Even pure water has ions
Lesson 2.7.5 called water a weak electrolyte. With an ordinary bulb tester, pure water seems not to conduct at all, but sensitive instruments do pick up a tiny conductivity, so pure water must contain a few free ions. Where do they come from? And where did lesson 2.12.3’s “[H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C” come from?
The autoionization of water
The last reaction in lesson 2.12.1 already showed it: water molecules can pass H⁺ to each other, one acting as an acid and the other as a base.
This is often shortened to
This is the autoionization水的电离 (or self-ionization) of water. It happens to a tiny extent: at 25 °C only about 1.0 × 10⁻⁷ mol of the roughly 55.5 mol of water in a liter ionizes, about one molecule in 550 million.
The ion-product constant Kw
Autoionization is an equilibrium. As with the equilibrium constants of lesson 2.11.4, pure liquid water is left out of the expression, so the product of [H⁺] and [OH⁻] is a constant, the ion-product constant for water水的离子积, Kw:
At 25 °C pure water has [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M, so
Kw holds not just for pure water but for any dilute water solution. Whatever acid, base, or salt you add, at constant temperature [H⁺][OH⁻] still equals Kw. That is where pH + pOH = 14.00 in lesson 2.12.3 comes from.
Kw changes with temperature
Like any equilibrium constant, Kw depends only on temperature. Autoionization breaks O–H bonds, so it is endothermic. By Le Châtelier’s principle (lesson 2.11.5), raising the temperature shifts the equilibrium toward the ions and Kw grows:
| Temperature | Kw | pH of a neutral solution |
|---|---|---|
| 0 °C | 1.1 × 10⁻¹⁵ | 7.48 |
| 25 °C | 1.0 × 10⁻¹⁴ | 7.00 |
| 50 °C | 5.5 × 10⁻¹⁴ | 6.63 |
| 75 °C | 2.0 × 10⁻¹³ | 6.35 |
| 100 °C | 5.6 × 10⁻¹³ | 6.13 |
The neutral pH is calculated from [H⁺] = √Kw.
What neutral really means
Whether a solution is acidic or basic depends on how [H⁺] and [OH⁻] compare:
- [H⁺] > [OH⁻]: acidic
- [H⁺] = [OH⁻]: neutral
- [H⁺] < [OH⁻]: basic
“pH 7 is neutral” is only true at 25 °C. At 100 °C pure water has a pH of about 6.13, below 7, yet [H⁺] still equals [OH⁻], so it is still neutral. At that temperature a solution at pH 7 is actually basic.
Acids and bases suppress autoionization
Add an acid to water and [H⁺] rises, so the autoionization equilibrium shifts left: water ionizes less and [OH⁻] falls. A base does the same in reverse, raising [OH⁻] and lowering [H⁺]. At a given temperature the product always equals Kw.
For example, in 0.010 M HCl at 25 °C, [OH⁻] = 1.0 × 10⁻¹⁴ ÷ 0.010 = 1.0 × 10⁻¹² M. All of that OH⁻ comes from water, so water ionizes to only 1.0 × 10⁻¹² M, far less than the 1.0 × 10⁻⁷ M in pure water.
Drag the temperature slider below and compare pure water, a strong acid, and a strong base. The bars are on a log scale: when [H⁺] goes up by some powers of ten, [OH⁻] goes down by the same number. The dashed line marks a neutral solution at that temperature:
Kw data: measured values at 0, 25, 50, 75, and 100 °C (Bandura & Lvov, 2006); temperatures in between are interpolated linearly. For the acid and base solutions, the H⁺ or OH⁻ from water itself is ignored.
How Chinese textbooks differ
- Chinese textbooks write H₂O ⇌ H⁺ + OH⁻ and Kw = c(H⁺)·c(OH⁻), and call Kw 水的离子积.
- Many Chinese practice problems use Kw = 1 × 10⁻¹² at 100 °C to make the arithmetic easy, which makes neutral pH exactly 6. The measured value is about 5.6 × 10⁻¹³. Always use the value a problem gives you.
Example 1: [H⁺] in a basic solution
At 25 °C, find [H⁺] and the pH of 0.010 M NaOH. What concentration of OH⁻ comes from the water itself?
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[OH⁻]. NaOH dissociates completely, so [OH⁻] = 0.010 M. The OH⁻ from water is negligible.
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[H⁺]. In any dilute aqueous solution, [H⁺][OH⁻] = Kw:
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pH.
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OH⁻ from water. All the H⁺ in the solution comes from water, and water releases one OH⁻ for every H⁺. So water contributes 1.0 × 10⁻¹² M of OH⁻ too.
