pH Definition
pH = −log[H+] compresses tiny hydrogen-ion concentrations into a compact, unitless scale running roughly from 0 to 14.
What it means
Because hydrogen ion concentrations span enormous ranges — from 10 M in strong acids down to 10⁻¹⁴ M in strong bases — chemists take the negative base-10 logarithm to get manageable numbers. Each pH unit is a tenfold change in [H+]: a solution at pH 3 has ten times the hydrogen ions of one at pH 4. The negative sign keeps everyday values positive.
Variables
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| Hydrogen ion concentration | mol/L (M) | The molar concentration of hydrogen ions (equivalently hydronium, H3O⁺) in the solution. | |
| Potential of hydrogen | unitless | The negative base-10 logarithm of the hydrogen ion concentration; pH is a pure number with no units. |
Assumptions
- The solution is dilute enough that concentration approximates activity.
- The value applies to aqueous solutions at the temperature of measurement.
- pH is unitless — it is never reported with units like 'pH units'.
- At 25 °C, pH 7.00 is neutral; below is acidic and above is basic.
Worked example
A solution has [H⁺] = 2.50 × 10⁻³ M. Calculate its pH.
Given:
- [H⁺] = 2.50 × 10⁻³ M
Write pH = −log[H⁺] = −log(2.50 × 10⁻³).
Split the log: log(2.50 × 10⁻³) = log(2.50) + log(10⁻³).
log(2.50) = 0.398 and log(10⁻³) = −3, so the sum is −2.602.
Apply the negative sign: pH = −(−2.602) = 2.60.
A pH of 2.60 is well below 7, so the solution is distinctly acidic — roughly the acidity of vinegar.