Henderson–Hasselbalch calculator
Buffer pH from the pKa and the base to acid ratio, and the ratio for a target pH.
Buffer pH from the pKa and the base to acid ratio, and the ratio for a target pH.
[A⁻] is the conjugate base, the deprotonated form, and [HA] the acid, the protonated form. Only their ratio matters for the pH; the total concentration sets how much acid or base the buffer can absorb before the pH moves, not where the pH sits. When the two forms are equal the logarithm is zero and the pH equals the pKa, which is the centre of the buffer's working range.
Turned around, that is the recipe: pick the pH you want, look up the pKa and the ratio falls out. A pH one unit above the pKa needs ten parts base to one part acid; one unit below needs one to ten.
Tris has a pKa of 8.06 at 25 °C. Mixing 60 mM of the free base with40 mM of the protonated form gives pH = 8.06 + log₁₀(60 ÷ 40) = 8.06 + 0.176 = 8.24. Warm the same solution to 37 °C and the pKa falls by 0.028 × 12 = 0.336 to 7.724, so the pH becomes 7.90: the buffer has moved a third of a unit without anything being added to it.
The other direction: to hit pH 8.00 with Tris, the ratio must be 10^(8.00 − 8.06) = 0.871, which is 46.6 % of the buffer as the free base. For 500 mL of a 50 mM buffer that is 25 mmol in total, 11.64 mmol as the base and13.36 mmol as the acid.
| Buffer | pKa (25 °C) | ΔpKa per °C | Useful range |
|---|---|---|---|
| Acetate | 4.76 | 0.000 | 3.8–5.8 |
| MES | 6.15 | −0.011 | 5.2–7.2 |
| Bis-Tris | 6.46 | −0.017 | 5.5–7.5 |
| PIPES | 6.76 | −0.009 | 5.8–7.8 |
| MOPS | 7.20 | −0.015 | 6.2–8.2 |
| Phosphate pK2 | 7.20 | −0.003 | 6.2–8.2 |
| HEPES | 7.48 | −0.014 | 6.5–8.5 |
| Tris | 8.06 | −0.028 | 7.1–9.1 |
| Bicine | 8.26 | −0.018 | 7.3–9.3 |
| CHES | 9.30 | −0.029 | 8.3–10.3 |
| CAPS | 10.40 | −0.032 | 9.4–11.4 |
The temperature coefficient is the reason two labs following the same recipe can end up a quarter of a unit apart: one titrated warm, the other cold. Phosphate is nearly flat, which is why it is the buffer of choice when a solution is autoclaved or moved between a cold room and an incubator. Tris is the worst of the common ones. The calculator applies the coefficient of the buffer you pick, not one blanket figure.
β is how many moles of strong acid or base one litre absorbs per unit of pH change. It is largest when the two forms are equal, which is at the pKa, and it falls off quickly on either side: at one pH unit away it is down to about a third of the maximum, at two units to a thirtieth. That is the whole reason to choose a buffer whose pKa is close to the pH you want. Capacity is shown under Details for the composition you enter.
It links the pH of a buffer to the pKa of the weak acid in it and the ratio of the conjugate base to the acid. Given the ratio it gives the pH; given a target pH it gives the ratio you have to mix. It is the equation behind every buffer recipe, and it is also how you tell in advance whether a buffer will hold the pH you need.
Because its pKa falls by about 0.028 units for every degree Celsius. A Tris buffer titrated to pH 8.0 on the bench at 25 degrees is close to pH 7.7 in a 37 degree incubator and about pH 8.5 in a cold room at 4 degrees. Titrate Tris at the temperature it will be used at, or pick HEPES, which moves less than half as much, or phosphate, which barely moves at all.
About one pH unit either side. At pKa plus or minus 1 the mixture is ten parts to one, nine tenths of the capacity is gone, and a small addition of acid or base moves the pH a long way. The calculator warns you when the target pH is more than a unit from the pKa; the answer is to choose a different buffer rather than to push this one.
No, and neither do the tabulated pKa values, which are thermodynamic values at zero ionic strength or at a stated one. At the 50 to 200 mM concentrations used in the lab the real pH can sit a tenth of a unit or so from the calculated one, and more for a buffer whose acid and base forms differ in charge, such as phosphate. Use the calculation to get close, then check with a meter and titrate.
Enter the total buffer concentration and the volume under the result and it gives the millimoles of each form. Multiply by the formula weight on the bottle for grams. In practice most people weigh out the whole amount as one form and titrate to the target pH with HCl or NaOH, which is the same thing done with a meter watching.