Lab-Tacular

Buffer pH Calculator

Finds a buffer's pH, or the amounts to weigh out for a target pH.Choose whether you want the pH or the recipe.
pH equals pKa plus the base-ten logarithm of the conjugate base concentration divided by the weak acid concentration.pH=pKa+log10[A⁻][HA]

Given the concentrations of the acid and base forms, find the pH of the buffer.

The literature pKa of Phosphate (pKa2) (reported at 20–25 ℃ — see the references below). You can edit it.

How to use

  1. Choose a mode. Find the pH works out the pH from the concentrations of the acid and base forms; Find the recipe takes a target pH and works out how much of each form to use.
  2. Pick a buffer or enter a pKa of your own. Choosing from the list fills the pKa in.
  3. Find the pH — enter the concentrations of the base form and the acid form.
  4. Find the recipe — enter a target pH and a total concentration and you get the concentration of each form. Add a total volume and the molecular weights and you also get the mass (g) to weigh out. Leave them empty and only the concentrations are shown.

💡 Exponents can be entered with e — for example, 1.5×10⁻⁵ is entered as 1.5e-5.

Formula and practical notes

A buffer is a solution holding a weak acid and its conjugate base together. Acid coming in is taken up by the conjugate base and base coming in by the acid, so the pH does not move much.

Starting from the acid dissociation equilibrium and taking −log of both sides gives this:

Henderson-Hasselbalch
pH = pKa + log₁₀( [base form] ÷ [acid form] )

Two things can be read straight off it. When the two forms are at the same concentration the log term is zero, so pH = pKa. And what matters is the ratio, not the absolute concentration — dilute the whole thing two-fold and the pH stays (approximately) where it was.

Working out the recipe

The target pH fixes the ratio between the two forms.

Ratio
r = [base form] ÷ [acid form] = 10^(pH − pKa)

Splitting the total concentration by that ratio gives each one.

Base form
[base form] = total × r ÷ (1 + r)
Acid form
[acid form] = total × 1 ÷ (1 + r)

Multiply by volume and molecular weight and you have the mass to put on the balance.

Mass
mass(g) = concentration(mol/L) × volume(L) × MW(g/mol)

Practical notes

  • The pKa of Tris depends strongly on temperature. At roughly −0.028 / °C, a buffer titrated to pH 8.0 at 25℃ sits near 8.6 at 4℃. Set the pH at the temperature you will actually use it. The pKa values in this calculator are literature values reported between 20 and 25 ℃ — the references below say which value comes from where.
  • This calculation is an approximation. The Henderson-Hasselbalch equation ignores ionic strength and activity coefficients. At high concentrations, or with a lot of salt present, the real pH can differ from the calculated one. Always confirm with a pH meter and adjust.
  • Buffering capacity only holds near the pKa. Once the target pH is more than one unit from the pKa, one form makes up almost everything and there is little buffering left. Pick a different buffer in that case.
  • Where a system has several pKa values, as phosphate and citrate do, pick the one that matches your target pH. Phosphate has three — 2.15 / 7.20 / 12.35 — and 7.20 is the one used near neutral.
  • For a hydrate, use the molecular weight that includes the water of crystallisation. It changes the mass considerably.
  • Think about what the buffer does to the experiment too. Phosphate precipitates with calcium and magnesium and inhibits some enzymes. Tris reacts with aldehydes.

FAQs

References

Where the pKa list and the Tris temperature correction come from. The Henderson-Hasselbalch equation itself is a definition and is not cited.

  1. Good NE, Winget GD, Winter W, Connolly TN, Izawa S, Singh RMM. (1966) Hydrogen Ion Buffers for Biological Research. Biochemistry 5:467–477.doi:10.1021/bi00866a011The source of MES 6.15, PIPES 6.8 and HEPES 7.55. This paper reports apparent pKa measured at 20 ℃ in 0.1 M solutions.
  2. Goldberg RN, Kishore N, Lennen RM. (2002) Thermodynamic Quantities for the Ionization Reactions of Buffers. J Phys Chem Ref Data 31(2):231–370.doi:10.1063/1.1416902Acetate 4.76, Bis-Tris 6.5, Phosphate (pKa2) 7.2, MOPS 7.2 and Carbonate (pKa2) 10.33 round-match the 25 ℃ values in this review (4.756 · 6.484 · 7.198 · 7.184 · 10.329). The Tris coefficient of −0.028/℃ also follows from the ionization enthalpy it reports, 47.45 kJ/mol.

Tris 8.06, Tricine 8.05 and CHES 9.3 match neither document to the last digit — Goldberg 2002 gives 8.072, 8.135 and 9.394 at 25 ℃, and Good 1966 gives Tricine 8.15 at 20 ℃. No primary source for these three values was obtained.

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