About calcium carbonate

It is the physical property of CaCO3 , it cannot ionize in water to form soluble ions . Pls refer to its solubility in water , then going further you need to understand the bond energy, .....something about physical chem. But it can be dissolved in acid solution.
CaCO3+CO2+H2O------>Ca(HCO3)2 so when more CO2 in water , the water is slightly weak acid because of the present of carbonic acid.
I donot know what common solvents can dissolve CaCO3 . It is misleading to use polar or nonpolar to explain the solubility of CaCO3 in water.

Calicum carbonate is a kind of giant ionic structure with ionic bond. It is usually soluble in aqueous solvents.However, it is usually insoluble in non-polar solvents. :)
In this case, because the solvent is non polar, calcium carbonate becomes insoluble.