how to solve problems in ionic equilibrium

Perhaps the most important ionic equilibrium is the ratio
of hydrogen ions to hydroxide ions in pure water. This can be used to deduce the
dissociation constant of water.

It is known, from
measurements, that the equilibrium constant for water @STP (standard temperature = zero
celcius, standard pressure = 101.3 kilopascals) is ten to the power of minus
fourteen.

Expressed
mathematically:

[H+] x [OH-] =
10^-14

Where [H+] is the concentration of hydrogen ions in
moles per litre, and [OH-] is the concentration of hydroxide ions in moles per
litre.

This simple formula is the basis for the solving of
a multitude of problems in preparation for university entrance to do
chem.

One example:

What is the
pH of a 0.1 mole per litre (0.1M) solution of sodium hydroxide
solution?

NaOH is a strong base and it is assumed that it
dissociates in water completely so that the concentration of OH- can be assumed to be
0.1M ( = 0.1 moles per litre OH minus ions) = 10^-1M

This
affects the above mathematical equation like this:

[H+] x
[10^-1] = 10^-14

Rearranging for
[H+]:

[H+] = (10^-14)/[10^-1] =
10^-13.

pH = -log[H+] = 13 the correct value for a dilute
alkali solution.