# Auto-Ionization of Water

## $$K_{w}$$

Water ionizes to a very small extent:

$$\text{H}_{2}\text{O}(\text{l}) + \text{H}_{2}\text{O}(\text{l})$$ $$\rightleftharpoons$$ $$\text{H}_{3}\text{O}^{+}(\text{aq}) + \text{OH}^{-}(\text{aq})$$

This type of reaction (the transfer of a proton between identical molecules) is known as auto-protolysis. This reaction is also known as the auto-ionisation of water and the ions formed are a conjugate acid and base pair of water:

### Definition: Auto-protolysis and auto-ionisation of water

Auto-protolysis is the transfer of a proton between two of the same molecules. The auto-ionisation of water is one example of auto-protolysis.

$$\text{K}_{\text{w}}$$ is the equilibrium constant for this process:

$$\text{K}_{\text{w}}$$ = $$[\text{H}_{3}\text{O}^{+}][\text{OH}^{-}]$$

At $$\text{25}$$ $$\text{℃}$$: $$[\text{H}_{3}\text{O}^{+}]$$ = [$$\text{H}^{+}$$] = $$\text{1} \times \text{10}^{-\text{7}}$$, therefore:

$$\text{K}_{\text{w}}$$ = $$\text{1} \times \text{10}^{-\text{14}}$$ at $$\text{25}$$ $$\text{℃}$$