Many ionic metal compounds are insoluble in water. We call these compounds insoluble salts, although, as we shall see, it is usually better to describe them as sparingly soluble salts. Calcium carbonate, copper (I) chloride, and lead sulfide are examples of such salts.
If an insoluble salt forms by the reaction of soluble substances in water and falls out of solution, we call it a precipitate (see image). Common insoluble (sparingly soluble) salts are carbonates, hydroxides, sulfates, and sulfides.
Sodium hydroxide is added to cobalt (II) nitrate. The reaction produces sodium nitrate (soluble) and cobalt (II) hydroxide, which is only sparingly soluble. The cobalt (II) hydroxide forms a dark precipitate. Image: Capaccio.
When a salt such as sodium chloride (table salt) dissolves in water, its ionic lattice holding the salt crystals together is pulled apart so that the individual sodium and chloride ions go into solution.
NaCl (s) → Na+(aq) + Cl-(aq)
As noted above, in practice, many salts that are described as insoluble do actually ionize very slightly in water, releasing ions into solution. The great majority of the salt remains as an undissolved solid in the liquid.
The undissolved solid in contact with water will come into equilibrium with the ions it has released. In simple cases, where there are no common ions or competing equilibria, the ion concentrations depend only on the equilibrium constant for the particular salt.
When we talk about solubility equilibria we always write the equilibrium with the solid on the left. For example:
Ba(IO3)2 (s) 
Ba2+(aq) + 2 IO3-(aq)
The equilibrium constant expression for an insoluble salt is written following the same rules as for any other equilibrium. The equilibrium constant is called the solubility product, Ksp. The Ksp expression for the above equilibrium is:
Ksp = [Ba2+ ] [IO3- ]2
You can learn more about solubility products here.
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