What Is Kw? The Ion Product of Water Explained
Pure water is supposed to be the definition of neutral. So why does a pH meter dipped into boiling distilled water read about 6.1 — and why is that water still neutral? The answer is one small constant that quietly underpins the entire pH scale.
The short answer: Kw is the ion product of water, the equilibrium constant for water reacting with itself: Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C. Because that product is fixed at a given temperature, knowing either ion concentration always gives you the other.
Water reacts with itself
Water is amphiprotic — it can donate a proton and accept one. Given enough molecules, some of them do both to each other:
2 H₂O ⇌ H₃O⁺ + OH⁻
This is called autoionisation (or self-ionisation). It happens in every sample of water, and in every aqueous solution, all the time. It is just extremely rare: at 25 °C only about one water molecule in 555 million is ionised at any instant.
The equilibrium constant for that reaction, with the solvent water folded in as usual, is:
Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ (at 25 °C)
Where pH 7 comes from
In pure water the two ions can only be made in pairs, so their concentrations are equal. Call each one x:
x × x = 1.0 × 10⁻¹⁴ x = 1.0 × 10⁻⁷ M
So [H₃O⁺] = 1.0 × 10⁻⁷ M, and pH = −log(1.0 × 10⁻⁷) = 7.00. The famous neutral point is not a definition handed down from above; it is the square root of Kw.
Take logs of the whole expression and you get the other relationship you already use:
pH + pOH = pKw = 14.00 (at 25 °C)
Kw applies to every aqueous solution
This is the part that does real work. Adding acid does not switch water's autoionisation off — it pushes the equilibrium, but the product stays at 1.0 × 10⁻¹⁴. So hydroxide never disappears from an acidic solution; it just becomes very scarce.
In 0.10 M HCl, [H₃O⁺] = 0.10 M, so
[OH⁻] = 1.0 × 10⁻¹⁴ ÷ 0.10 = 1.0 × 10⁻¹³ M
Tiny, but not zero. The same logic runs in reverse for bases, which is how you get a pH from a hydroxide concentration.
Worked examples
1. A solution has [OH⁻] = 2.5 × 10⁻³ M. What is its pH? [H₃O⁺] = 1.0 × 10⁻¹⁴ ÷ 2.5 × 10⁻³ = 4.0 × 10⁻¹² M pH = −log(4.0 × 10⁻¹²) = 11.40
2. A solution has pH 3.20. What is [OH⁻]? pOH = 14.00 − 3.20 = 10.80, so [OH⁻] = 10⁻¹⁰·⁸⁰ = 1.6 × 10⁻¹¹ M
3. What is [H₃O⁺] in 0.020 M NaOH? NaOH is strong, so [OH⁻] = 0.020 M, giving [H₃O⁺] = 1.0 × 10⁻¹⁴ ÷ 0.020 = 5.0 × 10⁻¹³ M, pH 12.30.
The temperature twist
Autoionisation is endothermic — pulling a proton off a water molecule costs energy. By Le Chatelier's principle, heating the water shifts the equilibrium to the right, so Kw increases with temperature:
| Temperature | Kw | Neutral pH |
|---|---|---|
| 0 °C | 1.14 × 10⁻¹⁵ | 7.47 |
| 25 °C | 1.00 × 10⁻¹⁴ | 7.00 |
| 50 °C | 5.48 × 10⁻¹⁴ | 6.63 |
| 100 °C | 5.13 × 10⁻¹³ | 6.14 |
Water at 100 °C has a pH of about 6.14 — and it is still perfectly neutral, because [H₃O⁺] and [OH⁻] have risen together and remain equal. Neutrality means the two are equal, not that pH is 7. Likewise, pH + pOH = 14.00 only holds at 25 °C; at 100 °C the sum is 12.29.
This also explains why pure water is never quite as clean an electrical insulator as you might expect — those trace ions carry a little current.
Common mistakes to avoid
- Believing pH 7 is neutral at any temperature. It is neutral only at 25 °C. Define neutral as [H₃O⁺] = [OH⁻] and you are safe everywhere.
- Thinking acid destroys all the hydroxide. The product [H₃O⁺][OH⁻] is fixed, so OH⁻ is suppressed, never eliminated.
- Using pH + pOH = 14 outside 25 °C. The correct general form is pH + pOH = pKw, and pKw moves with temperature.
FAQ
Is hot water acidic?
No. Its pH is lower than 7, but so is its neutral point, and [H₃O⁺] still equals [OH⁻]. It is neutral water on a shifted scale.
Why is Kw exactly 1.0 × 10⁻¹⁴?
It is not exact — it is a measured value that rounds very conveniently at 25 °C. Nature did not choose it; the Celsius scale and our choice of reference temperature made it look tidy.
Does Kw change when I add salt or acid?
Not for anything you will be asked to calculate. Kw is set by temperature; adding solutes changes the individual concentrations, not their product. (Very concentrated salt solutions nudge it slightly, but that correction belongs to a later course.)
Can pH be negative or above 14?
Yes. Concentrated strong acids can give pH below 0 and concentrated strong bases above 14. The 0–14 range is a convenient window, not a hard limit.
The takeaway
Kw is the constant that ties the two halves of the pH scale together. Water quietly ionises itself, the product of the two ion concentrations is fixed at any given temperature, and that single fact gives you pH 7 for neutral water at 25 °C, the pH + pOH = 14 shortcut, and a route between [H₃O⁺] and [OH⁻] in any aqueous solution you meet.
Pair this with pH vs pOH: What's the Difference? and What Is pH? The pH Scale Explained Simply; the temperature effect is What Is Chemical Equilibrium? The Balance Point in action. Come from [Strong vs Weak Bases], next up [Monoprotic vs Polyprotic Acids].
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