The Ionic Product of Water, Kw
Simple Explanation
Pure water very slightly ionises into H⁺ and OH⁻ ions. The product of these two concentrations, Kw, is a constant (1.0 × 10⁻¹⁴ at 25°C) that holds true not just for pure water, but for ANY aqueous solution — acidic, neutral, or basic.
Why Do We Need It?
Kw is what connects [H⁺] and [OH⁻] together in every aqueous solution — it means you never need to measure both; knowing one always lets you calculate the other.
Formula
Ionic Product of Water, Kw
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ (at 25°C)
The product of hydrogen ion and hydroxide ion concentrations is always constant in water at a given temperature — true for pure water AND for any aqueous acid or base solution.
- Kw
- — the ionic product (self-ionisation constant) of water, 1.0 × 10⁻¹⁴ at 25°C
- [H⁺]
- — hydrogen ion (hydronium) concentration, in mol/L
- [OH⁻]
- — hydroxide ion concentration, in mol/L
When to use it: Whenever you know either [H⁺] or [OH⁻] in an aqueous solution at 25°C and need the other.
Worked Example
Find [OH⁻] from [H⁺] using Kw
A solution has [H⁺] = 1.0 × 10⁻³ mol/L. Find [OH⁻] (at 25°C).
Why Does This Work?
Water constantly self-ionises (H₂O ⇌ H⁺ + OH⁻) and this is itself an equilibrium — Kw is simply the equilibrium constant for this reaction. Adding acid raises [H⁺], which by Le Chatelier's principle pushes this equilibrium to suppress [OH⁻] — and the two changes always multiply out to the same constant Kw.
Real-Life Example
Why a very acidic solution still contains some OH⁻
Even a strongly acidic solution, like stomach acid, technically still contains a tiny amount of OH⁻.
Kw guarantees that [H⁺] and [OH⁻] can never independently reach zero — as [H⁺] increases in an acidic solution, [OH⁻] decreases correspondingly, but their product always stays fixed at 1.0 × 10⁻¹⁴.
Practice
A solution has [OH⁻] = 1.0 × 10⁻² mol/L. Find [H⁺] (in mol/L, at 25°C).
MediumCommon mistake
Thinking Kw only applies to pure water — it applies to the H⁺ and OH⁻ concentrations in ANY aqueous solution, no matter how acidic or basic, as long as the temperature is the same.
Quick Review
- Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C.
- Holds true for pure water AND any aqueous acid or base solution.
- Knowing [H⁺] or [OH⁻] lets you calculate the other.