pH and pOH

Overview

pH and pOH compress very large ranges of ion concentration into manageable numbers. For dilute aqueous solutions, pH describes hydrogen-ion concentration and pOH describes hydroxide-ion concentration. Always state the temperature when using a pH–pOH sum because K_w changes with temperature.

Core equations

$\mathrm{pH}=-\log[\mathrm{H_3O^+}] \qquad \mathrm{pOH}=-\log[\mathrm{OH^-}]$

At any stated temperature, pH + pOH = pK_w. At 25 °C, pK_w ≈ 14.00. The inverse relationships are [H₃O⁺] = 10^−pH and [OH⁻] = 10^−pOH.

Worked example

For [H₃O⁺] = 3.2 × 10⁻⁵ M, pH = −log(3.2 × 10⁻⁵) = 4.49. At 25 °C, pOH = 14.00 − 4.49 = 9.51.

Common mistakes

• Forgetting the negative sign in the logarithm.
• Treating a one-unit pH change as a one-unit concentration change; it is a tenfold change.
• Using pH + pOH = 14.00 without the 25 °C assumption.
• Entering a concentration with units other than mol/L without converting first.

Practice

1. Find the pH of 1.0 × 10⁻³ M H₃O⁺. Answer: 3.00.
2. Find [OH⁻] when pOH = 2.50. Answer: 3.16 × 10⁻³ M.

Use the pH and pOH calculator to check your work.