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1.10.3Physical Chemistry

The Ionic Product of Water, Kw — Oxford AQA International A Level Chemistry Revision Notes & Topical Questions

5 min read 5 parts Lesson 53 of 63

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Part 1 of 5Ionisation of Water

1.10.3 The Ionic Product of Water, Kw

Water is very slightly ionised into hydrogen and hydroxide ions.

Ionisation of Water
Equilibrium
  • H₂O(l) ⇌ H⁺(aq) + OH⁻(aq) is an endothermic equilibrium with a very small extent of ionisation.
Expression
  • Kw = [H⁺][OH⁻], and water is omitted because its concentration is effectively constant.
Value
  • Kw = 1.00 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K, so [H⁺] = [OH⁻] = 1.00 × 10⁻⁷ mol dm⁻³ in pure water.
Neutral
  • Water is neutral because [H⁺] equals [OH⁻], and this is true at every temperature.

Part 2 of 5Calculations for Strong Bases

Use Kw to turn [OH⁻] into [H⁺] and then pH.

1
For NaOH, a strong monobasic base, [OH⁻] equals the concentration of the alkali.
2
Rearrange to find [H⁺] = Kw ÷ [OH⁻].
3
Convert [H⁺] to pH using pH = −log₁₀[H⁺].
4
Alternatively find pOH = −log₁₀[OH⁻] and use pH = 14.00 − pOH at 298 K.
5
For Ba(OH)₂ or Ca(OH)₂, double the concentration because each formula unit gives two hydroxide ions.

Part 3 of 5Effect of Temperature

Le Chatelier
  • Ionisation of water is endothermic, so a higher temperature moves the equilibrium to the right and Kw increases.
Neutral pH falls
  • At a higher temperature [H⁺] in pure water is greater than 1.00 × 10⁻⁷, so the pH of neutral water is below 7.
Still neutral
  • The water remains neutral because [H⁺] and [OH⁻] are still equal even though pH is not 7.
Example
  • If Kw = 4.0 × 10⁻¹⁴, then [H⁺] = √(4.0 × 10⁻¹⁴) = 2.0 × 10⁻⁷ mol dm⁻³ and the pH of pure water is 6.70.

Part 4 of 5Worked Example

Question Calculate the pH of 0.0500 mol dm⁻³ NaOH at 298 K, where Kw = 1.00 × 10⁻¹⁴ mol² dm⁻⁶.

  1. NaOH is fully ionised, so [OH⁻] = 0.0500 mol dm⁻³.
  2. [H⁺] = Kw ÷ [OH⁻] = 1.00 × 10⁻¹⁴ ÷ 0.0500 = 2.00 × 10⁻¹³ mol dm⁻³.
  3. pH = −log₁₀(2.00 × 10⁻¹³) = 12.70.

Answer The pH of the NaOH solution is 12.70.

Part 5 of 5Exam Checklist & Tips

1.10.3 – Key Points for the Exam

  • Ionic product of water Kw, the product [H⁺][OH⁻] in aqueous solution.
  • Neutral solution A solution in which [H⁺] equals [OH⁻].
  • pOH The negative logarithm of the hydroxide ion concentration.
  • Endothermic A change that takes in heat from the surroundings.

Common Mistakes

  • Using pH = 14 − pOH at temperatures other than 298 K when Kw has a different value.
  • Stating that pure water at a high temperature is acidic because its pH is below 7.
  • Forgetting that the units of Kw are mol² dm⁻⁶.
  • Using the hydroxide concentration directly in the pH formula instead of first finding [H⁺].

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