The Ion Product of Water (DP IB Chemistry: SL): Revision Note
The ion product of water
pH of water
An equilibrium exists in water, where a few water molecules dissociate into proton and hydroxide ions
H2O (l) ⇌ H+ (aq) + OH– (aq)
The equilibrium constant for this reaction is:
Kc x [H2O] = [H+][OH–]
Since the concentration of the H+ and OH- ions is very small, the concentration of water is considered to be a constant
This means that the expression can be rewritten as:
Kw = [H+] [OH-]
Where Kw (ion product of water) = Kc x [H2O] = 1.00 x 10-14 at 298K
The product of the two ion concentrations is 1.00 x 10–14 at 298 K
This makes it straightforward to see the relationship between the two concentrations and the nature of the solution:
[H+] & [OH–] Table
[H+] | [OH–] | Type of solution |
|---|---|---|
0.1 | 1 x 10–13 | acidic |
1 x 10–3 | 1 x 10–11 | acidic |
1 x 10–5 | 1 x 10–9 | acidic |
1 x 10–7 | 1 x 10–7 | neutral |
1 x 10–9 | 1 x 10–5 | alkaline |
1 x 10–11 | 1 x 10–3 | alkaline |
1 x 10–13 | 0.1 | alkaline |
Worked Example
What is the pH of a solution of potassium hydroxide, KOH (aq) of concentration 1.0 × 10−3 mol dm−3 ?
Kw = 1.0 × 10−14 at 298 K
A. 3
B. 4
C. 10
D. 11
Answer:
The correct option is D
Rearrange Kw = [H+] [OH-]
[H+] =
Calculate the concentration of [H+]
[H+] = = 1.0 × 10−11 mol dm−3
So the pH = 11
How does temperature affect the ion product of water, Kw?
The ionisation of water is an endothermic process
2H2O (l) ⇌ H3O+ (aq) + OH- (aq)
According to Le Châtelier's principle, if the temperature is increased, the equilibrium will shift to the right to absorb the added heat
This causes the concentrations of both H+ and OH- ions to increase
As a result, the values of Kw increases
The effect on pH
Since the concentration of H+ ions has increased, the pH of the water must decrease
pH = -log10[H+]
Due to the negative sign in the formula, as [H+] increases, pH decreases
Increasing the temperature decreases the pH of water, but the water is still neutral because [H+] = [OH-]
Decreasing the temperature increases the pH of water, but the water is still neutral because [H+] = [OH-]
Graph to show how Kw changes with temperature
Examiner Tips and Tricks
Even though the pH of pure water is less than 7 at temperatures above 298 K, it is still neutral.
This is because the definition of neutrality is [H+] = [OH-], which remains true for pure water at any temperature.
The convention that "pH 7 is neutral" is only true at 298 K (25 °C).
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