Solubility Equilibria and the Solubility Product Constant ($K_{sp}$)

Solubility Equilibria

Introduction to Solubility Equilibria

Solubility equilibria involve the dissolution or precipitation of ionic compounds in water. These reactions are classified as heterogeneous equilibria because they involve both solid and aqueous phases.

• Solubility equilibria allow us to make both qualitative and quantitative predictions about the solubility of ionic compounds.

• General rules exist for predicting solubility in water, but these are typically qualitative.

• Quantitative predictions require the use of equilibrium constants.

Solubility Rules (Review)

General Solubility Guidelines

Understanding which ionic compounds are soluble or insoluble in water is essential for predicting precipitation reactions.

• All ionic solids have some degree of solubility in water.

• Group 1 metals (e.g., Na+, K+) and NH4+ are always soluble.

• Group 2 metals are mostly soluble.

• Pb2+, Ag+, and Hg22+ salts are usually insoluble.

• Reference tables (e.g., Table 4.1) are used to classify solubility.

Example: Predicting the products of mixing lead(II) nitrate and potassium iodide:

• $\mathrm{Pb(NO_3)_2 (aq) + 2 KI (aq) \rightarrow 2 KNO_3 (aq) + PbI_2 (s)}$

Solubility Product Equilibrium Constant ($K_{sp}$)

Definition and Significance

The solubility product constant ($K_{sp}$) quantifies the extent to which an ionic solid dissolves in water to form a saturated solution. All salts have a limited solubility, and $K_{sp}$ values can range widely (e.g., $K_{sp} = 10^{-60}$ to $10^{36}$).

• A saturated solution is in equilibrium with undissolved solute.

• The magnitude of $K_{sp}$ indicates how much solid dissolves to form a saturated solution.

• Example: For AgCl, $K_{sp} = 1.6 \times 10^{-10}$.

Saturated Solutions and Dynamic Equilibrium

When a solution is saturated:

• More solid salt is present than can be dissolved.

• There is a dynamic equilibrium between dissolution (solid to aqueous) and precipitation (aqueous to solid).

• Both solid and aqueous ions coexist.

Example:

• $\mathrm{Mg(OH)_2 (s) \rightleftharpoons Mg^{2+} (aq) + 2 OH^- (aq)}$

The molar solubility is the number of moles of solute that dissolve per liter of saturated solution (mol/L).

Writing $K_{sp}$ Expressions

For a general salt $A_xB_y$:

• $A_xB_y (s) \rightleftharpoons xA^{m+} (aq) + yB^{n-} (aq)$

• $K_{sp} = [A^{m+}]^x [B^{n-}]^y$

Always write the solid on the left and ions on the right. The exponents in the $K_{sp}$ expression correspond to the stoichiometric coefficients.

• Example 1: $\mathrm{Ca_3(PO_4)_2 (s) \rightleftharpoons 3 Ca^{2+} (aq) + 2 PO_4^{3-} (aq)}$ $K_{sp} = [Ca^{2+}]^3 [PO_4^{3-}]^2$

• Example 2: $\mathrm{BaS (s) \rightleftharpoons Ba^{2+} (aq) + S^{2-} (aq)}$ $K_{sp} = [Ba^{2+}][S^{2-}]$

Solubility vs. $K_{sp}$

• Solubility is the amount of substance that dissolves to form a saturated solution (usually in g/L).

• Molar solubility is the number of moles of solute that dissolve per liter (mol/L).

• $K_{sp}$ is the equilibrium constant for the dissolution of a solid in water.

Example:

• $\mathrm{BaSO_4 (s) \rightleftharpoons Ba^{2+} (aq) + SO_4^{2-} (aq)}$

Factors Affecting Solubility

• pH of the solution: Can increase or decrease solubility depending on the salt.

• Common ion effect: Presence of a common ion decreases solubility.

• Temperature: Solubility can increase or decrease with temperature.

The solubility of a given solute can change as the composition of the solution changes, but $K_{sp}$ is constant at a given temperature.

Converting Between Solubility and $K_{sp}$

There is a systematic procedure for converting between solubility and $K_{sp}$:

• From solubility to $K_{sp}$: Use the stoichiometry of the dissolution reaction to determine ion concentrations, then substitute into the $K_{sp}$ expression.

• From $K_{sp}$ to solubility: Set up an ICE (Initial, Change, Equilibrium) table, solve for the equilibrium concentrations, and relate to molar solubility.

Example Table: Relationship Between Solubility and $K_{sp}$

Given	Process	Find
Solubility (mol/L)	Stoichiometry, equilibrium	$K_{sp}$
$K_{sp}$	Stoichiometry, equilibrium	Solubility (mol/L)