How To Calculate H3O And OH

To understand how to calculate H3O 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 in an aqueous solution, the water molecules have the ability to attract and temporarily hold a donated proton (H+). This creates the hydronium ion (H₃O⁺).

In an acidic aqueous solution, the concentration of hydronium ions will be higher than the concentration of hydroxide (OH-) ions. There is a relationship between the H₃O⁺ and OH- concentrations that makes it quite easy to solve one if you know the other.

The formula is: K_w = 1 * 10^-14 = [H₃O⁺] * [OH-]

The formula for the ion-product constant for water can be rearranged to solve for either H₃O⁺ or OH-.

Calculate H₃O⁺ when you know OH-: [H₃O⁺] = (1 * 10^-14) / [OH-]

Calculate OH- when you know H₃O⁺: [OH-] = (1 * 10^-14) / [H₃O⁺]

Example 1: The hydroxide ion concentration is known to be 4.0 * 10-11. Determine the hydronium ion concentration using the ion-product constant for water.

[H₃O⁺] = 1 * 10^-14) / [OH-]

[H₃O⁺] = (1 * 10^-14) / (4.0 * 10^-11)

The calculation is simplified by subtracting the exponents:

10^-14 ÷ 10^-11 = 10^-3

[H3O+] = (1/4.0) * 10^-3

[H3O+] = 0.25 * 10^-3 which can also be written as 2.5 * 10^-4

Example 2: If you know the hydronium ion concentration is 3.7 * 10^-5, calculate the hydroxide ion concentration as follows.

[OH-] = (1 * 10^-14) / [H₃O⁺]

[OH-] = (1 * 10^-14) / (3.7 * 10^-5) Note: easily divide by subtracting the exponents (-14)-(-5)

[OH-] = 0.27 * 10^-9

If you know the concentration of an acid solution in molarity, you can use a formula to calculate the concentration of hydronium ions.

The stoichiometric coefficients in the equations (the numbers in front of each molecule in the equation) determine the outcome of the calculations.