Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- Water is amphiprotic, so it ionises itself: 2 H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq).
- The equilibrium constant is K_w = [H₃O⁺][OH⁻]. Water is left out because it is the pure liquid solvent.
- At 25 °C, K_w = 1.0 × 10⁻¹⁴, so pure water has [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ M.
- K_w applies to every aqueous solution: raise one ion and the other falls.
- H⁺(aq) and H₃O⁺(aq) mean the same ion; H₃O⁺ is preferred.
- Neutral means [H₃O⁺] = [OH⁻]. Acidic: [H₃O⁺] > [OH⁻]. Basic: [OH⁻] > [H₃O⁺].
- K_w increases with temperature (autoionization is endothermic), so pure water above 25 °C has pH below 7 and is still neutral.
Key relationships
| Relationship | Use it to |
|---|---|
| pH = −log[H₃O⁺] | turn a concentration into pH |
| [H₃O⁺] = 10⁻ᵖᴴ | turn a pH back into a concentration |
| pOH = −log[OH⁻]; [OH⁻] = 10⁻ᵖᴼᴴ | the same for hydroxide |
| K_w = [H₃O⁺][OH⁻] | find one ion concentration from the other |
| pH + pOH = pK_w (= 14.00 at 25 °C) | move between pH and pOH |
| Pure water: pH = pOH = pK_w ÷ 2 | neutral pH at any temperature |
Assumptions behind the numbers
- K_w = 1.0 × 10⁻¹⁴ and pK_w = 14.00 hold only at 25 °C. Use the value given for any other temperature.
- Concentrations stand in for the “effective” concentrations in dilute solutions.
- Each change of 1 pH unit is a factor of 10 in [H₃O⁺].
Mistakes to avoid
- “Neutral = pH 7” at every temperature. Check the temperature first.
- Thinking acidic solutions have no OH⁻. Find it with K_w.
- Reading the scale backwards. Lower pH means higher [H₃O⁺].
- Treating pH as linear. A solution at pH 3 has 100 times the [H₃O⁺] of one at pH 5, not “a bit more”.
- Using ln instead of log.
- Significant figures. Decimal places in pH = significant figures in [H₃O⁺].
Quick self-check
- What is the pH of a solution with [H₃O⁺] = 1.0 × 10⁻³ M at 25 °C? (3.00)
- A solution has pH 9.00 at 25 °C. What is [OH⁻]? (1.0 × 10⁻⁵ M)
- pH = 4.25 at 25 °C. What is pOH? (9.75)
- Pure water is heated. Does its pH go up or down, and is it still neutral? (Down; yes, still neutral)
Next: practice questions.