2CO3 < Rb2CO3` (Correct)