We represent the dissolution of an insoluble, or fairly insoluble salt, #MX_2# by the following equilibrium....
#MX_2(s) stackrel("some solvent")rarrM^(2+) + 2X^(-)#
And we write....#K_"sp"=([M^(2+)][X^(-)]^2)/([MX_2(s)])#, but since a solid cannot express a concentration, #[MX_2(s)]# is treated as unity, and the solubility expression simplifies to...
#K_"sp"=[M^(2+)][X^(-)]^2#
And if we frame the expression in terms of solubility, #S#, i.e. where #S="solubility of metal halide"#
#K_"sp"=[S][2S]^2=4S^3#
And thus #S=""^(3)sqrt(K_"sp"/4)#
Now #K_"sp"# must be MEASURED for a variety of insoluble or semi-soluble salts. Why would you want to do this? Well supposing you were isolating gold or platinum salts; you would want to know the concentration of precious metal salt in solution before throwing the solution down the drain. Likewise, if you were working with cadmium, lead, or mercury salts...you would like to know the concentration of these heavy metal salts before you poisoned the waterways.....
For a sample problem and more of the same spray, see here.
