# How can I calculate the molarity of a saturated solution?

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 ($P b C {l}_{2}$)? The solubility equilibrium constant is K_(sp)=5.89×10^(−5)

Solution:

Start by writing the chemical equation for dissolving the salt: $P b C {l}_{2} \left(s\right) \leftrightarrow P {b}^{2 +} \left(a q\right) + 2 C {l}^{-} \left(a q\right)$

Next write the equation for the equilibrium constant. Remember that only the dissolved aqueous species contribute to the equation: ${K}_{s p} = \left[P {b}^{2 +}\right] {\left[C {l}^{-}\right]}^{2} = 5.89 \times {10}^{- 5}$

If a saturated solution contains an unknown concentration $x$ of the salt, then we know that
$\left(x\right) {\left(2 x\right)}^{2} = 5.89 \times {10}^{- 5}$

The $2 x$ 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 $2.45 \times {10}^{- 2} M$.