The addition of  ${\mathrm{K}}_2{\mathrm{CO}}_3\left(\mathrm{aq}\right)$ to the following solution is expected to produce a precipitate in every case but the one which does not produce precipitate is :

Barium, calcium, and lead carbonates have extremely low solubility product values, making them insoluble in water. On the other hand, water may dissolve sodium carbonate. As a result, sodium carbonate that is soluble in water is produced when potassium carbonate and sodium sulphate are combined.

 ${\mathrm{K}}_2{\mathrm{CO}}_3+{\mathrm{Na}}_2{\mathrm{SO}}_4\to {\mathrm{Na}}_2{\mathrm{CO}}_3+{\mathrm{K}}_2{\mathrm{SO}}_4$

The above reaction does not give precipitate.