Question

How can I calculate the molarity of a saturated solution?

Answer 1

If you know the equilibrium constant for the solubility (sometimes called the solubility product constant), then you can set up and solve an equilibrium equation to find the molarity.

Example: What is the molarity of a saturated solution of lead chloride (`PbCl_2`)? The solubility equilibrium constant is `K_(sp)=5.89×10^(−5)`

Solution:

Start by writing the chemical equation for dissolving the salt: `PbCl_2(s) harr Pb^(2+)(aq) + 2 Cl^(-)(aq)`

Next write the equation for the equilibrium constant. Remember that only the dissolved aqueous species contribute to the equation: `K_(sp)=[Pb^(2+)][Cl^(-)]^2=5.89 times 10^(-5)`

If a saturated solution contains an unknown concentration `x` of the salt, then we know that
`(x)(2x)^2=5.89 times 10^(-5)`

The `2x` term is because the concentration of dissolved chloride ion is alway twice that of lead cations if all the species come from lead chloride.

Solving the last equation for `x`, we find that `x=2.45 times 10^(-2)`. Because `x` represents the concentration of dissolved salt, the molarity of the saturated solution is `2.45 times 10^(-2) M`.