The correct solubility order is/are
(I) `CaCO_(3)gtSrCO_(3)gtBaCO_(3)` (II)`Li_(2)CO_(3)ltNa_(2)CO_(3)gtK_(2)CO_(3)`
(III)`K_(2)CO_(3)ltRb_(2)CO_(3)ltCs_(2)CO_(3)` (IV)`Na_(2)CO_(3)gtK_(2)CO_(3)gtRb_(2)CO_(3)`

Options

A. II, IV
B. I, IV
C. II, III, IV
D. I, II, III

Answer

To determine the correct solubility order of the given carbonates, we will analyze each of the four options based on the principles of solubility in relation to the size of the cations involved.

### Step-by-Step Solution:

1. **Analyzing Option I: `CaCO3 > SrCO3 > BaCO3`**
- These are carbonates of alkaline earth metals (Ca, Sr, Ba).
- As we move down the group from calcium (Ca) to strontium (Sr) to barium (Ba), the size of the cation increases.
- Larger cations have lower hydration energy, which decreases solubility.
- Therefore, the solubility order should be `CaCO3 > SrCO3 > BaCO3` because calcium has the smallest size and thus the highest solubility.
- **Conclusion:** This option is **correct**.

2. **Analyzing Option II: `Li2CO3 < Na2CO3 < K2CO3`**
- These are carbonates of alkali metals (Li, Na, K).
- As we move down the group from lithium (Li) to sodium (Na) to potassium (K), the size of the cation increases.
- The solubility of alkali metal carbonates increases down the group due to increased ionic character as the cation size increases.
- Therefore, the correct order should be `Li2CO3 < Na2CO3 < K2CO3`.
- **Conclusion:** This option is **correct**.

3. **Analyzing Option III: `K2CO3 < Rb2CO3 < Cs2CO3`**
- Again, these are carbonates of alkali metals (K, Rb, Cs).
- As we move down the group from potassium (K) to rubidium (Rb) to cesium (Cs), the size of the cation increases.
- The solubility of alkali metal carbonates increases down the group, so the correct order should be `K2CO3 < Rb2CO3 < Cs2CO3`.
- **Conclusion:** This option is **correct**.

4. **Analyzing Option IV: `Na2CO3 > K2CO3 > Rb2CO3`**
- These are also carbonates of alkali metals (Na, K, Rb).
- As we move down the group from sodium (Na) to potassium (K) to rubidium (Rb), the size of the cation increases.
- The solubility of alkali metal carbonates increases down the group, so the correct order should be `Na2CO3 < K2CO3 < Rb2CO3`.
- **Conclusion:** This option is **incorrect**.

### Final Conclusion:
The correct solubility orders are:
- Option I: Correct
- Option II: Correct
- Option III: Correct
- Option IV: Incorrect

Thus, the correct options are **I, II, and III**.