Plasmid MapMake a buffer at a target pH
The Henderson–Hasselbalch equation links pH to the ratio of a buffer's two forms: pH = pKa + log([A⁻]/[HA]), where [A⁻] is the base form and [HA] the acid form. Choose a buffer, a target pH, the total concentration and the volume. The calculator returns the base : acid ratio and either the mass of each form to weigh, or the mass of one form and the volume of HCl or NaOH to titrate it with.
The pKa that belongs in the equation depends on temperature and on the ionic strength of the solution. The calculator starts from the thermodynamic values selected by NIST (Goldberg, Kishore and Lennen, 2002), moves them to your temperature, and corrects them for the buffer's own ions plus any salt you add. That is why its phosphate recipes differ from a ratio calculated with pKa 7.2.
Worked example: 100 mM sodium phosphate, pH 7.4
At 25 °C and zero ionic strength, the H₂PO₄⁻/HPO₄²⁻ pair has a pK of 7.198. A 100 mM phosphate buffer at pH 7.4 is itself a strong electrolyte: its ionic strength is about 260 mM, which lowers the working pKa to 6.80. The buffer therefore needs a base : acid ratio of 3.96, not the 1.59 that pKa 7.2 would suggest.
For 1 L that is 79.9 mM Na₂HPO₄ (11.34 g) and 20.1 mM NaH₂PO₄ (2.42 g). Both masses are for the anhydrous salts; edit a formula for a hydrate, such as NaH2PO4·H2O.
Worked example: 50 mM Tris-HCl, pH 8.0
Tris is usually made by dissolving Tris base and titrating it with HCl. For 1 L of 50 mM Tris at pH 8.0 and 25 °C, dissolve 6.06 g of Tris base in about 800 mL of water and add 29.0 mL of 1 M HCl before making up to volume. The chloride ions give an ionic strength of 29 mM, and the working pKa is 8.14.
Tris is sensitive to temperature: its pKa falls by about 0.028 per °C. The same solution reads about pH 8.64 at 4 °C and 7.68 at 37 °C. Set the temperature to the one at which you will use the buffer, and adjust the pH at that temperature.
Buffer range and capacity
A buffer resists pH change best near its pKa and loses most of its capacity more than one pH unit away; the calculator warns when the target is outside that range. The buffer list shows each pKa at 25 °C, so choose one within a unit of your target. Buffer capacity is reported in mM of strong acid or base per pH unit.
Assumptions
- Activities use the Davies equation, which is reliable up to an ionic strength of about 0.5 M. Enter added salt as ionic strength: 150 mM NaCl contributes 150 mM, and 50 mM MgCl₂ contributes 150 mM.
- Counter-ions are monovalent, such as Na⁺, K⁺ or Cl⁻.
- Acids with several steps use one step: phosphate, carbonate and glycine their second. Citrate, whose steps overlap, is not included.
- Masses use the formulas shown and CIAAW 2024 standard atomic weights, without purity or water-content corrections.
- Check the final pH with a calibrated meter at the temperature of use.
Sources: Goldberg RN, Kishore N, Lennen RM. Thermodynamic Quantities for the Ionization Reactions of Buffers. J. Phys. Chem. Ref. Data 31, 231–370 (2002). Davies CW. Ion Association. Butterworths, London (1962). For a reagent's molar mass or a stock solution, use the molar mass calculator and the molarity calculator.