What is pH: a logarithmic measure of acidity based on hydrogen ion activity in solution, connecting directly to equilibrium, buffers, and quantitative acid–base calculations.
Mathematical definition
The rigorous definition uses activity rather than concentration: \[ \mathrm{pH} = -\log_{10}\!\left(a_{\mathrm{H}^+}\right) \] In many dilute aqueous solutions, activity can be approximated by concentration: \[ \mathrm{pH} \approx -\log_{10}\!\left([\mathrm{H}^+]\right) \] where \([\mathrm{H}^+]\) is in \(\mathrm{mol\,L^{-1}}\) (M).
The logarithmic form compresses large concentration ranges into manageable numbers. A change of 1 pH unit corresponds to a factor of 10 change in \(a_{\mathrm{H}^+}\) (and approximately in \([\mathrm{H}^+]\) for dilute solutions).
Interpretation of the pH scale
Lower pH corresponds to higher hydrogen ion activity and greater acidity; higher pH corresponds to lower hydrogen ion activity and greater basicity. Neutrality in water depends on temperature because water’s autoionization constant \(K_w\) is temperature-dependent.
Connection to pOH and the ion product of water
The autoionization of water is \[ 2\mathrm{H_2O}(l) \rightleftharpoons \mathrm{H_3O^+}(aq) + \mathrm{OH^-}(aq) \] and the ion product of water is \[ K_w = a_{\mathrm{H_3O^+}}\,a_{\mathrm{OH^-}} \approx [\mathrm{H^+}][\mathrm{OH^-}] \] The definition of pOH mirrors pH: \[ \mathrm{pOH} = -\log_{10}\!\left(a_{\mathrm{OH^-}}\right) \approx -\log_{10}\!\left([\mathrm{OH^-}]\right) \] At 25 °C, \(K_w \approx 1.0\times 10^{-14}\), so \[ \mathrm{pH} + \mathrm{pOH} = 14.00 \]
Representative values and quick conversions
| pH | Approx. \([\mathrm{H}^+]\) (M) | Acid–base character (water, 25 °C) |
|---|---|---|
| 1 | \(1.0\times 10^{-1}\) | Strongly acidic |
| 3 | \(1.0\times 10^{-3}\) | Acidic |
| 7 | \(1.0\times 10^{-7}\) | Neutral (approx.) |
| 11 | \(1.0\times 10^{-11}\) | Basic |
| 13 | \(1.0\times 10^{-13}\) | Strongly basic |
Visualization of the logarithmic pH scale
Common pitfalls
- pH is based on activity; concentrated solutions can deviate from \(\mathrm{pH} \approx -\log_{10}[\mathrm{H}^+]\).
- Neutral pH is not always exactly 7; temperature changes \(K_w\) and shifts the neutral point.
- Strong acids and bases at appreciable concentration require careful accounting for stoichiometry, dilution, and water autoionization only when the added acid/base is extremely dilute.
Summary
pH is defined as the negative base-10 logarithm of hydrogen ion activity and serves as a quantitative acidity scale. Its relationship to pOH and \(K_w\) connects acid–base chemistry to equilibrium in water, enabling consistent calculations of \([\mathrm{H}^+]\), \([\mathrm{OH^-}]\), and reaction direction in aqueous solutions.