Why pH Controls Solubility
Some salts dissolve more as the pH changes, while others are completely unaffected by pH. The difference is whether an ion in the dissolution equilibrium reacts with H⁺ or OH⁻.
Hydroxides are the clearest case:
Mg(OH)₂(s) ⇌ Mg²⁺(aq) + 2OH⁻(aq)
Hydroxide ion is a product of this equilibrium, so anything that changes [OH⁻] changes the solubility. Adding acid lowers [OH⁻] by neutralizing it to water, so the equilibrium shifts right and more solid dissolves. Adding base raises [OH⁻] and pushes it left.
Salts of weak acids behave the same way through their anions:
CaF₂(s) ⇌ Ca²⁺(aq) + 2F⁻(aq)
Fluoride is the conjugate base of the weak acid HF, so in acid it is protonated:
F⁻(aq) + H⁺(aq) ⇌ HF(aq)
Removing fluoride pulls the dissolution equilibrium to the right.
Hydroxide Solubility at a Fixed pH
For a hydroxide salt the solubility at a fixed pH follows directly from the Ksp expression: the pH fixes [OH⁻] through pOH = 14 − pH, and then
s = Ksp/[OH⁻]ⁿ
where n is the number of hydroxide ions in the formula.
Take Mg(OH)₂ with Ksp = 5.6 × 10⁻¹²:
Ksp = [Mg²⁺][OH⁻]²
so s = Ksp/[OH⁻]². At pH 9, [OH⁻] = 1.0 × 10⁻⁵ M and s = 5.6 × 10⁻² M. At pH 10, s = 5.6 × 10⁻⁴ M. At pH 11, s = 5.6 × 10⁻⁶ M. Each unit of pH cuts the solubility by a factor of one hundred, because [OH⁻] is squared.
In pure water Mg(OH)₂ dissolves to s = 1.1 × 10⁻⁴ M. A saturated solution in pure water has [OH⁻] = 2s = 2.2 × 10⁻⁴ M, giving pOH = 3.65 and pH = 10.35, the dividing line: below it the salt dissolves more than in pure water, above it less.
The Exponent Rule
For Mg(OH)₂ and Ca(OH)₂ the exponent on [OH⁻] is 2, so a tenfold change in [OH⁻] changes the solubility by a factor of one hundred. For Fe(OH)₃ the exponent is 3, so the factor is one thousand.
Iron(III) hydroxide, with Ksp = 2.8 × 10⁻³⁹, shows this. At pH 7, s = 2.8 × 10⁻¹⁸ M, essentially nothing. At pH 4, s = 2.8 × 10⁻⁹ M. At pH 3, s = 2.8 × 10⁻⁶ M. Three pH units of acid raise the solubility by a factor of a billion.
Calcium hydroxide, with Ksp = 5.5 × 10⁻⁶, is much more soluble: at pH 12, s = 5.5 × 10⁻² M, and at pH 13, s = 5.5 × 10⁻⁴ M.
When a Hydroxide First Precipitates
The same Ksp expression predicts the pH at which a hydroxide first precipitates: precipitation begins when Qsp reaches Ksp, so the threshold hydroxide concentration is
[OH⁻] = (Ksp/[Mⁿ⁺])^(1/n)
and the threshold pH follows from pOH = −log[OH⁻].
For 0.010 M Mg²⁺, the threshold is [OH⁻] = sqrt((5.6 × 10⁻¹²)/0.010) = 2.4 × 10⁻⁵ M, giving pOH = 4.63 and pH = 9.37. Below pH 9.37 no solid forms; above it, Mg(OH)₂ precipitates.
For 1.0 × 10⁻⁴ M Fe³⁺, the threshold is [OH⁻] = ((2.8 × 10⁻³⁹)/(1.0 × 10⁻⁴))^(1/3) = 3.0 × 10⁻¹² M, giving pOH = 11.52 and pH = 2.48. For 0.10 M Ca²⁺, the threshold is [OH⁻] = sqrt((5.5 × 10⁻⁶)/0.10) = 7.4 × 10⁻³ M, giving pOH = 2.13 and pH = 11.87.
The threshold pH rises as the metal ion concentration falls.
Salts of Weak Acids
Acid increases the solubility of any salt whose anion is the conjugate base of a weak acid: the acid protonates the anion and removes it from the equilibrium. Calcium carbonate dissolves as
CaCO₃(s) ⇌ Ca²⁺(aq) + CO₃²⁻(aq)
and in acid the carbonate is protonated:
CO₃²⁻(aq) + H⁺(aq) ⇌ HCO₃⁻(aq)
With enough acid the bicarbonate is protonated again to carbonic acid, which breaks down to CO₂ and water: this is why limestone fizzes in acid.
The same reasoning applies to calcium fluoride through HF formation, to sulfides through H₂S formation, and to phosphates through HPO₄²⁻ and H₂PO₄⁻ formation.
The reverse case: salts of weak bases. Salts containing the ammonium ion, NH₄⁺, become more soluble in base: ammonium is the conjugate acid of the weak base NH₃, so hydroxide removes a proton:
NH₄⁺(aq) + OH⁻(aq) ⇌ NH₃(aq) + H₂O(l)
Removing NH₄⁺ pulls the dissolution equilibrium to the right.
