Self-Ionisation of Water

What is Self-Ionisation of Water?

Water is a neutral molecule, but it can undergo a process called self-ionisation or auto-ionisation, where a small fraction of water molecules react with each other to form ions.

In this reaction, one water molecule donates a proton ($H^+$) to another water molecule, producing a hydronium ion ($H_3O^+$) and a hydroxide ion ($OH^-$).

This reaction can be represented as:

$$2H_2O \rightleftharpoons H_3O^+ + OH^-$$

However, in simplified notation, we often use:

$$H_2O \rightleftharpoons H^+ + OH^-$$

This process is reversible and establishes a dynamic equilibrium.

Ionic Product of Water ($K_w$)

The ionic product of water ($K_w$) is the equilibrium constant for the self-ionisation of water.

It quantifies the concentration of $H^+$ and $OH^-$ ions in pure water and is given by the equation:

$$K_w = [H^+][OH^-]$$ $$\text{At 25°C,}\ K_w = 1.0 \times 10^{-14} \, \text{mol}^2 \, \text{dm}^{-6}$$

In pure water, the concentrations of $H^+$ and $OH^-$ are equal.

Thus, $[H^+] = [OH^-]$ , so:

$$[H^+] = [OH^-]$$ $$= \sqrt{K_w} = 1.0 \times 10^{-7} \, \text{mol} \, \text{dm}^{-3}$$

This gives water a neutral pH of 7 at 25°C.

Effect of Temperature on $K_w$

The value of $K_w$ increases as temperature increases because the self-ionisation of water is an endothermic reaction.

As a result, at higher temperatures, more $H^+$ and $OH^-$ ions are produced.

However, even though the concentration of ions increases, water remains neutral because the concentrations of $H^+$ and $OH^-$ remain equal.

pH of Water and Relationship to $K_w$

The pH of a solution is related to the concentration of $H^+$ ions:

$$\text{pH} = -\log[H^+]$$

For pure water at 25°C, since $[H^+] = 1.0 \times 10^{-7}$

$$\text{pH} = -\log(1.0 \times 10^{-7}) = 7$$

At higher temperatures, since $K_w$ increases, the concentration of $H^+$ increases and the pH decreases. However, the solution is still neutral because the $[H^+]$ and $[OH^-]$ concentrations are equal.