The Auto-Ionization of Water, K w

Water undergoes auto-ionization according to the following equation:

H 2 O(l) + H 2 O(l) H 3 O+(aq) + OH-(aq)

or

2 H 2 O(l) H 3 O+(aq) + OH-(aq)

The equilibirum expression for the above reaction is written below and is treated mathematically like all equilibrium expressions.

K w = [H 3 O+][OH-]

At 25oC, the value of K w has been determined to be 1 x 10-14. This value, because it refers to the auto-ionization of water, has been given a special symbol, K w , but, it is just a special case of K c .

If one knows the concentration of either the hydronium ions or of the hydroxide ions in a water solution,. the other ion concentration can be determined.

Example: What is the hydronium ion concentration in a water solution that is 0.050 M NaOH?

The NaOH is a strong base and will 100% dissociate into its component ions. Therefore, the concentration of the hydroxide ions will be 0.050 M. The hydronium ion concentration is then calculated.

[H 3 O+] = (1 x 10-14)/(0.050) = 2.0 x 10-13 M

Example: What is the hydroxide ion concentration in a water solution that is 4.0 x 10-5 M H 3 O+?