Autoionization of Water and the Ion-Product Constant Kw

Core Concept

Water is not just the solvent for acid–base chemistry — it is itself a weak acid and a weak base at once. In a tiny fraction of molecules, one H₂O donates a proton to a neighbor, producing H₃O⁺ and OH⁻ in a process called autoionization. This equilibrium is described by the ion-product constant Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C. Because the product of the two ion concentrations is fixed at a given temperature, knowing one ion's concentration instantly fixes the other in every aqueous solution — acidic, basic, or neutral.

Key Ideas

• Autoionization: 2 H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq); K is written as Kw.
• Kw value: 1.0 × 10⁻¹⁴ at 25 °C; the pure-liquid water is omitted from the expression (it is a pure liquid with constant activity).
• Neutral water: [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ M, so pH = 7.00 at 25 °C.
• Temperature dependence: Kw increases with temperature (autoionization is endothermic), so at 100 °C Kw ≈ 5.1 × 10⁻¹³ and "neutral" pH is about 6.14, not 7.
• Product is invariant: raising [H₃O⁺] (adding acid) forces [OH⁻] down, and vice versa, so the product stays equal to Kw.

Equations and Variables

• Kw = [H₃O⁺][OH⁻]
• At 25 °C: Kw = 1.0 × 10⁻¹⁴
• pKw = −log Kw = 14.00 (at 25 °C)
• In pure water: [H₃O⁺] = [OH⁻] = √Kw = 1.0 × 10⁻⁷ M
• Rearrangement: [OH⁻] = Kw / [H₃O⁺] and [H₃O⁺] = Kw / [OH⁻]

How It Works

1. Two water molecules collide; the O–H bond of one breaks heterolytically, and the released proton jumps onto the lone pair of the other water's oxygen.
2. The donor becomes OH⁻ (hydroxide); the acceptor becomes H₃O⁺ (hydronium). The proton hop is fast — it occurs constantly in every drop of water.
3. Because the forward reaction needs energy to break an O–H bond and separate charge, it is endothermic; raising temperature shifts the equilibrium right and enlarges Kw.
4. In any aqueous solution, whatever acid or base you add changes one ion's concentration, but the other ion adjusts so that the product [H₃O⁺][OH⁻] always equals Kw at that temperature.
5. This "product rule" is the master constraint behind every pH/pOH calculation.

Worked Example

The [OH⁻] in a sample of blood plasma is 2.5 × 10⁻⁷ M at 25 °C. Find [H₃O⁺] and state whether the plasma is acidic or basic.

Using [H₃O⁺] = Kw / [OH⁻]:

[H₃O⁺] = (1.0 × 10⁻¹⁴) / (2.5 × 10⁻⁷) = 4.0 × 10⁻⁸ M

Since [OH⁻] (2.5 × 10⁻⁷ M) is larger than [H₃O⁺] (4.0 × 10⁻⁸ M), the solution is basic. Check: (4.0 × 10⁻⁸)(2.5 × 10⁻⁷) = 1.0 × 10⁻¹⁴ ✓.

How it works

1. Two water molecules collide; the O–H bond of one breaks heterolytically, and the released proton jumps onto the lone pair of the other water's oxygen.
2. The donor becomes OH⁻ (hydroxide); the acceptor becomes H₃O⁺ (hydronium). The proton hop is fast — it occurs constantly in every drop of water.
3. Because the forward reaction needs energy to break an O–H bond and separate charge, it is endothermic; raising temperature shifts the equilibrium right and enlarges Kw.
4. In any aqueous solution, whatever acid or base you add changes one ion's concentration, but the other ion adjusts so that the product [H₃O⁺][OH⁻] always equals Kw at that temperature.
5. This "product rule" is the master constraint behind every pH/pOH calculation.

Common confusions

• "Kw is a universal constant." — It is fixed only at a given temperature; it doubles, triples, and more as you heat water.
• "pH 7 is always neutral." — Only at 25 °C; at 50 °C neutral water has pH < 7 even though [H₃O⁺] = [OH⁻].
• "Adding acid destroys OH⁻ entirely." — It drives [OH⁻] far down but never to zero; the product with [H₃O⁺] must stay at Kw.
• "Water should be written in the Kw expression." — Pure liquids and solids are omitted from equilibrium constants.

Quick review

• Autoionization: 2 H₂O ⇌ H₃O⁺ + OH⁻.
• Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C; pKw = 14.00.
• Endothermic → larger Kw at higher temperature.
• Knowing one ion's concentration fixes the other: [OH⁻] = Kw/[H₃O⁺].
• Neutral = equal concentrations, not a fixed pH number across temperatures.