3.1.12.3 - The Ionic Product of Water, Kw

Water dissociation and the meaning of Kw

Pure water is not made of only uncharged molecules. A very small fraction of water molecules dissociate at any moment, so pure water contains both hydrogen ions and hydroxide ions:

Because this dissociation is only slight, most of the particles are still $\ce{H2O(l)}$. That is why water is described as slightly dissociated.

To see where that expression comes from, start with the equilibrium constant for the dissociation of water:

In this equilibrium, water is a pure liquid, so its concentration is effectively constant. Chemists therefore combine $\ce{[H2O]}$ with $K_c$ to make a new constant:

At 25 °C, the value of $K_w$ is $1.00 \times 10^{-14}\,\mathrm{mol}^{2}\, \mathrm{dm}^{-6}$. In pure water, the concentrations of $\ce{H+}$ and $\ce{OH-}$ are equal, so each one must be $1.00 \times 10^{-7}\,\mathrm{mol}\, \mathrm{dm}^{-3}$.

At a fixed temperature this ionic-product relationship applies to acidic and alkaline aqueous solutions as well as pure water. Adding acid raises $[\ce{H+}]$, so $[\ce{OH-}]$ decreases but does not become zero. Neutrality means equal concentrations of these two ions; pH 7 is the neutral value specifically at about $25\,^{\circ}\mathrm C$.

Why Kw changes with temperature

$K_w$ is not one fixed number for all temperatures. The forward dissociation of water is endothermic, so increasing the temperature favours the forward reaction.

The diagram below summarises how the endothermic forward reaction leads to larger ion concentrations and a larger $K_w$ at higher temperature.

[DIAGRAM: asset_name: 1.12.3 - The Ionic Product of Water, Kw - Diagram 1; asset_slug: 1.12.3 - The Ionic Product of Water, Kw - Diagram 1; recommended_method: matplotlib_exact_plot; description: Neutral water at10,25,40 Celsius; Kw2.93e-15,1e-14,2.92e-14; neutral pH7.27,7.00,6.77; equal-ion neutrality and temperature effect.]

That means both $[\ce{H+}]$ and $[\ce{OH-}]$ increase as temperature rises, so the product $[\ce{H+}][\ce{OH-}]$ increases too. Therefore $K_w$ increases when temperature increases.

Hotter pure water does not become acidic. In pure water, the concentrations of $\ce{H+}$ and $\ce{OH-}$ increase together, so they remain equal. The pH of neutral water becomes lower than 7 at higher temperature, but the water is still neutral because $[\ce{H+}] = [\ce{OH^-}]$.