Final answer:
In a solution with increasing carbonate ion concentration and equal concentrations of various divalent cations, MnCO3 will precipitate first due to its smallest Ksp value, implying it's the least soluble. MgCO3·3H2O will be the last to precipitate because it has the largest Ksp value and is most soluble.
Step-by-step explanation:
When the carbonate ion concentration is gradually increased in a solution that contains equal concentrations of divalent cations of magnesium, calcium, strontium, barium, and manganese, the precipitate formation depends on the Ksp values of the corresponding carbonates. The carbonate with the smallest Ksp value will precipitate first because it is the least soluble, while the one with the largest Ksp will precipitate last because it is the most soluble.
MnCO3 has the smallest Ksp value, so it will precipitate first. On the other hand, MgCO3·3H2O has the largest Ksp value, indicating it will be the last to precipitate out of the given options.
Therefore, the correct answer is (c) MnCO3, BaCO3, as MnCO3 will precipitate first and BaCO3 will precipitate before MgCO3·3H2O, which precipitates last.