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What is the difference between solubility and Ksp

Simple question.  What is the difference between solubility and ksp?

I know ksp is the point where ppt will occur if it goes any higher.

Solubility is the quantity of substance that dissolves and is usually express as g/L or moles/L
e.g when sodium chloride dissolves in water, it breaks up in the ions
Na+Cl-(s) + aq ----> Na+(aq) + Cl-(aq). The quantity of ions in solution is relatively large.

However, some substances are so very poorly soluble that the number of ions formed in solution is very low.

Pb2+S2-(s) + aq Pb2+(aq) + S2-(aq)

Most of the PbS remains undissolved and an equilibrium is set up.
K = [Pb2+(aq)] [S2-(aq)]/[Pb2+S2-(s)]
(water does not appear in this equation as it is not used up)

The quantity of Pb2+S2-(s) is very large and the equation is rewritten as Ksp, the solubility product
Ksp = [Pb2+(aq)] [S2-(aq)]
Ksp is the product (multiple) of the ions in solution. The units will be dependant on the equation e.g mole/L x mol/L = mol^2 L^-2
In some expresssions, the quantity of ions is raised to the power of the coefficient of the that ion in the balanced equation
e.g. Ksp = [Ca2+][F-]^2. This will affect the units (mole^3 L^-3)

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