Ion Concentration from Dissociation

Salt dissolving in water does not stay as salt: the crystal comes apart into its ions. Sodium chloride gives one Na⁺ and one Cl⁻ for every formula unit, so a 0.10 mol/L NaCl solution holds 0.10 mol/L of each. Calcium chloride gives one Ca²⁺ and two Cl⁻, so a 0.10 mol/L CaCl₂ solution holds 0.10 mol/L of calcium and 0.20 mol/L of chloride.

The count ν comes straight off the dissociation equation, and the dissociation equation comes straight off the formula: the subscript on each ion becomes its coefficient. CaCl₂(s) → Ca²⁺(aq) + 2Cl⁻(aq). Na₂SO₄(s) → 2Na⁺(aq) + SO₄²⁻(aq). Al₂(SO₄)₃(s) → 2Al³⁺(aq) + 3SO₄²⁻(aq). The sulfate stays in one piece: a polyatomic ion is one ion, and the subscripts inside it are not counted.

Check the charges. A dissociation equation balances charge as well as atoms: 2(+3) + 3(−2) = 0 for aluminium sulfate. If the charges do not cancel, an ion count is wrong.

The rule assumes the compound dissociates completely, which holds for soluble ionic compounds. Sugar dissolves without making any ions at all, and a weak acid such as the acetic acid in vinegar releases only a small fraction of its hydrogen. When two solutions carrying the same ion are mixed, find the moles of that ion from each, add them, and divide by the total volume.