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 (HX3OX+\ce{H3O+}) and a hydroxide ion (OHX−\ce{OH-}). Because the reaction is an equilibrium, its extent is described by an equilibrium constant — the ionic product of water, KwK_w. The value of KwK_w at 25 °C is 1.0×10−141.0 \times 10^{-14}, which means that in pure water at this temperature the concentrations of HX3OX+\ce{H3O+} and OHX−\ce{OH-} are each exactly 1.0×10−71.0 \times 10^{-7} mol dm−3^{-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 KwK_w is temperature-dependent. Because autoionization is endothermic (bond breaking requires energy), increasing temperature shifts the equilibrium to the right, raising KwK_w and therefore lowering the neutral pH. At 37 °C (human body temperature), Kw≈2.4×10−14K_w \approx 2.4 \times 10^{-14}, giving a neutral pH of about 6.8. The solution is still neutral — the concentrations of HX3OX+\ce{H3O+} and OHX−\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 KwK_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: HX2O(l)+HX2O(l)⇌HX3OX+(aq)+OHX−(aq)\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 KwK_w

Writing the equilibrium expression for the autoionization: Kc=[HX3OX+][OHX−][HX2O]2K_c = \frac{[\ce{H3O+}][\ce{OH-}]}{[\ce{H2O}]^2}. Because liquid water is a pure solvent, its concentration (55.5 mol dm−3^{-3}) is absorbed into the equilibrium constant, giving the simplified ionic product: Kw=[HX3OX+][OHX−]K_w = [\ce{H3O+}][\ce{OH-}]. At 25 °C, Kw=1.0×10−14K_w = 1.0 \times 10^{-14} mol2^2 dm−6^{-6}. This relationship holds in ALL aqueous solutions — not just pure water — making KwK_w the master equation of aqueous acid–base chemistry.

The pH and pOH Scales

pH is defined as pH=−log⁡10[HX3OX+]\text{pH} = -\log_{10}[\ce{H3O+}] and pOH as pOH=−log⁡10[OHX−]\text{pOH} = -\log_{10}[\ce{OH-}]. Taking the negative logarithm of KwK_w: pKw=pH+pOH\text{pK}_w = \text{pH} + \text{pOH}. At 25 °C, pKw=14\text{pK}_w = 14, so pH+pOH=14\text{pH} + \text{pOH} = 14. In pure water, [HX3OX+]=[OHX−]=1.0×10−7[\ce{H3O+}] = [\ce{OH-}] = 1.0 \times 10^{-7} mol dm−3^{-3}, giving pH = pOH = 7. Adding an acid increases [HX3OX+][\ce{H3O+}]; to maintain the product KwK_w, [OHX−][\ce{OH-}] must decrease proportionally.

Temperature Dependence and the True Meaning of Neutral

The autoionization reaction is endothermic (ΔH∘≈+55.8\Delta H^\circ \approx +55.8 kJ mol−1^{-1}). By Le Chatelier's principle, raising temperature shifts the equilibrium to produce more ions, increasing KwK_w. Consequently, pKw\text{pK}_w decreases and the neutral pH (where [HX3OX+]=[OHX−][\ce{H3O+}] = [\ce{OH-}]) equals 12pKw\frac{1}{2}\text{pK}_w, which is less than 7 above 25 °C. Neutrality is always the condition [HX3OX+]=[OHX−][\ce{H3O+}] = [\ce{OH-}]; pH = 7 is only the neutral value at exactly 25 °C.

The Key Equation

Kw=[HX3OX+][OHX−]=1.0×10−14 mol2 dm−6(25°C)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, Kw=9.55×10−14K_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.

pHneutral, 60°C=12 pKw=12(−log⁡(9.55×10−14))=12(13.02)=6.51\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
Kw and Neutral pH vs TemperatureTemperature (°C)Neutral pH02550751006.06.57.07.58.0pH 77.477.006.636.396.13Neutral pH decreasesas temperature risesAutoionization is endothermic↑T shifts equilibrium right⟹ Kw ↑, neutral pH ↓
SP
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.

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