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Think about it. In pure water, water supplies 1.0 × 10⁻⁷ M OH⁻; with NaOH added, only 1.0 × 10⁻¹² M. The added OH⁻ shifts water’s equilibrium to the left and suppresses its ionization.
Example 2: pure water at 50 °C
At 50 °C, Kw = 5.5 × 10⁻¹⁴. Find [H⁺] and the pH of pure water. Is it acidic, neutral, or basic?
In pure water [H⁺] = [OH⁻], so
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[H⁺].
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pH. Working from Kw directly is more accurate:
Rounding [H⁺] to 2.3 × 10⁻⁷ first and then taking the log gives 6.64; the difference comes from the intermediate rounding.
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Acidic or basic? The pH is below 7, but [H⁺] = [OH⁻], so pure water is still neutral.
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Why is Kw larger? Water’s ionization is endothermic, so heating shifts it to the right and raises both [H⁺] and [OH⁻].
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A common mistake. Calling it acidic because pH < 7. “pH 7 is neutral” holds only at 25 °C; neutral always means [H⁺] = [OH⁻].
- 25 °C, [H⁺] = 1.0 × 10⁻⁵ M
[OH⁻] = 1.0 × 10⁻⁹ M, so [H⁺] > [OH⁻].
- 25 °C, [OH⁻] = 1.0 × 10⁻⁵ M
[H⁺] = 1.0 × 10⁻⁹ M, so [H⁺] < [OH⁻].
- 25 °C, pH 7.00
At 25 °C, [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M.
- 25 °C, [H⁺] = 1.0 × 10⁻⁹ M
[OH⁻] = 1.0 × 10⁻⁵ M, larger than [H⁺].
- Pure water at 100 °C (pH 6.13)
In pure water [H⁺] always equals [OH⁻], whatever the pH.
- A solution at pH 7.00 and 100 °C
Neutral pH at 100 °C is 6.13. At pH 7.00, [H⁺] = 1.0 × 10⁻⁷ M and [OH⁻] = 5.6 × 10⁻¹³ ÷ 1.0 × 10⁻⁷ = 5.6 × 10⁻⁶ M, which is larger.
- A solution at pH 7.00 and 0 °C
Neutral pH at 0 °C is 7.48. At pH 7.00, [OH⁻] = 1.1 × 10⁻¹⁵ ÷ 1.0 × 10⁻⁷ = 1.1 × 10⁻⁸ M, which is smaller than [H⁺].
- Any temperature, [H⁺] = [OH⁻]
That is the definition of neutral.
Common mistakes
Mistake 1: “A solution at pH 7 is always neutral.” Only at 25 °C. To decide, compare [H⁺] with [OH⁻]; above 25 °C a neutral solution has a pH below 7.
Mistake 2: “An acid solution contains no OH⁻.” Water ionizes in every water solution, so an acid contains some OH⁻, just very little. 0.010 M HCl at 25 °C has [OH⁻] = 1.0 × 10⁻¹² M.
Mistake 3: “Adding acid makes Kw bigger.” Adding acid raises [H⁺] and lowers [OH⁻], and the product still equals Kw. Only temperature changes Kw.
Quick check
At 25 °C, what is [OH⁻] in 0.0010 M HCl?
[H⁺] = 1.0 × 10⁻³ M, so [OH⁻] = Kw ÷ [H⁺] = 1.0 × 10⁻¹⁴ ÷ 1.0 × 10⁻³ = 1.0 × 10⁻¹¹ M. 1.0 × 10⁻⁷ M is the value in pure water.
Pure water is heated from 25 °C to 80 °C. Which statement is correct?
Autoionization is endothermic, so heating raises Kw and [H⁺] and lowers the pH. But [H⁺] still equals [OH⁻] in pure water, so it stays neutral.
Summary
- Water ionizes very slightly: H₂O ⇌ H⁺ + OH⁻. Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C, in any dilute water solution.
- Kw depends only on temperature. Autoionization is endothermic, so Kw rises as temperature rises.
- Neutral means [H⁺] = [OH⁻]. Only at 25 °C is a neutral solution’s pH exactly 7. Acids and bases both suppress the autoionization of water.
On to AP (for later)
AP topic 8.1 asks you to write the autoionization of water, use Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C, and know that Kw changes with temperature: hotter pure water has a lower pH but is still neutral. Topic 8.3 also uses Ka × Kb = Kw, which links the strength of a weak acid to that of its conjugate base.
Data sources: Kw values from Bandura and Lvov’s 2006 evaluation (listed in the Wikipedia article “Self-ionization of water”).