How can I calculate the molarity of a saturated solution?

1 Answer
Jun 7, 2014

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#.