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 (H_{3}O^{+}).

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 H_{3}O^{+} and OH- concentrations that makes it quite easy to solve *one* if you know the *other*.

## Ion-product Constant for Water (Kw)

The formula is: K_{w} = 1 * 10^{-14} = [H_{3}O^{+}] * [OH-]

The formula for the ion-product constant for water can be rearranged to solve for either H_{3}O^{+} or OH-.

Calculate H_{3}O^{+} when you know OH-: [H_{3}O^{+}] = (1 * 10^{-14}) / [OH-]

Calculate OH- when you know H_{3}O^{+}: [OH-] = (1 * 10^{-14}) / [H_{3}O^{+}]

## Calculate H3O+ from OH-

**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.

[H_{3}O^{+}] = 1 * 10^{-14}) / [OH-]

[H_{3}O^{+}] = (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}

## Calculate OH- from H3O+

**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}) / [H_{3}O^{+}]

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

[OH-] = 0.27 * 10^{-9}

## Calculate H3O+ from Molarity

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.

2 Na | |

Molecule | Coefficient |

Na | 2 |

O | 1 |

Na | 2 |

**Example 3:** A 2.0 L solution of 0.5 M hydrochloric acid (HCl).

First, write the chemical equation for the dissociation of the acid.

HCl (aq) + H_{2}O = H_{3}O^{+} (aq) + Cl- (aq)

Second, calculate the concentration of hydronium ions.

In the case of hydrochloric acid, the stoichiometric **coefficients** of the acid and the hydronium ion are both **one**. They are the same, which makes this a very simple matter. The concentration of hydronium ions is the same as the concentration of hydrochloric acid.

[H_{3}O^{+}] = [HCl]

**Example 4:** A 2.0 L solution of 0.5 M sulfuric acid (H_{2}SO_{4}).

H_{2}SO_{4} + 2 H_{2}O = 2 H_{3}O^{+} + SO_{4}^{2-}

The **coefficient** of the *acid* is *one* and the coefficient of the *hydronium ion* is *two*. The concentration of hydronium ions is two times that of the acid.

[H_{3}O^{+}] = 2 * 0.5 M

[H3O+] = 1.0 M

#### References

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