Self-ionization of water

Water is never just a collection of H₂O molecules. This reaction occurs:

H₂O_(l) + H₂O_(l) ⇌ H₃O⁺_(aq) + OH⁻_(aq).

Only a couple molecules per billion react in this way (equilibrium favours reactants), but it is still significant. It can also be written more succinctly:

H₂O_(l) ⇌ H⁺_(aq) + OH⁻_(aq).

The $K$ value for this reaction is called the ion product constant for water:

$K_{\text{w}}=[{\text{H}}^{+}][{\text{OH}}^{-}]\text{.}$

For pure water at SATP, the value of $K_{\text{w}}$ is 1.0 × 10⁻¹⁴, and the concentration of both ions is 1.0 × 10⁻⁷ mol/L. This self-ionization occurs in all aqueous solutions. Given the hydrogen concentration, you can always find the hydroxide concentration using this formula (and vice versa).

When acids or bases are dissolved, the ion concentrations are no longer equal, but their product is still 1.0 × 10⁻¹⁴ (at SATP).

• $[{\text{H}}^{+}]=[{\text{OH}}^{-}]⟹$ neutral
• $[{\text{H}}^{+}]>[{\text{OH}}^{-}]⟹$ acidic
• $[{\text{H}}^{+}]<[{\text{OH}}^{-}]⟹$ basic

Example

What are the hydrogen and hydroxide ion concentrations in a 0.16 mol/L barium hydroxide solution?

First, we can write the dissociation equation (with a normal arrow because barium hydroxide is a strong base—more on that in the next section):

Ba(OH)_2(aq) → Ba²⁺_(aq) + 2 OH⁻_(aq).

We can find the hydroxide ion concentration using stoichiometry:

$[{\text{OH}}^{-}]=2[{\text{Ba(OH)}}_2]=2(0.16\text{mol/L})=0.32\text{mol/L}\text{.}$

Now, since $K_{\text{w}}=[{\text{H}}^{+}][{\text{OH}}^{-}]\text{,}$

$[{\text{H}}^{+}]=\frac{K_{\text{w}}}{[{\text{OH}}^{-}]}=\frac{1.0\times {10}^{-14}}{0.32\text{mol/L}}=3.1\times {10}^{-14}\text{mol/L}\text{.}$