Solubility Equilibria and Precipitation Reactions

Solubility Equilibria

Solubility and Solutions

Solubility describes the amount of solute that dissolves in a given quantity of solvent at a specific temperature, typically expressed in grams per liter (g/L). Molar solubility (S) is the amount of dissolved solute expressed in moles per liter (mol/L). The solubility of ionic compounds in water is governed by a set of solubility rules, which help predict whether a compound will dissolve or form a precipitate.

• Solubility Rules:

  • All compounds containing Group 1 elements (Li+, Na+, K+) and ammonium (NH4+) are soluble.

  • Acetates (C2H3O2-) and nitrates (NO3-) are soluble.

  • Most chlorides, bromides, and iodides are soluble except when paired with Cu+, Ag+, Hg22+, or Pb2+.

  • Most sulfates (SO42-) are soluble except with Ca2+, Sr2+, Ba2+, Ag+, Hg22+, or Pb2+.

• Electrolytes:

  • Strong electrolytes: Completely dissociate in solution (e.g., strong acids, strong bases, soluble salts).

  • Weak electrolytes: Partially dissociate (e.g., weak acids, weak bases).

  • Nonelectrolytes: Do not dissociate (e.g., molecular compounds like sugars).

Precipitation Reactions

Precipitation occurs when two solutions are mixed and an insoluble product (precipitate) forms. The formation of a precipitate can be predicted using solubility rules and is often represented by a net ionic equation.

• Example: Mixing sodium hydroxide (NaOH) and silver nitrate (AgNO3) results in the formation of a precipitate, silver hydroxide (AgOH).

Solubility Product Constant (Ksp)

Definition and Expression

The solubility product constant, Ksp, is the equilibrium constant for the dissolution of a sparingly soluble ionic compound. For a general salt MnXm:

$\mathrm{MnXm(s) \rightleftharpoons nMm^+(aq) + mXn^-(aq)}$

The Ksp expression is:

$K_{sp} = [Mm^+]^n [Xn^-]^m$

• Example:

  • SrCO3(s): $K_{sp} = [Sr^{2+}][CO_3^{2-}]$

  • Ag2S(s): $K_{sp} = [Ag^+]^2[S^{2-}]$

  • Mg3(AsO4)2(s): $K_{sp} = [Mg^{2+}]^3[AsO_4^{3-}]^2$

Solubility Product Table

The following table lists Ksp values for various slightly soluble salts, which are essential for predicting precipitation and calculating solubility.

Substance	Formula	Ksp
Aluminum hydroxide	Al(OH)3	4.6 x 10-33
Barium chromate	BaCrO4	1.2 x 10-10
Barium fluoride	BaF2	1.0 x 10-6
Calcium carbonate	CaCO3	3.8 x 10-9
Silver chloride	AgCl	1.8 x 10-10
Lead(II) sulfate	PbSO4	1.7 x 10-8

Molar Solubility Calculations

Calculating Molar Solubility from Ksp

Molar solubility (S) is the number of moles of solute that dissolve per liter of solution. For Mg(OH)2 (Ksp = 1.8 x 10-11):

$K_{sp} = [Mg^{2+}][OH^-]^2 = (x)(2x)^2 = 4x^3$

Solve for x (molar solubility):

$x = \sqrt[3]{\frac{K_{sp}}{4}} = 1.65 \times 10^{-4}~M$

Common Ion Effect

The presence of a common ion decreases the solubility of a sparingly soluble salt. For example, adding Na2SO4 to a BaSO4 solution increases [SO42-], shifting the equilibrium left and decreasing BaSO4 solubility.

Precipitation and the Reaction Quotient (Q)

Predicting Precipitation

To determine if a precipitate will form, compare the ion product (Q) to Ksp:

• If Q > Ksp, precipitation occurs.

• If Q < Ksp, no precipitation occurs.

• If Q = Ksp, the solution is saturated and at equilibrium.

Example: Mixing 0.050 M Pb(NO3)2 and 0.050 M NaCl:

$Q = [Pb^{2+}][Cl^-]^2 = (0.050)(0.050)^2 = 1.25 \times 10^{-4}$

Since Q > Ksp (1.6 x 10-5), PbCl2 will precipitate.

Factors Affecting Solubility

pH Effects

For salts containing basic anions, solubility increases as pH decreases (more acidic). For example, adding acid to CaF2 consumes F- ions, shifting equilibrium to dissolve more CaF2:

$F^-(aq) + H^+(aq) \rightleftharpoons HF(aq)$

Amphoteric Hydroxides

Some metal hydroxides (e.g., Zn(OH)2) can react with both acids and bases, increasing their solubility in both acidic and basic solutions:

• With acid: $Zn(OH)_2(s) + 2H^+(aq) \rightarrow Zn^{2+}(aq) + 2H_2O(l)$

• With base: $Zn(OH)_2(s) + 2OH^-(aq) \rightarrow [Zn(OH)_4]^{2-}(aq)$

Complex-Ion Equilibria

Formation of Complex Ions

Some metal ions form complex ions with ligands (Lewis bases), increasing the solubility of their salts. The equilibrium constant for complex ion formation is the formation constant (Kf):

$Cu^+(aq) + 2CN^-(aq) \rightleftharpoons [Cu(CN)_2]^-(aq)$

$K_f = \frac{[Cu(CN)_2^-]}{[Cu^+][CN^-]^2}$

The dissociation constant (Kd) is the reciprocal of Kf.

Combined Equilibria: Ksp and Kf

When a slightly soluble salt forms a complex ion, the overall equilibrium constant (Kc) is the product of Ksp and Kf:

$AgCl(s) + 2NH_3(aq) \rightleftharpoons [Ag(NH_3)_2]^+(aq) + Cl^-(aq)$

$K_c = K_{sp} \times K_f$

Learning Objectives and Practice

• Understand and write solubility product expressions.

• Calculate Ksp from solubility and vice versa.

• Predict precipitation using Q and Ksp.

• Analyze the effect of common ions and pH on solubility.

• Calculate solubility in the presence of complex ions using Kf.