The exact formula for calculating pH is a fundamental concept in chemistry used to determine the acidity or alkalinity of an aqueous solution.
The pH Formula
The primary formula for pH is defined based on the concentration of hydrogen ions (H⁺) in a solution. As stated in the definition, "pH is defined as the negative log base 10 of the hydronium concentration."
The formula is:
pH = −log([H⁺])
This means that the pH is the negative logarithm (base 10) of the molar concentration of hydrogen ions. Although often written as [H⁺], in aqueous solutions, this typically refers to the concentration of hydronium ions (H₃O⁺), which are formed when hydrogen ions react with water molecules.
Understanding the Formula Components
Let's break down the elements of the pH formula:
- pH: This abbreviation stands for "potential of Hydrogen". It is a dimensionless number that indicates the acidity or basicity of a solution. The scale usually ranges from 0 to 14.
- −log: This signifies the negative logarithm base 10. The logarithmic scale is used because the concentration of hydrogen ions in solutions can vary across a very wide range. Using a logarithm compresses this range into more manageable numbers.
- [H⁺]: This represents the molar concentration of hydrogen ions (or more accurately, hydronium ions, [H₃O⁺]) in moles per liter (M). It indicates the amount of hydrogen ions dissolved in the solution.
| Component | Description | Unit |
|---|---|---|
| pH | Measure of acidity or alkalinity | Unitless |
| −log | Negative logarithm (base 10) | N/A |
| [H⁺] | Molar concentration of hydrogen ions (or hydronium ions, [H₃O⁺]) in solution | moles per liter (M) |
Practical Application
To calculate the pH of a solution, you need to determine the molar concentration of hydrogen ions, [H⁺]. Once you have this value, you apply the formula. For instance, if the hydrogen ion concentration is 1.0 x 10⁻⁷ M (which is the concentration in pure water at 25°C), the pH would be calculated as:
pH = −log(1.0 x 10⁻⁷)
pH = −(−7)
pH = 7
This is why pure water is considered neutral, with a pH of 7.
Conversely, if you know the pH of a solution, you can find the hydrogen ion concentration using the inverse formula:
[H⁺] = 10⁻ᵖᴴ
Understanding this formula is key to working with acids and bases in chemistry and various scientific fields.
