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.