Example 13.1: Ion Concentrations in Pure Water
What are the hydronium ion concentration and the hydroxide ion concentration in pure water at
25 °C?
Solution
\([\ce{H3O+}]\) = ?
\([\ce{OH-}]\) = ?
The autoionization of water yields the same number of hydronium and hydroxide ions. Therefore, in pure
\(Failed to interpret math QQQwater, [H3O+] QQQ = [\ce{OH-}]\) At
25 °C:.
\(K_{\mathrm{w}} = [\ce{H3O+}] \cdot [\ce{OH-}] = 1.0\times 10^{-14}\)
Because in this
\(Failed to interpret math QQQcase, [H3O+] QQQ = [\ce{OH-}]\),
\(K_{\mathrm{w}} = {[\ce{H3O+}]}^{2}\)
So we can calculate [H3O+] from
\(K_{\mathrm{w}}\) for pure water (also works for any neutral aqueous solution):
\(K_{\mathrm{w}}\) \(= 1.0\times 10^{-14}\)
\([\ce{H3O+}]\) \(= \sqrt{K_{\mathrm{w}}}\)
\(\ \ \ =\sqrt{1.0\times 10^{-14}}\)
\(\ \ \ =1.00\times 10^{-7}\)
\([\ce{OH-}]\) \(= [\ce{H3O+}]\)
\(\ \ \ =1.00\times 10^{-7}\)
\(\ \ \ =1.00\times 10^{-7}\)
The hydronium ion concentration and the hydroxide ion concentration are the same, and we find that both equal
\(1.0\times 10^{-7 }\)M.