When will a sparingly soluble salt precipitate from a solution?

Answer 1

Revised my answer a bit for you after clarifying my own understanding!

Ksp= the concerntration of ions in solution which has been worked out experimentally and can be looked up.
ie in BaSO4 Ksp = [Ba2+][SO42-]
A low Ksp indicates a low solubility because the values of these concerntrations (only this amont of the compound will be in the form of ions and the rest will form precipitate) will be low.
As soon as the concertration of the ions in the solution exceeds the Ksp value a preciptate will appear.

An example:
BaF2(aq) --> Ba2+(aq) + 2F-(aq) (reversible reaction)
Ksp = [Ba2+] [F-}2 = 1.7x10-6

100mL BaNO3 (0.2molL-1) is added to 400mL NH4F at 25oC. Will a precipitate of BaF2 appear?

Before precipitation
[Ba2+] = (0.2{molar conc}*0.1{vol of Ba compund added})/0.5{total vol of solution} = 0.04mol/L
[F-] = (0.5*0.4)/0.5 = 0.4 mol/L

Since [Ba2+][F-] = 6.4x10-3 is larger than Ksp of 1.7x10-6 a precipitate will form

Answer 2

When the product of the molar concentration of its ions raised to the power of the subscripts of the ions exceeds the Solubility Product (Ksp) of the salt.