Solubility Product ($K_{sp}$)
Equilibrium of Sparingly Soluble Salts | Ionic Equilibrium
1. What are Sparingly Soluble Salts?
Salts like $AgCl, BaSO_4, PbCl_2$ have very low solubility in water (less than 0.01 M). In a saturated solution of such salts, a dynamic equilibrium exists between the undissolved solid and the dissolved ions.
$$ A_xB_y(s) \rightleftharpoons xA^{y+}(aq) + yB^{x-}(aq) $$2. Solubility Product Constant ($K_{sp}$)
Note: $K_{sp}$ depends only on temperature.
3. Relation between Solubility ($S$) and $K_{sp}$
Let $S$ be the solubility in mol/L.
| Salt Type | Example | Ionization | Relationship |
|---|---|---|---|
| 1:1 Type ($AB$) | $AgCl$ | $S$ and $S$ | $K_{sp} = S^2$ |
| 2:1 or 1:2 ($AB_2$) | $CaCl_2, Ag_2CrO_4$ | $S$ and $2S$ | $K_{sp} = S \cdot (2S)^2 = 4S^3$ |
| 3:1 or 1:3 ($AB_3$) | $AlCl_3, Fe(OH)_3$ | $S$ and $3S$ | $K_{sp} = S \cdot (3S)^3 = 27S^4$ |
| General ($A_xB_y$) | - | $xS$ and $yS$ | $K_{sp} = x^x y^y S^{x+y}$ |
4. Condition for Precipitation (Ionic Product)
The Ionic Product ($Q_{sp}$ or $IP$) has the same expression as $K_{sp}$ but uses concentrations at any instant (not necessarily equilibrium).
- If $Q_{sp} < K_{sp}$: Solution is Unsaturated (More salt can dissolve).
- If $Q_{sp} = K_{sp}$: Solution is Saturated (Equilibrium).
- If $Q_{sp} > K_{sp}$: Precipitation Occurs (Supersaturated).
5. Applications: Common Ion Effect
The solubility of a sparingly soluble salt decreases in the presence of a common ion.
Example: Solubility of $AgCl$ is less in $0.1 M \, NaCl$ than in pure water because $[Cl^-]$ increases, shifting equilibrium backward ($Ag^+ + Cl^- \leftarrow AgCl$).
Practice Quiz
Test your numerical skills on Solubility.
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