7.3 Ions in Solution & Solubility Equilibria

Ions in Solution: Anions and Cations

Aqueous acid–base and solubility chemistry depends on recognizing common ions by name, formula, and charge. The MCAT expects fluency with this vocabulary without hesitation.

Charge magnitude tracks valence or the number of protons a polyatomic ion has lost: phosphate (PO₄³⁻) has lost three protons from phosphoric acid (H₃PO₄), while sulfate (SO₄²⁻) carries a 2− charge. Recognizing charge from formula (and vice versa) is essential for writing correct Ksp expressions — an off-by-one charge error ruins both stoichiometry and the power on each concentration term.

Solubility rules (high-yield shortcuts)

Memorize the "always soluble" set so you can predict when a solid will appear in a precipitation question: salts of Na⁺, K⁺, NH₄⁺, NO₃⁻, and acetate are essentially always soluble; most Cl⁻, Br⁻, I⁻ salts are soluble except with Ag⁺, Pb²⁺, and Hg₂²⁺; most SO₄²⁻ salts are soluble except with Ba²⁺, Pb²⁺, and Ca²⁺/Sr²⁺ (borderline). Carbonates, phosphates, sulfides, and hydroxides of most metals are sparingly soluble — which is why Ksp math centers on those families.

Hydration, Hydronium, and Molarity

When an ionic solid dissolves in water, polar water molecules surround each ion in a process called hydration: the partially negative oxygen of water orients toward cations, and the partially positive hydrogens orient toward anions. This ion–dipole interaction stabilizes the separated ions and is a major energetic driver of dissolution. The same polarity that makes water an excellent solvent for ions also enables the hydrogen-bond network that gives water its high heat capacity and boiling point — content that passages sometimes link back to 5A's "unique nature of water."

A bare proton (H⁺) does not exist freely in aqueous solution — it is immediately captured by a lone pair on water to form the hydronium ion, H₃O⁺. Although "[H⁺]" is used as shorthand throughout acid–base chemistry (including on the MCAT), it represents hydrated H₃O⁺. That is why water's autoionization is more precisely 2 H₂O ⇌ H₃O⁺ + OH⁻.

The MCAT's standard concentration unit is molarity (M):

Molarity (M) = moles of solute / liters of solution

Every equilibrium expression in this chapter — Ka, Kb, Kw, Ksp — is written in molar concentrations of aqueous species. Watch for problems that give milligrams of solid or microliters of stock solution and force a unit conversion before you plug into Ksp. Molality (moles per kg solvent) appears mainly in colligative-property contexts and is not the default for Ksp.

Solubility Product Constant (Ksp)

Many ionic compounds are only sparingly soluble. For a generic salt that dissolves according to

MaXb(s) ⇌ a Mⁿ⁺(aq) + b Xᵐ⁻(aq)

the equilibrium expression is the solubility product constant, Ksp:

Ksp = [Mⁿ⁺]ᵃ [Xᵐ⁻]ᵇ

(the pure solid is omitted, exactly as with any heterogeneous equilibrium). A smaller Ksp means a less soluble compound only when comparing salts of the same stoichiometry — you cannot rank AgCl (Ksp ≈ 1.8×10⁻¹⁰) against Ag₂CrO₄ by Ksp alone without converting each to molar solubility s.

Molar solubility (s) is the moles of solid that dissolve per liter of saturated solution. Link s to ion concentrations with stoichiometry, then substitute into Ksp:

Worked Example: Ksp from Molar Solubility

Problem: The molar solubility of silver chromate (Ag₂CrO₄) in water is 6.5 × 10⁻⁵ M. What is Ksp?

Solution: Ag₂CrO₄(s) ⇌ 2 Ag⁺ + CrO₄²⁻. With s = 6.5 × 10⁻⁵ M, [CrO₄²⁻] = s and [Ag⁺] = 2s.

Ksp = [Ag⁺]²[CrO₄²⁻] = (2s)²(s) = 4s³ = 4 × (6.5 × 10⁻⁵)³ ≈ 1.1 × 10⁻¹²

The classic trap is forgetting the stoichiometric coefficient: two silver ions per formula unit means [Ag⁺] must be doubled and then squared — skipping the 2 changes the answer by nearly an order of magnitude.

Common-Ion Effect, Complex Ions, and pH-Dependent Solubility

Just as a common ion suppresses weak-acid dissociation, adding a common ion suppresses solubility of a sparingly soluble salt. Solid NaCl added to saturated AgCl shifts AgCl(s) ⇌ Ag⁺ + Cl⁻ left, lowering equilibrium [Ag⁺]. Laboratories exploit this in selective precipitation: controlled addition of an anion can drop one metal ion out of a mixture while a more soluble partner stays dissolved.

A complex ion forms when a central metal cation bonds to surrounding molecules or ions (ligands) through coordinate covalent (Lewis acid–base) bonds. Complexation removes free metal cation and pulls the dissolution equilibrium forward. Classic MCAT example:

Ag⁺ + 2 NH₃ ⇌ Ag(NH₃)₂⁺

Insoluble AgCl therefore dissolves in excess aqueous ammonia as free Ag⁺ is continuously sequestered. Similar chemistry appears with [Cu(NH₃)₄]²⁺ and with EDTA chelation in clinical or laboratory passages.

Solubility and pH are tightly linked when the anion is the conjugate base of a weak acid (OH⁻, CO₃²⁻, PO₄³⁻, S²⁻, C₂O₄²⁻). In acidic solution, excess H⁺ protonates the anion (e.g., CO₃²⁻ + H⁺ ⇌ HCO₃⁻ → H₂CO₃ → CO₂), removing the anion and dragging dissolution forward — so these salts are more soluble in acid. This principle underlies kidney-stone chemistry (calcium oxalate and calcium phosphate stones are pH-sensitive), dissolution of bone mineral (hydroxyapatite) under local acidosis, and why acid rain weathers carbonate rock. Conversely, raising pH can precipitate metal hydroxides used in water treatment.

Ion product Qsp uses the same form as Ksp but with instantaneous (not necessarily equilibrium) concentrations. If Qsp > Ksp, precipitation is favored; if Qsp < Ksp, the solution is unsaturated and more solid can dissolve. Passages often ask you to compare Qsp and Ksp after mixing two solutions — compute the diluted ion concentrations first, then Qsp.