The pH scale is related to the concentration of hydrogen ions in solution. Water can disassociate into hydrogen and hydroxide ions. Chemically this can be expressed as:

H₂O -> H⁺ + OH^-

Within a certain amount of water, molecules are constantly disassociating into hydrogen and hydroxide ions, which then may recombine to form water again. When the rate of disassociation and recombination are equal, the concentration of hydrogen and hydroxide ions remains constant, which is called equilibrium. There is an equation that predicts what concentrations of hydrogen and hydroxide ions can be present in equilibrium.

In equilibrium, the logarithm of the hydrogen ion concentration plus the logarithm of the hydroxide ion concentration is -14. This can be written:

log[H⁺] + log[OH^-] = -14

or equivalently:
[H⁺]*[OH^-] = 0.00000000000001

(note that brackets mean concentration, so [H⁺] is the concentration of hydrogen ions in moles per liter). The pH scale is based on the concentration of hydrogen ions. The pH is equal to the logarithm of the hydrogen concentration multiplied by negative one.

pH = -1 * log[H⁺]

If pH is low, the solution contains more hydrogen ions. If the pH is below 7, there are more hydrogen ions than hydroxide ions.

Can you find an equation to determine how many hydroxide ions are in a solution of a given pH?
(Answer: log[OH^-] = pH - 14 )