KEY2CHEM

Autoionization of Water 

A neutralization reaction is \([\require{mhchem}\ce{H+}] = [\require{mhchem}\ce{OH-}]\). This is derived from the autoionization reaction of water: \(\require{mhchem}\ce{ H2O(l) + H2O(l) <=> H3O+(aq) + OH^{-}(aq)}\). The equilibrium constant for this reaction is the ion product constant of water,\( K_w\), and has a value of \(1.0 \times 10 ^{-14}\) at \(25^\circ C\). Since \(K_w = [\require{mhchem}\ce{H+}][\require{mhchem}\ce{OH-}]\), the pH of pure water at \(25^\circ C\)  is \(pH = -log[\require{mhchem}\ce{H3O+}] = -log(1.0 \times 10 ^{-7}) = 7.00\).

At \(37^\circ C\) (biological pH), the \(K_w\) has a value of \(2.1 \times 10 ^{-14}\). As such, the concentration of \([\require{mhchem}\ce{H3O+}]\) at this temperature is \(1.5 \times 10 ^{-7}\), yielding a pH of \(6.84\). Although the solution at this temperature is neutral, since\( [\require{mhchem}\ce{H+}] = [\require{mhchem}\ce{OH-}]\), its pH is not equal to \(7\).


Example 1.

Which statement about neutral solutions is true?

 

 

A. \(pH = 7\)

B. \( [\require{mhchem}\ce{H+}] = [\require{mhchem}\ce{OH-}]\)

C. \( [\require{mhchem}\ce{H+}] > [\require{mhchem}\ce{OH-}] \)

 

 

Solution

 

 

B. \([\require{mhchem}\ce{H+}] = [\require{mhchem}\ce{OH-}]\)

 

A neutral solution is one where \([\require{mhchem}\ce{H+}] = [\require{mhchem}\ce{OH-}]\).


Example 2.

The \(K_w\) of water at \(0^\circ C\) is \(1.14 \times 10^{-15}\). What is the pH of pure water at this temperature?

 

 

A. 7.00

B. 14.94

C. 7.47

 

 

 

Solution

 

C. 7.47

 

\(K_w = [\require{mhchem}\ce{H+}][\require{mhchem}\ce{OH-}] = 1.14 \times 10 ^{-15} \)

\([\require{mhchem}\ce{H+}] = \sqrt{1.14 \times 10^{-15}} = 3.4 \times 10 ^{-8}\)

\(pH = -log[\require{mhchem}\ce{H3O+}] = -log(3.4 \times 10 ^{-8}) = 7.47\)


Example 3.

 

Which statement about the autoionization of water is true?

 

A. Autoionization of water is described by a \(K_a\) value, which has a value of 7.00.

B. The equilibrium constant for the process at any temperature is \(1.0 \times 10 ^{-14}\).

C. The ion product constant for autoionization of water is \(K_w\) and its value depends on temperature.

 

 

 

 

 

Solution

 

C. The ion product constant for autoionization of water is \(K_w \)and its value depends on temperature.

 

The equilibrium constant for the autoionization of water (\(K_w\)) is temperature dependent.