Which of the following carbonates does not evolve `CO_(2)` on heating?

Options

A. `Li_(2)CO_(3)`
B. `MgCO_(3)`
C. `Na_(2)CO_(3)`
D. `K_(2)CO_(3)`

Explanation

To determine which of the following carbonates does not evolve \( CO_2 \) on heating, we will analyze the stability of each carbonate when subjected to heat. The carbonates in question are \( Li_2CO_3 \), \( MgCO_3 \), \( Na_2CO_3 \), and \( K_2CO_3 \).

### Step 1: Understand the thermal stability of carbonates
Carbonates decompose upon heating to form metal oxides and carbon dioxide (\( CO_2 \)). The stability of a carbonate generally increases as the size of the cation increases. Alkali metal carbonates tend to be more stable than those of alkaline earth metals.

### Step 2: Analyze each carbonate
1. **Lithium Carbonate (\( Li_2CO_3 \))**:
- Lithium ion (\( Li^+ \)) is small, leading to a strong polarization of the carbonate ion. This results in the weakening of the \( C-O \) bond, causing it to decompose upon heating:
\[ Li_2CO_3 \rightarrow Li_2O + CO_2 \]
Therefore, \( Li_2CO_3 \) evolves \( CO_2 \) on heating.

2. **Magnesium Carbonate (\( MgCO_3 \))**:
- Magnesium also has a relatively small ionic size and shows a diagonal relationship with lithium. It similarly decomposes upon heating:
\[ MgCO_3 \rightarrow MgO + CO_2 \]
Thus, \( MgCO_3 \) also evolves \( CO_2 \) on heating.

3. **Sodium Carbonate (\( Na_2CO_3 \))**:
- Sodium ion (\( Na^+ \)) is larger than lithium, which leads to a more stable carbonate. Sodium carbonate does not decompose upon heating:
\[ Na_2CO_3 \text{ does not evolve } CO_2 \]

4. **Potassium Carbonate (\( K_2CO_3 \))**:
- Potassium ion (\( K^+ \)) is even larger than sodium, making potassium carbonate stable as well. It also does not decompose upon heating:
\[ K_2CO_3 \text{ does not evolve } CO_2 \]

### Step 3: Conclusion
Based on the analysis, the carbonates that do not evolve \( CO_2 \) upon heating are:
- \( Na_2CO_3 \)
- \( K_2CO_3 \)

### Final Answer
The carbonates that do not evolve \( CO_2 \) on heating are \( Na_2CO_3 \) and \( K_2CO_3 \).

---