To determine which pairs can be distinguished by the action of heat, we will analyze each pair of compounds and their behavior upon heating.
### Step-by-Step Solution:
1. **Analyze the first pair: K₂CO₃ and CaCO₃**
- **K₂CO₃ (Potassium carbonate)**: When heated, it does not decompose and remains stable. Therefore, it gives no reaction.
- **CaCO₃ (Calcium carbonate)**: When heated, it decomposes to form calcium oxide (CaO) and carbon dioxide (CO₂).
\[
\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \uparrow
\]
- **Conclusion**: K₂CO₃ does not react, while CaCO₃ does react. Thus, these two can be distinguished by heat.
2. **Analyze the second pair: Na₂CO₃ and Mg(NO₃)₂**
- **Na₂CO₃ (Sodium carbonate)**: When heated, it remains stable and does not decompose, giving no reaction.
- **Mg(NO₃)₂ (Magnesium nitrate)**: When heated, it decomposes to form magnesium oxide (MgO), nitrogen dioxide (NO₂), and oxygen (O₂).
\[
\text{Mg(NO}_3\text{)}_2 \rightarrow \text{MgO} + 2\text{NO}_2 \uparrow + \frac{1}{2}\text{O}_2 \uparrow
\]
- **Conclusion**: Na₂CO₃ does not react, while Mg(NO₃)₂ does react. Thus, these two can also be distinguished by heat.
3. **Analyze the third pair: Mg(NO₃)₂ and NaNO₂**
- **Mg(NO₃)₂ (Magnesium nitrate)**: As previously mentioned, it decomposes upon heating to form magnesium oxide, nitrogen dioxide, and oxygen.
- **NaNO₂ (Sodium nitrite)**: When heated, it decomposes to form sodium nitrate (NaNO₃) and nitrogen gas (N₂).
\[
2\text{NaNO}_2 \rightarrow \text{NaNO}_3 + \text{N}_2 \uparrow
\]
- **Conclusion**: Mg(NO₃)₂ and NaNO₂ produce different products upon heating, thus they can also be distinguished.
### Final Conclusion:
All three pairs can be distinguished by the action of heat:
- i. K₂CO₃ and CaCO₃
- ii. Na₂CO₃ and Mg(NO₃)₂
- iii. Mg(NO₃)₂ and NaNO₂
Thus, the answer is that all pairs (1, 2, and 3) can be distinguished by the action of heat.
