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How to Calculate Buffer pH With Henderson-Hasselbalch
Heshan Fernando
Co-founder & COO
You need a buffer at pH 4.9 and you have acetic acid with a pKa of 4.76. What ratio of acid to conjugate base gets you there, and does it matter whether you make it at 0.1 M or 0.01 M?
The Henderson-Hasselbalch equation answers both, and the second answer is the more interesting one.
The equation
pH = pKa + log₁₀([A⁻] ÷ [HA])
Where [A⁻] is the conjugate base concentration and [HA] is the weak acid concentration.
With a pKa of 4.76, 0.10 M acid and 0.15 M conjugate base:
4.76 + log₁₀(0.15 ÷ 0.10) = 4.76 + 0.176 = 4.94
Notice what’s in the equation: a ratio. Not the absolute concentrations — just how they relate to each other.
Why dilution doesn’t change buffer pH
Halve both concentrations and the ratio is unchanged, so the pH is unchanged. Dilute a buffer tenfold and its pH stays essentially the same — which is genuinely surprising the first time you meet it, and it’s the defining property of a buffer.
What does change is capacity. A dilute buffer holds its pH just as well against nothing and much worse against an actual addition of acid or base, because there’s less of the conjugate pair to absorb it. Concentration sets capacity; ratio sets pH.
This is also why buffer pH is stable against small additions. Add a little acid and some A⁻ converts to HA. The ratio shifts slightly, and because pH depends on the logarithm of the ratio, the pH barely moves. That’s the whole mechanism.
Choosing a pKa
A buffer works over roughly one pH unit either side of its pKa. At the pKa itself the ratio is 1:1 and capacity is maximal in both directions. Move a unit away and the ratio is 10:1 — still workable but lopsided. Two units away and it’s 100:1, and a small addition swings the pH sharply.
So pick a buffer system whose pKa is close to your target pH. Trying to buffer at pH 7.4 with an acetate system (pKa 4.76) doesn’t work, however you set the ratio.
| Target pH − pKa | Ratio [A⁻]/[HA] | Capacity |
|---|---|---|
| 0 | 1:1 | Maximal both ways |
| +1 | 10:1 | Poor against base |
| −1 | 1:10 | Poor against acid |
| ±2 | 100:1 | Effectively not buffering |
Why people get stuck here
- Concentration confused with pH. Concentration sets capacity, not pH.
- pKa mismatched to target. No ratio rescues a buffer chosen two units away.
- Ideal behaviour assumed. The equation ignores ionic strength and activity coefficients, and at higher concentrations the deviation is measurable.
- Temperature. pKa values are temperature-dependent, and some systems — Tris notably — shift substantially between room temperature and 37°C.
Common mistakes to avoid
- Preparing a buffer by calculation alone for work that needs accuracy, instead of adjusting with a meter.
- Ignoring the temperature dependence of pKa when the buffer will be used at a different temperature from where it was made.
- Using a buffer too far from its pKa and being surprised when the pH drifts.
- Diluting a working buffer and expecting the same capacity.
- Forgetting that adding a strong acid or base changes both concentrations, not just one.
How to do it with Buffer pH Calculator
The Buffer pH Calculator applies the equation and can solve for the ratio a target pH needs.
- Enter the pKa of your acid system.
- Add the molar concentrations of acid and conjugate base.
- Check the result sits within about one unit of the pKa.
- For accurate work, use the calculation as a starting point and adjust with a pH meter.
The IUPAC guidance on buffer solutions covers the standards used in metrology. Other chemistry tools are in the tools directory.
Frequently asked questions
Why does dilution not change buffer pH?
Because the equation depends on the ratio of base to acid, and dilution changes both equally. Capacity falls, but pH holds — until the buffer becomes dilute enough that activity effects and water’s own equilibrium matter.
How far from the pKa can a buffer work?
About one pH unit either side. Beyond that the ratio becomes extreme and a small addition of acid or base swings the pH sharply.
Is this accurate for real solutions?
It assumes ideal behaviour and ignores ionic strength and activity coefficients. For precise work at higher concentrations, measure with a meter rather than trusting the calculation.
Final thought
Ratio sets the pH, concentration sets the capacity, and the pKa decides whether the buffer can do the job at all. Choose the system first and the ratio second.