Barium carbonate (BaCO₃) will be more soluble in acidic solution than in pure water, because Ksp (solubility constant) in water for this salt is very low.
In acid (for example hydrochloric acid) barium carbonate dissolves more because it forms weak electrolyte carbonic acid:
BaCO₃(s) + 2HCl(aq) → BaCl₂(aq) + H₂CO₃(aq).