Is calcium carbonate or potassium carbonate more soluble in water?

Yes and no depending on what you mean by the Word potassium. By itself, potassium is a metal and cannot dissolve in water because it reacts with water very rapidly. So rapidly and with so much energy given off, the hydrogen the reaction produces ignites! The reason this happens is that potassium as an element (metal) has a loosely held single electron in its atom. The atom is so very high strung with this loose electron and would be so much more relaxed if it got rid of it that it'll practically give it to almost any other atom it comes in contact with. That's why potassium doesn't exist in nature as an element and why it reacts with water, even the oxygen in air. After it gives up that single electron, it becomes an ion and part of an ionic compound. It the case of reacting with water - potassium hydroxide (KOH). The OH comes from ripped apart water (H2O) and the left over H becomes H2 when it meets up with another left over H atom. Potassium ion, on the other hand is very soluble in water. So, is it possible that potassium ions can exist in water? Yes! Is it possible that potassium metal can exist in water? No! Never!