Group 2 trends: increasing hydroxide solubility and reactivity, decreasing sulfate solubility down the group

Steps:

• Identify key trends: hydroxide solubility increases down Group 2 due to larger ions lowering lattice energy faster than hydration energy.
• Apply to A: radium below barium means Ra(OH)₂ more soluble than Ba(OH)₂.
• Check B: reactivity with water increases down group (more electropositive), so barium less vigorous than radium.
• Check C: sulfate solubility decreases down group (lattice energy dominates), so barium sulfate more soluble than radium sulfate.

Why A is correct:

• Hydroxide solubility increases down Group 2, as defined by the relative decrease in lattice energy (∝ 1/r⁺ + r⁻) versus hydration energy, making Ra(OH)₂ more soluble than Ba(OH)₂.

Why the others are wrong:

• B: Reactivity increases down the group, so barium actually reacts less vigorously than radium.
• C: Sulfate solubility decreases down the group, so barium sulfate is actually more soluble than radium sulfate.

Final answer: A