Concentration of Hydronium ion [H3O+] and hydroxide ion [OH-]
To understand how to calculate [H 3O+] from [OH-], and how to calculate [OH -] from [H3O+], it
is helpful to understand the balance between these two ions. An aqueous solution is a solution
in which water is the solvent.
Water molecules (H2O) are polar, meaning that they have a negative end (the oxygen) and a
positive end (the hydrogens). When there is a reaction of and acid and a base in an aqueous
solution, the water molecules have the ability to attract and temporarily hold a donated proton
(H+) from the acid. This creates the hydronium ion (H 3O+).
In an acidic aqueous solution, the concentration of hydronium ions [H 3O+] will be higher than
the concentration of hydroxide [OH -] ions. There is a relationship between the [H 3O+] & [OH]concentrations that makes it quite easy to solve one if you know the other.
The formula for the ion-product constant for water can be rearranged to solve for either [H 3O+]
or [OH-]:
To Calculate [H3O+] when you know [OH-]: [H3O+] = (1 x 10-14) / [OH-]
To Calculate [OH-] when you know [H3O+]: [OH-] = (1 x 10-14) / [H3O+]
 Calculate [H3O+] from [OH-]
Example 1: The hydroxide ion concentration is known to be 4.0 x 10 -11 M. Determine the
hydronium ion concentration.
[H3O+] = (1 x 10-14) / [OH-]
[H3O+] = (1 x 10-14) / (4.0 x 10-11) = 0.25 x 10-3
Which can also be written as 2.5 x 10 -4 M
 Calculate [OH-] from [H3O+]
Example 2: If you know the hydronium ion concentration is 3.7 x 10 -5 M, calculate the
hydroxide ion concentration.
[OH-] = (1 x 10-14) / [H3O+]
[OH-] = (1 x 10-14) / (3.7 x 10-5) = 0.27 * 10-9
Which can also be written as 2.7 x 10 -10 M