Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- A weak acid HA reacts with water to make H₃O⁺, but only a small percentage of molecules ionize. [H₃O⁺] is much less than the starting concentration c.
- In a weak acid solution: [HA] ≫ [H₃O⁺] ≈ [A⁻] ≫ [OH⁻].
- A weak base B reacts with water to make OH⁻ and HB⁺, again only slightly. [OH⁻] is much less than c.
- K_a and K_b are equilibrium constants. They change only with temperature, not with dilution.
- Percent ionization rises on dilution, even though [H₃O⁺] (or [OH⁻]) falls.
Key relationships
| Relationship | Use it to |
|---|---|
| K_a = [H₃O⁺][A⁻] / [HA]; pK_a = −log K_a | describe a weak acid; smaller K_a (larger pK_a) = weaker acid |
| K_b = [OH⁻][HB⁺] / [B]; pK_b = −log K_b | describe a weak base |
| x ≈ √(K × c) | find [H₃O⁺] (acid) or [OH⁻] (base) when x < 5% of c |
| % ionization = (x ÷ c) × 100% | from K and c, or from c and a measured pH |
| K_a = x² / (c − x) with x = 10^(−pH) | find K_a from a measured pH |
| K_a × K_b = K_w; pK_a + pK_b = 14.00 (25 °C) | switch between a conjugate acid and base |
Assumptions
- The temperature is 25 °C, so K_w = 1.0 × 10⁻¹⁴.
- The acid is monoprotic: one H₃O⁺ per molecule.
- Water’s own H₃O⁺ (or OH⁻) is negligible next to what the acid (or base) makes.
- c − x ≈ c only when x is under about 5% of c. Otherwise solve the quadratic.
Mistakes to avoid
- Treating a weak acid as strong. pH ≠ −log c.
- Forgetting to convert pOH. A weak base calculation gives [OH⁻] first.
- Mixing up pK_a direction. Larger pK_a = weaker acid.
- Skipping the 5% check.
- Using K_a in a K_b problem. Convert with K_b = K_w ÷ K_a.
- Thinking dilution lowers percent ionization. It raises it.
Quick self-check
- Find the pH of 0.20 M of an acid with K_a = 5.0 × 10⁻⁶. (x = 1.0 × 10⁻³ M; pH 3.00; 0.50% ionized)
- An acid has pK_a 4.00. What are pK_b and K_b of its conjugate base? (pK_b 10.00; K_b = 1.0 × 10⁻¹⁰)
- Find the pH of 0.10 M of a base with K_b = 1.0 × 10⁻⁵. ([OH⁻] = 1.0 × 10⁻³ M; pOH 3.00; pH 11.00)
Next: practice questions.