The Ionization Constant of Water and its Ionic Product

The Amphoteric Nature of Water

Water occupies a unique position in acid-base chemistry because it can act as both an acid and a base. This dual behaviour is called amphoteric nature. When water meets an acid like HCl, it accepts a proton and behaves as a base. When it meets a base like NH$_3$, it donates a proton and behaves as an acid. But the most important case is what happens in pure water itself.

In absolutely pure water, one water molecule donates a proton to another water molecule. The donor acts as an acid, the acceptor acts as a base, and the process is perfectly symmetrical:

This is called the autoionization or self-ionization of water. The products are the hydronium ion ($\text{H}_3\text{O}^+$) and the hydroxide ion ($\text{OH}^-$). Notice that water itself provides both the conjugate acid ($\text{H}_3\text{O}^+$) and the conjugate base ($\text{OH}^-$) in this equilibrium.

The Equilibrium Constant for Autoionization

For the autoionization reaction, we can write an equilibrium constant expression in the usual way:

But water is a pure liquid. Its concentration does not change measurably during the reaction — it remains essentially constant. By convention, the concentration of a pure liquid is omitted from the equilibrium expression and is absorbed into the value of the constant. This gives us a new constant, called the ionic product of water, denoted $K_w$:

Since $\text{H}_3\text{O}^+$ is simply a hydrated proton, we often write this more simply as:

This is one of the most important relationships in all of aqueous chemistry. It tells us that in any aqueous solution at a given temperature, the product of the hydrogen ion concentration and the hydroxide ion concentration is a constant.

The Numerical Value of $K_w$ at 298 K

Experimental measurements show that in pure water at 298 K (25 °C), the concentration of $\text{H}^+$ ions is $1.0 \times 10^{-7}$ M. Because the dissociation of one water molecule produces exactly one $\text{H}^+$ and one $\text{OH}^-$ ion, the concentrations are equal:

Therefore:

Temperature Dependence of $K_w$

$K_w$ is an equilibrium constant, and like all equilibrium constants, its value changes with temperature. The autoionization of water is an endothermic process (it absorbs heat), so according to Le Chatelier's principle, increasing the temperature shifts the equilibrium to the right, producing more ions. This means $K_w$ increases as temperature rises.

At 373 K (100 °C), for example, $K_w$ is roughly $5.5 \times 10^{-13}$, which is about 55 times larger than at 298 K. This is why "neutral" water at 100 °C has a pH of about 6.1, not 7.0. The neutral point shifts with temperature because the condition for neutrality is always $[\text{H}^+] = [\text{OH}^-]$, and that equality gives a different pH when $K_w$ is different.

The Extent of Dissociation in Pure Water

It is useful to see just how little water actually dissociates. The molarity of pure water is calculated from its density and molar mass:

The concentration of dissociated water is $1.0 \times 10^{-7}$ M (since each dissociated molecule gives one $\text{H}^+$). The ratio of dissociated water to undissociated water is:

This means that only about 2 molecules in every billion water molecules are dissociated at any instant. The equilibrium lies overwhelmingly to the left, toward undissociated water. This explains why pure water is such a poor conductor of electricity — there are very few ions to carry charge.

Classifying Aqueous Solutions Using $[\text{H}_3\text{O}^+]$ and $[\text{OH}^-]$ …