Salts That Ignore pH
A salt does not respond to pH when both of its ions come from a strong acid and a strong base. AgCl is unaffected by pH, since Cl⁻ is the conjugate base of the strong acid HCl. BaSO₄ and PbI₂ are likewise unaffected.
The exam uses these salts as distractors: if a question asks which of several salts becomes more soluble when acid is added, look for the anion that can be protonated.
Acid dissolves salts of weak acids and hydroxides, base dissolves salts of weak bases, and salts of strong acids and strong bases ignore pH entirely.
Worked Examples
Example 1: Mg(OH)₂ solubility at pH 10. Mg(OH)₂ has Ksp = 5.6 × 10⁻¹². At pH 10, pOH = 4, so [OH⁻] = 1.0 × 10⁻⁴ M. Then s = Ksp/[OH⁻]² = (5.6 × 10⁻¹²)/(1.0 × 10⁻⁴)² = 5.6 × 10⁻⁴ M. That is about five times the pure-water solubility of 1.1 × 10⁻⁴ M.
Example 2: Fe(OH)₃ solubility at pH 4. Fe(OH)₃ has Ksp = 2.8 × 10⁻³⁹. At pH 4, pOH = 10, so [OH⁻] = 1.0 × 10⁻¹⁰ M. Then s = Ksp/[OH⁻]³ = (2.8 × 10⁻³⁹)/(1.0 × 10⁻¹⁰)³ = 2.8 × 10⁻⁹ M. Forgetting the cube would give 2.8 × 10⁻²⁹ M, wrong by twenty orders of magnitude.
Example 3: the precipitation threshold for Mg²⁺. A solution is 0.010 M in Mg²⁺. Precipitation begins when [OH⁻] = sqrt(Ksp/[Mg²⁺]) = sqrt((5.6 × 10⁻¹²)/0.010) = 2.4 × 10⁻⁵ M. Then pOH = −log(2.4 × 10⁻⁵) = 4.63, and pH = 14 − 4.63 = 9.37.
Example 4: Ca(OH)₂ at pH 12 and pH 13. Ca(OH)₂ has Ksp = 5.5 × 10⁻⁶. At pH 12, [OH⁻] = 1.0 × 10⁻² M, so s = (5.5 × 10⁻⁶)/(1.0 × 10⁻²)² = 5.5 × 10⁻² M. At pH 13, [OH⁻] = 0.10 M, so s = (5.5 × 10⁻⁶)/(0.10)² = 5.5 × 10⁻⁴ M. One pH unit cut the solubility by a factor of one hundred.
Traps That Cost Marks in Topic 7.13
“Ksp changes when the pH changes.” Ksp is fixed at a given temperature. Only the solubility changes, because [OH⁻] is imposed by the solution.
“s = Ksp/[OH⁻] for every hydroxide.” The exponent is the number of hydroxide ions in the formula: Mg(OH)₂ and Ca(OH)₂ need [OH⁻]², Fe(OH)₃ needs [OH⁻]³.
“pH 9 means [OH⁻] = 1.0 × 10⁻⁹ M.” pH 9 means pOH 5 and [OH⁻] = 1.0 × 10⁻⁵ M. Always convert through pOH = 14 − pH first.
“AgCl dissolves more in acid.” Neither Ag⁺ nor Cl⁻ reacts with H⁺ or OH⁻. AgCl, BaSO₄ and PbI₂ ignore pH entirely.
“Fe(OH)₃ is the most soluble because its Ksp is the smallest.” A smaller Ksp means a less soluble salt. Fe(OH)₃, with Ksp = 2.8 × 10⁻³⁹, is the least soluble salt in this unit by an enormous margin.
“The precipitate forms as soon as any OH⁻ is added.” Precipitation starts only when Qsp reaches Ksp. Below the threshold pH the metal ion stays dissolved.
Key Relationships
- pH + pOH = 14 at 25 °C; [OH⁻] = 10^(−pOH)
- For a hydroxide salt, s = Ksp/[OH⁻]ⁿ, where n is the number of hydroxide ions in the formula
- Mg(OH)₂, Ksp = 5.6 × 10⁻¹²: s = 5.6 × 10⁻² M at pH 9, 5.6 × 10⁻⁴ M at pH 10, 5.6 × 10⁻⁶ M at pH 11
- Fe(OH)₃, Ksp = 2.8 × 10⁻³⁹: s = 2.8 × 10⁻⁶ M at pH 3, 2.8 × 10⁻⁹ M at pH 4, 2.8 × 10⁻¹⁸ M at pH 7
- Ca(OH)₂, Ksp = 5.5 × 10⁻⁶: s = 5.5 × 10⁻² M at pH 12, 5.5 × 10⁻⁴ M at pH 13
- Precipitation begins when Qsp = Ksp; threshold [OH⁻] = (Ksp/[Mⁿ⁺])^(1/n)
- Acid dissolves salts of weak acids and hydroxides; base dissolves salts of weak bases
- Salts of strong acids and strong bases (AgCl, BaSO₄, PbI₂) ignore pH
- Ksp is fixed at a given temperature; only solubility changes with pH
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