This question tests your understanding of solubility trends for group I (alkali metals) and group II (alkaline earth metals) compounds. The key concept is that solubility depends on the balance between the lattice energy (the energy holding the ions together in the solid) and the hydration energy (the energy released when ions are surrounded by water molecules).

Let's analyze each statement step-by-step:

Step 1: Sulphates

The table states: Least soluble is BaSO₄ and most soluble is BeSO₄.

For group II sulphates (MSO₄), solubility decreases down the group. Be²⁺ is a small ion with high hydration energy, which favors solubility. Ba²⁺ is a large ion; its compounds have high lattice energy, making them less soluble. BaSO₄ is famously insoluble. This statement is correct.

Step 2: Hydroxides

The table states: Least soluble is LiOH and most soluble is CsOH.

For group I hydroxides (MOH), solubility increases down the group. Li⁺ is a small ion, so LiOH has high lattice energy, making it the least soluble hydroxide in group I. Cs⁺ is the largest ion, so CsOH has the lowest lattice energy and is the most soluble. This statement is correct.

Step 3: Fluorides

The table states: Least soluble is BaF₂ and most soluble is BeF₂.

For group II fluorides (MF₂), the trend is the opposite of sulphates. Solubility increases down the group. BeF₂ has a high lattice energy due to the small size of Be²⁺, making it the least soluble. BaF₂ is relatively more soluble. Therefore, claiming BaF₂ is the least soluble and BeF₂ is the most soluble is incorrect.

Step 4: Carbonates

The table states: Least soluble is Cs₂CO₃ and most soluble is Li₂CO₃.

For group I carbonates (M₂CO₃), the solubility trend is not as simple. However, all group I carbonates are soluble in water. Li₂CO₃ is an exception; it is sparingly soluble due to the high lattice energy from the small Li⁺ ion. The carbonates of the heavier alkali metals (e.g., Na₂CO₃, K₂CO₃, Cs₂CO₃) are highly soluble. Therefore, Li₂CO₃ is the least soluble, and Cs₂CO₃ is among the most soluble. Claiming the opposite is incorrect.

Final Answer: The statements about Fluorides and Carbonates are incorrect.

Related Topics & Formulae

Lattice Energy (ΔH_lattice): The energy released when one mole of an ionic crystal is formed from its gaseous ions. It is inversely proportional to the size of the ions. $\mathrm{\Delta <!--\; \Delta \; -->}{H}_{\mathrm{lattice}}\propto <!--\; \propto \; -->\frac{q_{+}{q}_{-}}{r_{+}+r_{-}}$

Hydration Energy (ΔH_hyd): The energy released when one mole of gaseous ions is dissolved in water. It is directly proportional to the charge density (charge/size) of the ion. $\mathrm{\Delta <!--\; \Delta \; -->}{H}_{\mathrm{hyd}}\propto <!--\; \propto \; -->\frac{q}{r}$

Solubility: A salt dissolves if the hydration energy is sufficient to overcome the lattice energy. $\left|\mathrm{\Delta <!--\; \Delta \; -->}{H}_{\mathrm{hyd}}\right|>\left|\mathrm{\Delta <!--\; \Delta \; -->}{H}_{\mathrm{lattice}}\right|$