The Auto-Ionisation of Water
Water is not just a passive solvent; it is an active participant in acid-base chemistry. Even completely pure water conducts electricity slightly because it undergoes auto-ionisation.
Water molecules collide and transfer protons to one another, acting as both an acid and a base (amphoteric).
Or, simplified:
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The position of equilibrium lies extremely far to the left. Only about 1 in every 500 million water molecules is ionised at room temperature.
Deriving
If we write the Equilibrium Constant expression (
Since the dissociation is so small, the concentration of water is effectively constant.
We multiply
Insight: Why is
taken as constant? What does
actually mean?
- Square brackets
mean “concentration in ” - So,
literally asks: “How many moles of water molecules are there in one cubic decimetre of water?” Let’s calculate it for pure water at
:
- Mass of
water: Density is , so mass is . - Molar Mass of water (
): - Number of Moles
: So, the concentration of pure water is a massive
Why is it taken to be constant? The equilibrium for water dissociation is:
\ce{H_{2}O_{(l)} \rightleftharpoons H+{(aq)} + OH-{(aq)}}$$
We know that water dissociates extremely weekly. At equilibrium, the concentration of ions formed is only
. (from conductivity experiments) Let’s compare the Initial concentration vs. the Equilibrium concentration:
- Initial
- Change:
- Final
The Conclusion: The value has changed by such an infinitesimally small amount that mathematically, it is considered unchanged.
Definition of
- Standard Value at 298K:
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- From conductivity experiments, it has been found that the concentration of ions in pure water at 298K is
- This means that
of pure water at room temperature contains:
- Applying this to
we get that:
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In any aqueous system, water behaves in such a way that:
- Temperature Dependence: Like all equilibrium constants,
changes with temperature. - The ionisation of water is endothermic (bond breaking).
- As temperature increases, the equilibrium shifts to the right.
- Therefore,
increases as water gets hotter.
The Definition of Neutrality
This is a critical conceptual point: “Neutral” does not mean pH 7:
- Neutral means:
- Acidic means:
- Alkaline means:
Why is Pure Water pH 7 at 25°C?
In pure water, for every
Substitute this into the
Critical: Non room-temperature water
- At higher temperatures (e.g. 100°C),
is larger (e.g. ). - The pH of boiling water is roughly 6.1.
- Does this mean boiling water is acidic? ABSOLUTELY NOT
- It is still neutral because
. - There is simply a higher concentration of both ions.
(Same reasoning for cold water not being more alkaline)
Using
is the key to calculating the pH of strong bases like . - Since
fully dissociates, we know , but the PH equation requires .
The Relationship:
In any aqueous solution (acid, base, or neutral), the product of the ions must always equal