Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- A buffer contains a weak acid HA and its conjugate base A⁻, both in large amounts.
- Its pH is set by the pKa of the acid and the ratio [A⁻]/[HA].
- The equation is the K_a expression in log form. You do not need to derive it.
- In a buffer, the equilibrium amounts are almost exactly the amounts mixed, so no ICE table is needed.
- Adding a little strong acid or base changes the ratio only slightly, so the pH changes only slightly. You must explain this in words; calculating the new pH is not assessed.
Key relationships
| Relationship | Meaning | Use it to |
|---|---|---|
| pH = pKa + log([A⁻]/[HA]) | buffer pH from the pair | find the pH of a buffer |
| [A⁻]/[HA] = 10^(pH − pKa) | rearranged form | find the ratio needed for a target pH |
| n_A⁻ / n_HA = [A⁻]/[HA] | volume cancels | work in moles after mixing solutions |
| pKa(BH⁺) = 14.00 − pKb(B) | 25 °C | handle weak-base buffers such as NH₃/NH₄⁺ |
| Ratio [A⁻]/[HA] | 0.10 | 1 | 10 |
|---|---|---|---|
| pH | pKa − 1 | pKa | pKa + 1 |
Assumptions behind the numbers
- Both components are present in large amounts compared with the H₃O⁺ from ionisation.
- The salt that supplies A⁻ is fully dissociated.
- Temperature is 25 °C (pKa values and K_w depend on temperature).
- A useful buffer keeps the ratio between about 0.1 and 10, so pH ≈ pKa ± 1.
Mistakes to avoid
- Ratio upside down. Base on top. More base → pH above pKa.
- pKb instead of pKa. For NH₃/NH₄⁺ use 9.25, not 4.75.
- Pre-mixing molarities. After mixing different volumes, use moles.
- Wrong pair for the target. Choose the pKa closest to the pH you want.
- “Dilution changes buffer pH.” The ratio is unchanged, so the pH is unchanged.
- Using the equation on a weak acid alone. With no A⁻ added, use the weak-acid method.
Quick self-check
- An ammonia buffer has [NH₃] = [NH₄⁺]. What is its pH? (9.25)
- An acetate buffer has [CH₃COO⁻]/[CH₃COOH] = 10. pKa 4.76. pH? (5.76)
- What ratio [HPO₄²⁻]/[H₂PO₄⁻] gives pH 6.90? pKa 7.20. (0.50)
Next: practice questions.