The correct solubility order is/are
I. `CaCO_3 gt SrCO_3 gt BaCO_3`
II. `Li_2CO_3 lt Na_2CO_3 lt K_2CO_3`
III. `K_2CO_3 lt Rb_2CO_3 lt Cs_2CO_3`
IV. `Na_2CO_3 gt K_2CO_3 gt Rb_2CO_3`

Options

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

Answer

To determine the correct solubility order of the given carbonates, we need to analyze each statement based on the solubility trends of alkaline earth metals and alkali metals.

### Step-by-Step Solution:

1. **Analyzing Statement I: `CaCO_3 > SrCO_3 > BaCO_3`**
- The solubility of alkaline earth metal carbonates decreases down the group.
- Therefore, calcium carbonate (CaCO₃) is more soluble than strontium carbonate (SrCO₃), which is more soluble than barium carbonate (BaCO₃).
- **Conclusion**: This statement is **correct**.

2. **Analyzing Statement II: `Li_2CO_3 < Na_2CO_3 < K_2CO_3`**
- The solubility of alkali metal carbonates increases down the group.
- Lithium carbonate (Li₂CO₃) is less soluble than sodium carbonate (Na₂CO₃), which is less soluble than potassium carbonate (K₂CO₃).
- **Conclusion**: This statement is **correct**.

3. **Analyzing Statement III: `K_2CO_3 < Rb_2CO_3 < Cs_2CO_3`**
- Following the trend for alkali metals, the solubility increases down the group.
- Potassium carbonate (K₂CO₃) is less soluble than rubidium carbonate (Rb₂CO₃), which is less soluble than cesium carbonate (Cs₂CO₃).
- **Conclusion**: This statement is **correct**.

4. **Analyzing Statement IV: `Na_2CO_3 > K_2CO_3 > Rb_2CO_3`**
- According to the solubility trend for alkali metals, sodium carbonate (Na₂CO₃) should be less soluble than potassium carbonate (K₂CO₃), which should be less soluble than rubidium carbonate (Rb₂CO₃).
- Therefore, the correct order should be `Rb_2CO_3 > K_2CO_3 > Na_2CO_3`.
- **Conclusion**: This statement is **incorrect**.

### Final Conclusion:
The correct solubility orders are statements I, II, and III. Thus, the answer is that statements I, II, and III are correct.