|Concentration of cation in sea water||Molarity||Concentration of anion in sea water|
Seawater contains just about every element in some small quantity. The materials over 1mmol/L is a shorter list.
Removal of calcium and magnesium
With Calcium and Magnesium combined for 0.06 mol/L, adding 0.06mol of soluble ash (7-8g/L) should precipitate most of the alkali earth metal content. Hypothetically just bubbling carbon dioxide through the material for a brief period should do it.
Removal of sulfate and bicarbonate
To remove the 0.011 mol of these, add a small amount soluble calcium. (0.5g/L calcium oxide or 0.75g/L of calcium hydroxide) This will cause calcium bicarbonate, calcium carbonate, and calcium sulfate to precipitate. Use the same soda ash/carbon dioxide system as before to remove any remaining calcium hydroxide.
Alternatively, use fractional crystallization. Potassium and Sodium bicarbonate are less than one tenth as soluble as the chlorides, so they will precipitate first. The sulfates are almost 2/3 as soluble, so it will be more difficult. doing it very very slowly might grow large enough crystals to physically sort them.