Kw: The Ionic Product of Water and Why Neutral Isn't Always pH 7

Pure water is usually described as a covalent substance made of neutral H₂O molecules. That’s almost true. But if you measure the electrical conductivity of extremely pure water very carefully, you find it isn’t zero. A tiny current flows. Something in the water is carrying charge, and that something is a small population of ions that water makes all by itself.

Those ions, and the constant that describes them, sit underneath every pH calculation you’ll ever do.

Water ionises itself

In any sample of water, a very small fraction of molecules transfer a proton to a neighbour:

H₂O + H₂O ⇌ H₃O⁺ + OH⁻

This is usually simplified to:

H₂O ⇌ H⁺ + OH⁻

The process is called self-ionisation or autoionisation. One water molecule acts as a Brønsted–Lowry acid and the other as a base, which is possible because water is amphiprotic (see amphoteric and amphiprotic substances).

The ions don’t last. Within a tiny fraction of a second, H₃O⁺ and OH⁻ ions meet and recombine, while elsewhere other molecules ionise. At any given instant, though, a fixed small number of ions is present, because the forward and backward reactions run at the same rate. It’s a dynamic equilibrium.

Defining Kw

Write the equilibrium expression for water’s self-ionisation. The concentration of water itself is huge (about 55.5 mol/dm³) and effectively constant, so it’s absorbed into the constant. What’s left is:

Kw = [H⁺][OH⁻]

Kw is called the ionic product of water. At 25 °C:

Kw = 1.0 × 10⁻¹⁴ mol² dm⁻⁶

In pure water, every H⁺ produced comes with one OH⁻, so the two concentrations are equal:

[H⁺] = [OH⁻] = √(1.0 × 10⁻¹⁴) = 1.0 × 10⁻⁷ mol/dm³

and pH = −log(1.0 × 10⁻⁷) = 7.00. That’s where “pH 7 is neutral” comes from.

How many molecules is that? With 55.5 mol/dm³ of water and 1.0 × 10⁻⁷ mol/dm³ of H⁺, only about 2 molecules in every billion are ionised at any moment. It’s a very small effect with very big consequences.

Kw applies to every aqueous solution

Here’s the crucial point. Kw doesn’t just describe pure water. It holds in every dilute aqueous solution, whatever else is dissolved in it. Adding an acid or a base changes [H⁺] and [OH⁻], but their product stays at 1.0 × 10⁻¹⁴ (at 25 °C).

• Add acid → [H⁺] rises → water’s equilibrium shifts left → [OH⁻] falls.
• Add alkali → [OH⁻] rises → the equilibrium shifts left → [H⁺] falls.

That’s why acidic solutions still contain hydroxide ions, and alkaline solutions still contain hydrogen ions:

Solution	[H⁺] (mol/dm³)	[OH⁻] (mol/dm³)	Product
0.10 mol/dm³ HCl	1.0 × 10⁻¹	1.0 × 10⁻¹³	1.0 × 10⁻¹⁴
Pure water	1.0 × 10⁻⁷	1.0 × 10⁻⁷	1.0 × 10⁻¹⁴
0.010 mol/dm³ NaOH	1.0 × 10⁻¹²	1.0 × 10⁻²	1.0 × 10⁻¹⁴

So once you know one of the two concentrations, Kw gives you the other:

[H⁺] = Kw ÷ [OH⁻] and [OH⁻] = Kw ÷ [H⁺]

Taking logs of Kw = [H⁺][OH⁻] gives the familiar pH + pOH = 14.00 at 25 °C. Our guide to pOH and pH has worked examples.

Kw changes with temperature

Self-ionisation breaks an O–H bond, so it takes in energy. It’s endothermic, with ΔH of about +56 kJ/mol (the reverse of the heat released when H⁺ and OH⁻ neutralise each other).

By Le Chatelier’s principle, raising the temperature shifts an endothermic equilibrium to the right. More ions form, and Kw gets bigger:

Temperature	Kw (mol² dm⁻⁶)	pH of pure water
0 °C	1.1 × 10⁻¹⁵	7.47
10 °C	2.9 × 10⁻¹⁵	7.27
25 °C	1.0 × 10⁻¹⁴	7.00
37 °C	2.4 × 10⁻¹⁴	6.81
50 °C	5.5 × 10⁻¹⁴	6.63
100 °C	5.1 × 10⁻¹³	6.14

Hot water isn’t acidic

Look at the table again. At 100 °C, pure water has a pH of about 6.14. Does that mean boiling water is acidic?

