BaCO3 is most stable because
Thermal stability of carbonates increases along group.

Introduction:
Metal carbonates are compounds that contain a metal cation bonded to a carbonate anion. These compounds can undergo thermal decomposition when heated to produce metal oxides and carbon dioxide gas. The stability of metal carbonates can vary depending on the metal cation involved. In this case, we need to determine which of the given metal carbonates (MgCO3, CaCO3, SrCO3, or BaCO3) is the most thermally stable.

Thermal Stability of Metal Carbonates:
The thermal stability of metal carbonates is influenced by several factors, including the size and charge of the metal cation, as well as the stability of the carbonate anion.

Size and Charge of the Metal Cation:
Generally, smaller metal cations with higher charges stabilize carbonate anions more effectively, making the corresponding metal carbonates more thermally stable.

Stability of the Carbonate Anion:
The carbonate anion is composed of a carbon atom bonded to three oxygen atoms. It has a trigonal planar structure with a delocalized π bond. The stability of the carbonate anion can be affected by factors such as resonance and electron delocalization. Carbonates with greater resonance stability are more likely to be thermally stable.

Comparing the Metal Carbonates:
To determine the most thermally stable metal carbonate among MgCO3, CaCO3, SrCO3, and BaCO3, we need to consider the size and charge of the metal cation, as well as the stability of the carbonate anion for each compound.

Magnesium Carbonate (MgCO3):
- Magnesium (Mg) is a smaller metal cation with a charge of +2.
- The carbonate anion is relatively stable, but not as stable as in other metal carbonates.
- MgCO3 decomposes on heating to form MgO and CO2.

Calcium Carbonate (CaCO3):
- Calcium (Ca) is a larger metal cation with a charge of +2.
- The carbonate anion is stable due to resonance and electron delocalization.
- CaCO3 decomposes on heating to form CaO and CO2.

Strontium Carbonate (SrCO3):
- Strontium (Sr) is a larger metal cation with a charge of +2.
- The carbonate anion is stable due to resonance and electron delocalization.
- SrCO3 decomposes on heating to form SrO and CO2.

Barium Carbonate (BaCO3):
- Barium (Ba) is a larger metal cation with a charge of +2.
- The carbonate anion is stable due to resonance and electron delocalization.
- BaCO3 decomposes on heating to form BaO and CO2.

Conclusion:
Among the given metal carbonates, BaCO3 (Barium Carbonate) is the most thermally stable. This is because barium is a larger metal cation with a charge of +2, and the carbonate anion in BaCO3 is stabilized by resonance and electron delocalization. The thermal decomposition of BaCO3 yields BaO and CO2.