Buffers: Henderson–Hasselbalch
A buffer keeps the pH steady: cells, blood and almost every lab experiment depend on one. Find the pH of a buffer from its weak acid and its base form, or the ratio or pKa you need for a target pH. See how much acid or base it can take, and what happens to the pH when you add some.
How Does a Buffer Work?
A buffer is a mix of a weak acid HA and its base form A⁻. Add a strong acid and the A⁻ takes up the extra H⁺; add a strong base and the HA hands over H⁺ to neutralise it. Either way, only the ratio [A⁻]/[HA] shifts a little, and the pH barely moves. In pure water the same drop of acid would change the pH by several units.
The Henderson–Hasselbalch equation gives the pH from that ratio. When the two forms are equal, the pH equals the pKa: there the buffer is strongest. A buffer works well from about pKa − 1 to pKa + 1 (a ratio between 1:10 and 10:1), so choose a buffer whose pKa is close to the pH you need. A higher concentration gives a bigger buffer capacity: more acid or base is needed to shift the pH.
Acid and Base Form Against pH
pHWorked Techniques
Only the ratio counts, so you can use concentrations or amounts (mol), as long as both are in the same unit.
Turn the equation around to find how much of each form you need.
Each mole of H⁺ turns one mole of A⁻ into HA. Work in amounts (mmol), then use the new ratio. A strong base does the opposite.
Sources & Verification
- D. L. Nelson & M. M. Cox, Lehninger Principles of Biochemistry, 8th ed., W. H. Freeman, 2021 — Ch. 2 (Buffering against pH changes; the Henderson–Hasselbalch equation).
- N. E. Good et al., “Hydrogen Ion Buffers for Biological Research”, Biochemistry 5(2), 1966, pp. 467–477 — MES and HEPES pKa and their temperature dependence.
- D. D. Van Slyke, “On the measurement of buffer values”, J. Biol. Chem. 52, 1922, pp. 525–570 — buffer capacity β.
Frequently Asked Questions
What is the Henderson–Hasselbalch equation?
pH = pKa + log([A⁻]/[HA]): the pH of a buffer follows from the pKa of its weak acid and the ratio of the base form A⁻ to the acid form HA. When both are equal, log 1 = 0 and the pH equals the pKa. Every tenfold change in the ratio shifts the pH by one unit.
How do I calculate the pH of a buffer?
Example: a buffer with 60 mmol/L sodium acetate (the base form) and 40 mmol/L acetic acid (the acid form). The pKa of acetic acid is 4.76.
1. The ratio [A⁻]/[HA] = 60/40 = 1.5.
2. log 1.5 = 0.176.
3. pH = 4.76 + 0.176 = 4.94. Only the ratio matters, so you can also use amounts in mmol, as long as both are in the same unit.
How do I choose the right buffer for a pH?
Choose a buffer whose pKa lies within about one unit of the pH you need: a buffer works well from pKa − 1 to pKa + 1. Common choices (pKa at 25 °C): acetate 4.76, MES 6.10, phosphate 7.20, HEPES 7.48, Tris 8.06 and ammonium 9.25. For pH 7.4, phosphate and HEPES are good choices. The calculator warns when your pH falls outside the buffer range.
What happens when you add acid to a buffer?
The base form A⁻ takes up the extra H⁺ and turns into HA, so only the ratio shifts. Example: adding 1 mmol HCl to 100 mL of the acetate buffer above (6 mmol A⁻, 4 mmol HA) gives 5 mmol of each, and the pH drops only from 4.94 to 4.76. The same 1 mmol HCl in 100 mL of pure water would bring the pH from 7 down to 2. Once all the A⁻ is used up, the buffer stops working and the pH falls quickly.
What is buffer capacity?
How much strong acid or base it takes to change the pH by one unit, in mmol per litre per pH unit. It is largest when pH = pKa and grows with the total buffer concentration. A 100 mM acetate buffer has a capacity of about 57.6 mmol/L per pH unit at pH 4.76, and 55.3 at pH 4.94. The calculator gives it with every result.
When is the Henderson–Hasselbalch equation not accurate?
It is an approximation. It becomes inaccurate at very low buffer concentrations (below about 1 mmol/L), far outside the buffer range, and with very strong or very weak acids, where the water's own H⁺ and OH⁻ start to count. It also uses concentrations instead of activities, so high salt concentrations shift the real pH a little. In the lab, always check with a pH meter.