Relating solubility to ion concentrations

The solubility of a substance is a measure of the amount dissolving in a given volume of solution at a certain temperature.

The solubility of an ionic solid is related, through the balanced equation for dissolving, to the change in concentration of the ions that are the products of the reaction.
 
CaF2(s) Ca2+(aq) + 2F(aq)
For slightly soluble solids the reaction is reactant-favoured, as shown by the equilibrium arrow.
 
s(CaF2)=Δ [Ca2+]=Δ [F]
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Δ is the Greek letter delta
meaning change in

Solubility varies with temperature and may also depend on what other solutes are present.
 
The solubility of CaF2 in aqueous CaCl2 is different than it is in water at the same temperature. 
 
Qs is the reaction quotient for dissolving of an ionic solid to give its ions.
At equilibrium Qs = Ks.
 
For CaF2
Qs = [Ca2+][F]2
Ks(CaF2) is constant for all aqueous solutions of CaF2 at the same temperature.

Solutions at equilibrium are saturated and contain the maximum amount of solid dissolved in the presence of excess solid. Thus at constant temperature for any saturated aqueous solution containing Ca2+ and F, Qs = Ks.