No. Neutral means [H⁺] = [OH⁻], not pH = 7. In pure water at any temperature, the two ions are always formed in equal numbers, so pure water is always exactly neutral. What changes is the pH value that corresponds to neutral. At 25 °C that value happens to be 7.00; at 100 °C it’s about 6.14.

The general definitions are:

• Acidic: [H⁺] > [OH⁻]
• Neutral: [H⁺] = [OH⁻]
• Alkaline: [H⁺] < [OH⁻]

This is a favourite exam question precisely because it tests whether you understand what pH means rather than just remembering “7 is neutral”.

Worked example 1: pure water at 50 °C

Kw at 50 °C is 5.5 × 10⁻¹⁴. Calculate the pH of pure water and state whether it is acidic, neutral or alkaline.

• [H⁺] = √(5.5 × 10⁻¹⁴) = 2.35 × 10⁻⁷ mol/dm³
• pH = 6.63
• It is neutral, because [H⁺] = [OH⁻].

Worked example 2: an alkali at 50 °C

Calculate the pH of 0.010 mol/dm³ NaOH at 50 °C.

• [OH⁻] = 0.010 mol/dm³
• [H⁺] = Kw ÷ [OH⁻] = 5.5 × 10⁻¹⁴ ÷ 0.010 = 5.5 × 10⁻¹² mol/dm³
• pH = 11.26

At 25 °C the same solution has pH 12.00. The alkali hasn’t become weaker; the pH scale has simply shifted because Kw has changed.

Worked example 3: [OH⁻] in an acid

What is [OH⁻] in a solution with pH 3.20 at 25 °C?

• [H⁺] = 10⁻³·²⁰ = 6.3 × 10⁻⁴ mol/dm³
• [OH⁻] = 1.0 × 10⁻¹⁴ ÷ 6.3 × 10⁻⁴ = 1.6 × 10⁻¹¹ mol/dm³

How Kw was measured

You can’t measure [H⁺] in pure water by adding an indicator, because the indicator itself is a weak acid and would change the answer. Instead, chemists in the late 1800s turned to electrical conductivity. Friedrich Kohlrausch spent years purifying water, distilling it dozens of times in apparatus designed to keep out dissolved carbon dioxide and traces of glass. The purer his water became, the lower its conductivity fell, but it never reached zero. It levelled off at a tiny, reproducible value.

From that limiting conductivity, and the known mobility of H⁺ and OH⁻ ions, he could calculate how many ions must be present. The answer corresponded to about 10⁻⁷ mol/dm³ of each ion at room temperature, matching the value used today. Later measurements with electrochemical cells confirmed it independently.

Why Kw matters beyond calculations

• It links acid and base strength. For any conjugate pair, Ka × Kb = Kw. See Ka × Kb = Kw.
• It sets the limit for very dilute acids. Water’s own 10⁻⁷ mol/dm³ of H⁺ means even a trace of strong acid can’t push pH above 7.
• It matters in the body. At 37 °C, neutral is pH 6.81, so blood at pH 7.4 is more alkaline relative to neutral than the raw number suggests.
• It matters in industry. Power stations and chip factories use ultrapure water, whose conductivity is so low that it’s used as a purity test. The limiting conductivity comes from water’s own ions.

Common mistakes

• Saying hot pure water is acidic because its pH is below 7.
• Using Kw = 1.0 × 10⁻¹⁴ at every temperature.
• Thinking acids contain no OH⁻ or alkalis contain no H⁺. Both ions are always present in water.
• Including [H₂O] in the Kw expression. It’s already built into the constant.

Key takeaways

• Water self-ionises: H₂O ⇌ H⁺ + OH⁻, with Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C.
• Kw holds in every aqueous solution, so [H⁺] and [OH⁻] are always linked.
• Self-ionisation is endothermic, so Kw rises with temperature and neutral pH falls below 7.
• Neutral means [H⁺] = [OH⁻], at any temperature.
• Put it into practice with the pH calculations practice problems.