Buffers & Henderson–Hasselbalch
How your blood holds its pH to within a whisker of 7.4 — and how to design a solution that does the same.
⏱️ About 20 min
Add a drop of strong acid to pure water and the pH lurches. Add the same drop to your bloodstream and… almost nothing happens. Blood is a buffer, and buffers are the quiet stabilisers that keep chemistry — and life — from swinging wildly.
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The big idea: A buffer is a weak acid and its conjugate base living together. The acid mops up added base; the base mops up added acid. The Henderson–Hasselbalch equation, pH = pKa + log([A⁻]/[HA]), tells you the pH from their ratio — and why buffers work best when that ratio is near 1.
A weak acid and its base, working as a team
A buffer contains meaningful amounts of both a weak acid (HA) and its conjugate base (A⁻) at the same time — for example acetic acid plus sodium acetate. Together they form a two-way sponge:
- Add acid (extra H⁺)? The base A⁻ soaks it up, becoming HA.
- Add base (extra OH⁻)? The acid HA neutralises it, becoming A⁻.
Either way the added H⁺ or OH⁻ is quietly converted, and the pH barely moves. The buffer trades one form for the other instead of letting free H⁺ or OH⁻ pile up.
\[ \ce{HA + OH- -> A- + H2O} \qquad \ce{A- + H+ -> HA} \]
The two neutralising reactions inside a buffer: HA absorbs added base; A⁻ absorbs added acid.
The Henderson–Hasselbalch equation
Start from the weak-acid equilibrium Ka = [H⁺][A⁻]/[HA], take −log of everything, and rearrange. You get a beautifully practical formula that reads a buffer's pH straight off the ratio of base to acid:
\[ \text{pH} = \text{p}K_a + \log\frac{[\ce{A-}]}{[\ce{HA}]} \]
Henderson–Hasselbalch. When [A⁻] = [HA], the log term is 0 and pH = pKa exactly.
🔑 pH sits near pKa
The log term only nudges the pH within about ±1 of pKa across the useful range. So the first thing that sets a buffer's pH is its pKa; the ratio [A⁻]/[HA] fine-tunes from there. Want a buffer at pH 4.7? Pick a weak acid with pKa near 4.7 (acetic acid, pKa 4.74, is the classic choice).
📝 Worked example: A buffer is made with equal concentrations of acetic acid and acetate (each 0.10 M). Acetic acid has pKa = 4.74. What is the pH?
- Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]).
- Equal concentrations means [A⁻]/[HA] = 0.10/0.10 = 1, and log(1) = 0.
- So pH = 4.74 + 0 = 4.74 — the pH equals the pKa.
✓ pH = 4.74 (equal to pKa when acid and base are equal).
✏️ Practice: An acetate buffer (pKa = 4.74) has [A⁻] = 0.20 M and [HA] = 0.10 M. What is the pH? (Round to two decimals.)
Solution
- pH = pKa + log([A⁻]/[HA]) = 4.74 + log(0.20/0.10).
- log(2.0) = 0.30.
- pH = 4.74 + 0.30 = 5.04. More base than acid, so pH sits above pKa.
✏️ Practice: Now the same buffer has [A⁻] = 0.10 M and [HA] = 0.20 M (more acid than base). What is the pH?
Solution
- pH = 4.74 + log(0.10/0.20) = 4.74 + log(0.50).
- log(0.50) = −0.30.
- pH = 4.74 − 0.30 = 4.44. More acid than base, so pH sits below pKa.
✨ Where buffers are strongest
A buffer resists change best when [A⁻] ≈ [HA], i.e. when pH ≈ pKa, because it has plenty of both partners to absorb whatever you throw at it. Push the ratio past roughly 10:1 (about one pH unit from pKa) and one partner runs low — the buffer's capacity fades and the pH starts to swing.
Check your understanding
1. What two things must a buffer contain?
A buffer needs a weak acid and its conjugate base together (e.g. acetic acid + acetate). The acid neutralises added base; the conjugate base neutralises added acid.
2. In the Henderson–Hasselbalch equation, when does pH exactly equal pKa?
When [A⁻] = [HA], the ratio is 1 and log(1) = 0, so pH = pKa. This is also where the buffer is most effective.
3. You need a buffer at pH 7.2. Which weak acid is the best starting point?
A buffer works best within about ±1 pH unit of its pKa, so choose a weak acid whose pKa is close to the target pH — here, pKa near 7.2.
✅ Key takeaways
- A buffer = a weak acid HA plus its conjugate base A⁻ in the same solution.
- HA absorbs added base; A⁻ absorbs added acid — so pH barely moves.
- Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]).
- When [A⁻] = [HA], pH = pKa — and the buffer is at its strongest.
- Buffer range is roughly pKa ± 1; choose a pKa near your target pH.
➡️ Buffers appear naturally partway through a titration — the slow, controlled process of adding base to acid drop by drop. Plotting pH against volume gives a titration curve, and it tells a rich story. That's next.
Want to test yourself on this?
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