Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Barium carbonate is insoluble in water and is highly stable.
Reason (R): The thermal stability of the carbonates increases with increasing cationic size.
Choose the most appropriate answer from the options given below:

We have the Assertion (A): “Barium carbonate is insoluble in water and is highly stable.” To analyse this, we recall the general solubility trend of group-2 carbonates. As we move down the alkaline-earth metal column from $$\mathrm{Mg^{2+}}$$ to $$\mathrm{Ba^{2+}},$$ the lattice energy decreases more slowly than the hydration energy, causing the net energy change for dissolution to become more positive. Consequently, $$\mathrm{BaCO_3}$$ does not obtain sufficient hydration enthalpy to break its crystal lattice, so it remains practically insoluble in water. Furthermore, its large, low-charge-density cation $$\mathrm{Ba^{2+}}$$ exerts only weak polarising power on the carbonate ion $$\mathrm{CO_3^{2-}},$$ making the salt reluctant to decompose when heated. Hence, barium carbonate is indeed highly thermally stable. Therefore, statement (A) is true.

Now we examine the Reason (R): “The thermal stability of the carbonates increases with increasing cationic size.” The thermal decomposition of any group-2 carbonate may be represented as

$$\mathrm{MCO_3(s) \;\xrightarrow{\Delta}\; MO(s) + CO_2(g)}$$

where $$\mathrm{M^{2+}}$$ is the alkaline-earth metal ion. The enthalpy change for this reaction depends largely on the lattice energies of the carbonate and the oxide produced. As we descend the group, the ionic radius of $$\mathrm{M^{2+}}$$ increases. Because a larger cation has lower polarising power, it disturbs the electron cloud of the carbonate ion less, so the bond between $$\mathrm{C}$$ and $$\mathrm{O}$$ in $$\mathrm{CO_3^{2-}}$$ is less weakened. Consequently, more heat is required to break the carbonate lattice, and the decomposition temperature rises. Thus, the trend “larger cation → greater thermal stability” is correct. Therefore, statement (R) is also true.

We further notice that (R) directly provides the underlying principle that explains why $$\mathrm{BaCO_3}$$ in (A) is highly stable: barium has the largest cationic size among the common alkaline-earth metals, so its carbonate possesses the greatest thermal stability. Hence, the truth of (R) supports and rationalises the truth of (A).

Because both (A) and (R) are true, the most appropriate choice is Option B.

Hence, the correct answer is Option B.