Why are alkali salts so soluble?
So the reason for carbonates and phosphates being insoluble in water because in an acidic environment, they are both protonated and lose their negative charges. The symmetry of their binding groups produces identical resonance structures at high pH values (since rotating one double bond will shape it into a superimposable structure of another). This allows any given oxygen at a time to posses the double bond (in reality the pi bond to the phosphorus or carbon is shared throughout all the bonded oxygens and each oxygen maintains an equal distance away from the central atom). 

This partial negative charge (created by lack of firm placement of the pi electrons) can be neutralized by bonded hydrogens (this will create a small positive charge, however hydrogen's ionization energy is much less than oxygen's electron affinity). The lack of polar-ness of the phosphates and carbonates makes them insoluble in water. 

In a basic environment, (created by hydroxides) the carbonates and phosphates will become deprotonated and charged. The charge on these molecules will allow them to be more miscible with water. 



https://en.wikipedia.org/wiki/Carbonate