Ionization of Water

Water is often described as a neutral solvent, yet it is never perfectly inert — even the purest water conducts a tiny electric current, revealing that a small fraction of its molecules are always ionized. This self-ionization, or autoionization, of water is a reversible proton-transfer reaction in which one water molecule acts as a Brønsted–Lowry acid and donates a proton to a neighbouring water molecule acting as a base. The result is the formation of a hydronium ion ( $\ce{H3O+}$ ) and a hydroxide ion ( $\ce{OH-}$ ). Because the reaction is an equilibrium, its extent is described by an equilibrium constant — the ionic product of water, $K_w$ . The value of $K_w$ at 25 °C is $1.0 \times 10^{-14}$ , which means that in pure water at this temperature the concentrations of $\ce{H3O+}$ and $\ce{OH-}$ are each exactly $1.0 \times 10^{-7}$ mol dm $^{-3}$ . The pH scale — invented by Søren Sørensen in 1909 — converts these inconveniently small numbers into a practical logarithmic scale. At 25 °C, pure water has pH 7, which we define as neutral. Acids have pH < 7 and bases have pH > 7 at this temperature. A crucial and often overlooked insight is that $K_w$ is temperature-dependent. Because autoionization is endothermic (bond breaking requires energy), increasing temperature shifts the equilibrium to the right, raising $K_w$ and therefore lowering the neutral pH. At 37 °C (human body temperature), $K_w \approx 2.4 \times 10^{-14}$ , giving a neutral pH of about 6.8. The solution is still neutral — the concentrations of $\ce{H3O+}$ and $\ce{OH-}$ remain equal — but the neutral pH is no longer 7. Understanding this distinction between neutrality (equal ion concentrations) and pH = 7 is essential for advanced chemistry and biology.

Key takeaways

The Autoionization Reaction
Deriving the Ionic Product $K_w$
The pH and pOH Scales
Temperature Dependence and the True Meaning of Neutral

The Autoionization Reaction

Two water molecules collide with sufficient energy for one to transfer a proton to the other: $\ce{H2O(l) + H2O(l) <=> H3O+(aq) + OH-(aq)}$ . The equilibrium lies far to the left — only about 1 in every 555 million water molecules is ionized at any instant at 25 °C. Yet this tiny fraction is enormously important for all acid–base chemistry.

Deriving the Ionic Product $K_w$

Writing the equilibrium expression for the autoionization: $K_c = \frac{[\ce{H3O+}][\ce{OH-}]}{[\ce{H2O}]^2}$ . Because liquid water is a pure solvent, its concentration (55.5 mol dm $^{-3}$ ) is absorbed into the equilibrium constant, giving the simplified ionic product: $K_w = [\ce{H3O+}][\ce{OH-}]$ . At 25 °C, $K_w = 1.0 \times 10^{-14}$ mol $^2$ dm $^{-6}$ . This relationship holds in ALL aqueous solutions — not just pure water — making $K_w$ the master equation of aqueous acid–base chemistry.

The pH and pOH Scales

pH is defined as $\text{pH} = -\log_{10}[\ce{H3O+}]$ and pOH as $\text{pOH} = -\log_{10}[\ce{OH-}]$ . Taking the negative logarithm of $K_w$ : $\text{pK}_w = \text{pH} + \text{pOH}$ . At 25 °C, $\text{pK}_w = 14$ , so $\text{pH} + \text{pOH} = 14$ . In pure water, $[\ce{H3O+}] = [\ce{OH-}] = 1.0 \times 10^{-7}$ mol dm $^{-3}$ , giving pH = pOH = 7. Adding an acid increases $[\ce{H3O+}]$ ; to maintain the product $K_w$ , $[\ce{OH-}]$ must decrease proportionally.

Temperature Dependence and the True Meaning of Neutral

The autoionization reaction is endothermic ( $\Delta H^\circ \approx +55.8$ kJ mol $^{-1}$ ). By Le Chatelier's principle, raising temperature shifts the equilibrium to produce more ions, increasing $K_w$ . Consequently, $\text{pK}_w$ decreases and the neutral pH (where $[\ce{H3O+}] = [\ce{OH-}]$ ) equals $\frac{1}{2}\text{pK}_w$ , which is less than 7 above 25 °C. Neutrality is always the condition $[\ce{H3O+}] = [\ce{OH-}]$ ; pH = 7 is only the neutral value at exactly 25 °C.

The Key Equation

K_w = [\ce{H3O+}][\ce{OH-}] = 1.0 \times 10^{-14} \text{ mol}^2\text{ dm}^{-6} \quad (25°C)

K_w — Ionic product of water (mol² dm⁻⁶): The equilibrium constant for the autoionization of water; dimensionless in the strict thermodynamic sense but commonly quoted with units. Its value depends on temperature.
[\ce{H3O+}] — Hydronium ion concentration (mol dm⁻³): Molar concentration of hydronium ions in the aqueous solution; determines acidity.
[\ce{OH-}] — Hydroxide ion concentration (mol dm⁻³): Molar concentration of hydroxide ions; determines basicity. Related to [H₃O⁺] through Kw.

Worked Example

Problem. At 60 °C, $K_w = 9.55 \times 10^{-14}$ mol² dm⁻⁶. (a) Calculate the pH of pure water at 60 °C. (b) Is a solution with pH = 7.0 at 60 °C acidic, neutral, or basic? Explain.

\text{pH}_{\text{neutral, 60°C}} = \tfrac{1}{2}\,\text{p}K_w = \tfrac{1}{2}(-\log(9.55\times10^{-14})) = \tfrac{1}{2}(13.02) = 6.51

Answer. The neutral pH at 60 °C is 6.51. A solution of pH 7.0 at 60 °C is basic because [OH⁻] > [H₃O⁺].

Figure

Diagram

Origins · 1 minSøren Peter Lauritz Sørensen and how this was discovered

Søren Peter Lauritz Sørensen

1868–1939 · Danish

Sørensen introduced the pH scale in 1909 while working at the Carlsberg Laboratory in Copenhagen. He recognized that expressing hydrogen ion activity as a logarithm — 'potentia hydrogenii' — was far more practical for biochemical work than quoting concentrations in scientific notation. His original definition used electrode potential measurements, which he standardized using carefully prepared buffer solutions, a practice still fundamental to pH measurement today. Sørensen's famous pH paper was motivated by the practical need to control the conditions during the brewing of beer at the Carlsberg brewery — one of history's most delicious applications of physical chemistry!

Equilibrium Constant Expressions — Kw is derived by applying the equilibrium constant expression to the autoionization reaction and absorbing the constant concentration of liquid water.
Le Chatelier's Principle — The temperature dependence of Kw is explained by Le Chatelier's principle: because autoionization is endothermic, increasing temperature shifts equilibrium toward more ions.
Brønsted–Lowry Acid–Base Theory — Autoionization of water is the prototypical Brønsted–Lowry proton-transfer reaction, with water acting simultaneously as both acid and base (amphoteric behaviour).
Weak Acids and Ka — The acid dissociation constant Ka is directly analogous to Kw and is used alongside Kw to calculate the pH of weak acid solutions.
Buffer Solutions — Buffer calculations use the relationship pH + pOH = pKw and require an understanding of how Kw constrains ion concentrations in aqueous solution.