5.3: Precipitation Stoichiometry
Practicing Precipitation Stoichiometry
Recall that precipitation reactions occur when the concentrations of ions in solution exceed the solubility limit of a compound, leading to the formation of a solid. The solubility product constant K sp governs these equilibria, providing a quantitative measure of a compound's solubility in water. In this example, we will calculate whether a precipitate forms when two solutions are mixed and determine the amount of precipitate based on stoichiometry.
Example
Suppose you mix 50.0 mL of 0.010 M AgNO 3 with 50.0 mL of 0.020 M Na 2 SO 4 . Does a precipitate of form? If so, what is the mass of the precipitate? The K sp for Ag 2 SO 4 is 1.2 ×10 −5 .
Figure 5.3.1: Solid Ag 2 SO 4 precipitate forming as a result of ion concentrations becoming equal to the maximum possible concentration allowed by K sp . (CC-BY-SA 3.0; 2015, Wikimedia Commons )
Solution
The dissociation of solid Ag 2 SO 4 in water is:
Ag 2 SO 4 (s) ⇌ 2 Ag + (aq) + SO 4 2 − (aq)
The solubility product expression is:
Ksp=[Ag + ] 2 [SO 4 2 − ]
When the solutions are mixed, the concentrations of Ag + and SO 4 2 − change due to dilution. We can calculate the new concentrations using the dilution formula:
[Ag + ] = (0.010 M) × 50.0 mL / 100.0 mL = 0.0050 M
[SO 4 2 − ] = (0.020 M) × 50.0 mL / 100.0 mL= 0.010 M
The ion product, Q, is calculated using the initial concentrations of the potentially-precipitating ions in solution:
Q=[Ag + ] 0 2 [SO 4 2 − ] 0
Substituting in the concentrations upon mixing:
Q = (0.0050 M) 2 (0.010 M) = 2.5 x 10 -7
Comparing to Ksp:
- If Q>Ksp a precipitate forms.
- If Q≤Ksp no precipitate forms.
Here, Q=2.5 x 10 -7 and K sp = 1.2 ×10 −5 . Since Q<Ksp, a precipitate of Ag 2 SO 4 will NOT form, despite the presence of, "typically-insoluble" ion products as described by the solubility rules in General Chemistry I.