Water is slightly dissociated.

The idea

Water ionises to a tiny extent: H₂O ⇌ H⁺ + OH⁻. Writing an ordinary equilibrium constant would put [H₂O] on the bottom, but water is in such vast excess that its concentration is effectively constant, so it is absorbed into the constant to give the ionic product Kw = [H⁺][OH⁻], with units mol² dm⁻⁶. At 298 K, Kw = 1.00 × 10⁻¹⁴. In pure water the two ions form in equal numbers, so [H⁺] = [OH⁻] = 1.00 × 10⁻⁷ mol dm⁻³ and pH = 7.00. Kw applies to every aqueous solution, which is how the pH of an alkali is found: for 0.100 mol dm⁻³ NaOH, [H⁺] = Kw/0.100 = 1.00 × 10⁻¹³ mol dm⁻³ and pH = 13.00. The dissociation is endothermic, so heating raises Kw, lowers the pH of water, and still leaves it neutral.

What earns the marks

• The equation H₂O ⇌ H⁺ + OH⁻.
• Kw = [H⁺][OH⁻] with units mol² dm⁻⁶.
• [H⁺] = [OH⁻] = 1.00 × 10⁻⁷ mol dm⁻³ in pure water at 298 K.
• Explaining that Kw rises with temperature because the dissociation is endothermic.
• Using [H⁺] = Kw/[OH⁻] to find the pH of a strong base.

Common mistakes and how to put them right

• Writing Kw = [H⁺][OH⁻]/[H₂O] and still quoting the value 1.00 × 10⁻¹⁴.

• Giving the units of Kw as mol dm⁻³.

• Stating that water becomes acidic when heated, when [H⁺] = [OH⁻] still holds.

• Using 1.00 × 10⁻¹⁴ at a temperature other than 298 K when a different value has been supplied.

Exam tips

• For any strong base, find [OH⁻] first, then divide Kw by it; never take the log of [OH⁻] directly.
• Remember that Kw has units, and that they come from multiplying two concentrations together.