Buffer calculator (Henderson–Hasselbalch)

Choose a buffer, a target pH, the total concentration and the volume. The tool gives the mass of the acid form and of the conjugate base form to weigh, and an alternative recipe by titrating one form with NaOH or HCl.

pH = pKa + log₁₀([A⁻] ÷ [HA]) [A⁻] ÷ [HA] = 10^(pH − pKa)

With a total concentration C = [HA] + [A⁻], the acid form is C ÷ (1 + r) and the base form C × r ÷ (1 + r), where r is the ratio. Masses use molar masses computed from the formulas with CIAAW 2024 atomic weights, so a hydrate such as Na2HPO4·7H2O is handled by typing it.

Temperature

pKa changes with temperature according to the van ’t Hoff equation. With the standard ionisation enthalpy ΔH°, the tool uses pKa(T) = pKa(25 °C) + ΔH° ÷ (R ln 10) × (1/T − 1/298.15 K). Tris (ΔH° = 47.45 kJ/mol) loses about 0.028 pH units per kelvin, so a Tris buffer made at room temperature reads lower at 37 °C; phosphate and acetate hardly change.

Limits

The Henderson–Hasselbalch equation uses concentrations in place of activities and ignores water’s own ions, so it is best between pH 3 and 11 and within one unit of the pKa. Tabulated pKa values are for zero ionic strength: at working concentrations the apparent pKa is usually a little lower (by several tenths for phosphate), so always check the final pH with a calibrated meter and adjust.

Worked example

500 mL of 50 mM Tris at pH 8.00 and 25 °C: r = 10^(8.00 − 8.072) = 0.847, so 13.5 mmol Tris·HCl (2.13 g) and 11.5 mmol Tris base (1.39 g). Set the temperature to 37 °C and the pKa falls to 7.75, so pH 8.00 at 37 °C needs a ratio of 1.78 instead.

References

• Goldberg, Kishore and Lennen, Thermodynamic quantities for the ionization reactions of buffers, J. Phys. Chem. Ref. Data 31, 231–370 (2002)
• Po and Senozan, The Henderson–Hasselbalch equation: its history and limitations, J. Chem. Educ. 78, 1499 (2001)
• CIAAW, Abridged standard atomic weights (2024 table, five significant figures)