Equilibrium Concentrations when Precipitates are Present
When one takes a solid (like lead chloride, above) and puts it into water, some small amount of this material will dissolve, so that one has three things in equilibrium, solid, lead cations (aq) and chloride (aq) anions. If one calls x the concentration of lead cations, then the concentration of chloride anions is 2x, and
Ksp=x(2x)2 where (presumably) we know the numerical value of Ksp