Tris, HEPES and Phosphate Buffer pKa Temperature Shift Tool
Estimate a buffer pKa at the working temperature and the pH that a solution set at 25 °C reaches in the cold room or incubator. The workspace opens Tris set to pH 8.0 at 25 °C and read at 4 °C. This reference explains the Goldberg thermodynamic temperature correction and why Tris shifts so much more than phosphate.
Backed by the fifteen-buffer verification fixture computed from Goldberg et al. 2002 at 4 °C, 25 °C and 37 °C. Its worked example, which the workspace opens, is Tris set to pH 8.00 at 25 °C, estimated at pH 8.64 at 4 °C (a 0.638 shift). Reagent mass for a recipe is a separate Molarity calculation.
Match pKa and temperature enthalpy to your experimental assay
A biological buffer resists pH changes effectively only within roughly one pH unit of its acid dissociation constant at the actual working temperature of the experiment. Because amine-based buffers such as Tris and zwitterionic Good buffers such as HEPES have substantial ionization enthalpies, their effective buffering range moves as temperature changes from a 4 °C purification column to a 25 °C benchtop assay or a 37 °C cell culture incubator.
When an enzyme assay, thermal shift experiment or protein purification step is sensitive to protonation state, record both the nominal pH and the temperature at which the pH electrode was calibrated and read. Stating pH 8.0 without stating the measurement temperature leaves a 0.6-unit ambiguity for Tris solutions between the bench and the cold room.
Check hydrate state and free-acid vs hydrochloride salt forms
Buffer shelves commonly hold both Tris free base (MW 121.14 g/mol) and Tris hydrochloride (MW 157.60 g/mol), or multiple hydrates of sodium phosphate dibasic. Always verify the exact chemical formula printed on the reagent container before weighing, dissolve the solid in roughly eighty percent of the final water volume, adjust pH at a measured temperature, and bring the solution to final volume in a volumetric vessel.
Equations and variables
Buffer pKa temperature dependence (Goldberg relation)
pKa(T) = pKa(T0) + (ΔH° / (R ln 10)) × (1/T − 1/T0) + ΔCp° terms
- pKa(T), pKa(T0)
- Thermodynamic acid dissociation exponent at kelvin temperature T and reference T0 = 298.15 K
- ΔH°
- Standard molar enthalpy of ionization at 298.15 K (J mol⁻¹)
- ΔCp°
- Standard molar heat-capacity change of ionization (J mol⁻¹ K⁻¹)
- R
- Molar gas constant (J mol⁻¹ K⁻¹)
pH of a solution set at 25 °C and read at temperature T
pH(T) ≈ pH(25 °C) + [pKa(T) − pKa(25 °C)]
- pH(25 °C)
- pH to which the solution was adjusted at 25 °C
- pKa(T) − pKa(25 °C)
- Temperature shift of the buffer pKa from the Goldberg relation
- pH(T)
- Estimated pH at the working temperature, assuming the buffer ratio is unchanged
Scope and limitations
- Thermodynamic pKa values from Goldberg et al. 2002 describe infinite dilution (zero ionic strength); dissolved sodium chloride, potassium chloride and high buffer concentrations shift apparent operational pH.
- The calculator gives the pKa at temperature and an estimated pH; it does not compute reagent mass (use the Molarity calculator) or the volume of acid or base needed to titrate a mixture.
- Different hydrate forms of phosphate salts (such as anhydrous vs heptahydrate or dodecahydrate dibasic sodium phosphate) have vastly different molecular weights and cannot be substituted by equal mass.
Sources and provenance
- Calculator inputs and independent arithmetic verificationOriginal synthetic inputs; see individual fixture notices
- Independent Goldberg buffer temperature verification fixtureNumPy oracle reference at 4 °C, 25 °C and 37 °C
- Goldberg, Kishore and Lennen: thermodynamic quantities for the ionization reactions of buffersCited thermodynamic reference tables; NIST JPCRD 2002
Technical questions
Why does a Tris buffer adjusted to pH 8.0 at 25 °C read about pH 8.6 in a 4 °C cold room?
Protonated Tris has a large positive standard enthalpy of ionization (47.45 kJ/mol in Goldberg et al.), a temperature coefficient of about minus 0.028 pKa units per degree. The fixture gives pKa 8.072 at 25 °C and 8.710 at 4 °C, so cooling by twenty-one degrees raises the pKa by 0.638 and the estimated pH from 8.00 to 8.64.
How do I prepare a Tris buffer at the bench so that it has my target pH at 4 °C or 37 °C?
Instead of titrating the solution inside the cold room or incubator, use the temperature-pKa shift to find the equivalent room-temperature setpoint. For example, setting a Tris solution to a lower pH at 25 °C compensates for the upward pKa shift that occurs when the buffer is chilled to 4 °C.
Why do phosphate buffers shift much less with temperature than Tris or HEPES?
The second ionization of phosphoric acid has a small standard enthalpy of ionization (3.6 kJ/mol), so the fixture gives pKa2 7.279 at 4 °C and 7.183 at 37 °C, a change of about 0.1 units against 0.96 for Tris over the same span. However, phosphate buffers can precipitate divalent cations and inhibit certain phosphatases or kinases.
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