5.5.3 The Ionic Product of Water

Dissociation of Water

Water is only slightly dissociated, meaning it ionizes very minimally in solution. This dissociation creates a balance of hydrogen ions $\text{H}^+$ and hydroxide ions $\text{OH}^-$, represented by the equilibrium:

$$\text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^-$$

Since the dissociation is minimal, this equilibrium lies far to the left.

The Ionic Product of Water ($K_w$)

The equilibrium constant for the dissociation of water is called the ionic product of water $K_w$.

It is defined as:

$$K_w = [\text{H}^+][\text{OH}^-]$$

At 25°C, $K_w$ has a value of 1.00 × 10⁻¹⁴ mol² dm⁻⁶

This value varies with temperature, as water dissociation is an endothermic process, meaning $K_w$ increases with temperature.

Units of $K_w$: The units for $K_w$ are always mol² dm⁻⁶

Calculating the pH of Pure Water

In pure water, the concentration of $\text{H}^+$ is equal to the concentration of $\text{OH}^-$.

Therefore:

$$K_w = [\text{H}^+]^2$$ $$[\text{H}^+] = \sqrt{K_w}$$

Calculating the pH of a Strong Base Using $K_w$

For a strong base like sodium hydroxide $\text{NaOH}$, which fully dissociates, you can use $K_w$ to find the $\text{H}^+$ concentration and calculate the pH.