We have already seen that [latex]\ce{H_{2}O}[/latex] can act as an acid or a base, as shown below:

[latex]\begin{array}{lcll} \ce{NH3}+\ce{H2O}&\rightarrow&\ce{NH4^+}+\ce{OH^-}&\hspace{5mm}\ce{H2O}\text{ acts as an acid} \\ \ce{HCl}+\ce{H2O}&\rightarrow&\ce{H3O^+}+\ce{Cl^-}&\hspace{5mm}\ce{H2O}\text{ acts as a base} \end{array}[/latex]

It may not surprise you to learn, then, that within any given sample of water, some [latex]\ce{H_{2}O}[/latex] molecules are acting as acids, and other [latex]\ce{H_{2}O}[/latex] molecules are acting as bases. The chemical equation is as follows:

[latex]\ce{H2O}+\ce{H2O}\rightarrow \ce{H3O+}+\ce{OH-}[/latex]

This occurs only to a very small degree: only about 6 in 10⁸ [latex]\ce{H_{2}O}[/latex] molecules are participating in this process, which is called the autoionisation of water. At this level, the concentration of both [latex]\ce{H^{+}}{(aq)}[/latex] and [latex]\ce{OH^{-}}{(aq)}[/latex] in a sample of pure [latex]\ce{H_{2}O}[/latex] is about 1.0 × 10⁻⁷ M. If we use square brackets around a dissolved species to imply the molar concentration of that species, we have:

[latex][\ce{H+}]=[\ce{OH-}]=1.0\times 10^{-7}\text{ M}[/latex]

for any sample of pure water because [latex]\ce{H_{2}O}[/latex] can act as both an acid and a base. The product of these two concentrations is [latex]{1.0 × 10^{-14}}[/latex] as shown in the following equation:

[latex][\ce{H+}]\times [\ce{OH-}]=(1.0\times 10^{-7})(1.0\times 10^{-7})=1.0\times 10^{-14}[/latex]

In acids, the concentration of [latex]\ce{H^{+}}{(aq)}[/latex] — written as [latex]\ce{[H^{+}]}[/latex] — is greater than 1.0 × 10⁻⁷ M, while for bases the concentration of [latex]\ce{OH^{-}}{(aq)}[/latex] — [latex]\ce{[OH^{-}]}[/latex]— is greater than 1.0 × 10⁻⁷ M. However, the product of the two concentrations — [latex]\ce{[H^{+}]}\ce{[OH^{-}]}[/latex]— is always equal to 1.0 × 10⁻¹⁴, no matter whether the aqueous solution is an acid, a base, or neutral, which can be seen from the following:

[latex][\ce{H+}][\ce{OH-}]=1.0\times 10^{-14}[/latex]

This value of the product of concentrations is so important for aqueous solutions that it is called the autoionisation constant of water and is denoted K_w as shown by the following equation:

[latex]K_{\text{w}}=[\ce{H+}][\ce{OH-}]=1.0\times 10^{-14}[/latex]

This means that if you know [latex]\ce{[H^{+}]}[/latex] for a solution, you can calculate what [latex]\ce{[OH^{-}]}[/latex] has to be for the product to equal 1.0 × 10⁻¹⁴, or if you know [latex]\ce{[OH^{-}]}[/latex], you can calculate [latex]\ce{[H^{+}]}[/latex]. This also implies that as one concentration goes up, the other must go down to compensate so that their product always equals the value of K_w.

When you have a solution of a particular acid or base, you need to look at the formula of the acid or base to determine the number of [latex]\ce{H^{+}}[/latex] or [latex]\ce{OH^{-}}[/latex] ions in the formula unit because [latex]\ce{[H^{+}]}[/latex] or [latex]\ce{[OH^{-}]}[/latex] may not be the same as the concentration of the acid or base itself.

For strong acids and bases, [latex]\ce{[H^{+}]}[/latex] and [latex]\ce{[OH^{-}]}[/latex] can be determined directly from the concentration of the acid or base itself because these ions are 100% ionised by definition. However, for weak acids and bases, this is not so. The degree, or percentage, of ionisation would need to be known before we can determine [latex]\ce{[H^{+}]}[/latex] and [latex]\ce{[OH^{-}]}.[/latex]