Essentially, #K_"sp"# is another equilibrium constant, which measures the solubility of insoluble and sparingly soluble salts.
For an insoluble salt, we may represent its dissolution reaction in this fashion:
#MX_2(s) rightleftharpoonsM^+ + 2X^-#
And its equilibrium reaction may be quantified:
#([M^+][X^-]^2)/([MX_2(s)])# #=# #K_"sp"#
But you can't have the concentration of a solid, i.e. #[MX_2(s)]# is removed from the equilibrium expression, to give finally:
#[M^+][X^-]^2# #=# #K_"sp"#
#K_"sp"# values have been measured for a host of sparingly soluble and insoluble salts under standard conditions. If #M^+# in the above expression were a precious metal, addition of excess #X^-# to solution could salt the metal out for recovery.
