Which of the following ions is insoluble in water?

The carbonate ion is generally considered insoluble in water, especially in relation to many cations. While some carbonates, such as those of alkali metals (like sodium and potassium), are soluble, most transition and heavy metal carbonates do not dissolve well in water. This insolubility is due to the lattice energy of the carbonate salts, which is higher than the hydration energy provided by water molecules when attempting to solvate the ions.

In contrast, the other ions listed have different solubility properties. The cyanate ion is typically soluble in water. Hydroxide ions are generally soluble, especially when paired with alkali metal cations, and many hydroxides (like sodium hydroxide) are quite soluble. Nitrate ions are also known for their high solubility in water and form soluble compounds with nearly all cations.

Thus, among the options, carbonate stands out as the ion that is commonly insoluble in the context of most metal cations in water, which aligns with what is taught regarding solubility rules in chemistry.