Buffer pH at run temperature

A buffer’s pKa changes with temperature, and the pH follows it. Tris made up to pH 8.0 on a 25 °C bench is close to pH 8.6 in a 4 °C cold room. Phosphate and acetate barely move. The difference comes from how much heat the buffer’s ionization takes up, which is measured and tabulated for common buffers.

The estimate

The ratio of acid to base form is fixed when you make the buffer. If activity coefficients do not change, the Henderson–Hasselbalch relation keeps pH − pKa constant, so the pH moves by as much as the pKa:

pH(T₂) ≈ pH(T₁) + (dpKa/dT) · (T₂ − T₁)

The coefficient comes from the standard enthalpy of ionization ΔrH° through the van ’t Hoff equation: dpKa/dT = −ΔrH° / (R T² ln 10), with T = 298.15 K and R = 8.31451 J K⁻¹ mol⁻¹. A buffer that takes up a lot of heat when it ionizes, such as Tris (47.45 kJ/mol), loses about 0.028 pKa units per °C of warming. The critical compilation we use tabulates ΔrH°, not dpKa/dT, so the coefficients below are our arithmetic from its values.

Worked example. Tris: dpKa/dT = −47 450 / (8.31451 × 298.15² × 2.3026) = −0.0279 per °C. From 25 °C to 4 °C, T₂ − T₁ = −21 °C, so the pH rises by 21 × 0.0279 = 0.59: pH 8.0 becomes about 8.59.

Coefficients and where they come from

All pKa, ΔrH° and ΔrCp° values are the selected values of Goldberg, Kishore and Lennen (2002) at 25 °C and zero ionic strength, from their summary table and the buffer tables listed. The ± follows from their uncertainty code for ΔrH° (A ±0.2, B ±0.5 kJ/mol).

• Citrate is listed with its first pKa, 3.13, the one the Cytiva™ IEX handbook pairs with citric acid buffers at pH 2.6–3.6 for cation exchange. Citrate buffers near pH 4.8 or 6.4 work on its second and third ionizations (pKa 4.761 and 6.396; ΔrH° 2.23 and −3.38 kJ/mol in the same source), so this row does not apply there. The calculator warns when the pH is more than 1 unit from the listed pKa.
• Phosphate is its second ionization, the one used near neutral pH. Glycine is its amine, the one used near pH 10.
• Other tables differ. The Cytiva IEX handbook’s buffer appendix, which cites the CRC Handbook, lists −0.0110 per °C for MES and −0.0140 for HEPES, against −0.0087 and −0.0120 here. We use the critically evaluated enthalpies and show the arithmetic so you can compare.

How good is a straight line?

Bates and Hetzer measured the pKa of Tris from 0 to 50 °C with cells without liquid junction. Goldberg et al. tabulate their values: 8.850 at 0 °C, 8.677 at 5 °C, 8.075 at 25 °C and 7.677 at 40 °C. Against these, the straight line from 25 °C under-reads the cold shift slightly: at 4 °C it predicts a rise of 0.59, where the measured pKa rises by about 0.64. Over 0–40 °C the gap stays below 0.08 pH units for Tris.

The calculator’s second estimate uses Goldberg’s full temperature model (their eq. 12), which adds the heat capacity change ΔrCp°. For Tris it reproduces the Bates and Hetzer values within 0.006 over 0–40 °C (our check, in the test suite). For all ten buffers, the straight line and the curved model agree within 0.08 over 0–40 °C. That is the basis for the 0–40 °C range we state. Outside it, the calculator warns.

Assumptions

• Near its pKa. The buffer is used within about 1 pH unit of its pKa, so the pH tracks one ionization.
• 0–40 °C. The coefficient is the slope at 25 °C, checked as above over 0–40 °C.
• Ionic strength and concentration are ignored. The tabulated pKa values are for zero ionic strength. In Goldberg’s activity model, the ionic-strength correction is zero when the reaction has the same charges on both sides, as for Tris, Bis-Tris and imidazole (HL⁺ ⇌ H⁺ + L). It is not zero for the sulfonate buffers, glycine, acetate, citrate and phosphate, whose pKa in a real buffer differs from the table. By our reading of that model, phosphate, with a doubly charged base, is the most sensitive. This tool makes no ionic-strength correction.
• Calibrate the pH meter at the temperature you measure at. Automatic temperature compensation corrects the electrode’s response, not the sample: a meter does not convert a sample’s pH to another temperature. Calibration buffers and sample should be at the same temperature, and the temperature should be recorded with the pH. To know the pH in the cold room, measure it there, or use this estimate.
• The protein changes too. The groups that set a protein’s charge also ionize with heat uptake. Goldberg et al. list ΔrH° = 29.5 kJ/mol for the H₂L⁺ ⇌ H⁺ + HL ionization of free histidine (pKa 6.07), about −0.017 per °C by the same arithmetic. From this we infer that a protein’s pI and net charge also move with temperature, by an amount that depends on the protein. This tool does not model that.

Why it matters in ion exchange

In ion exchange chromatography, binding depends on the protein’s net surface charge, which changes with pH, and the Cytiva IEX handbook notes that proteins often begin to dissociate about 0.5 pH units from their pI at around 100 mM ionic strength. A Tris buffer that moves by 0.6 pH units between bench and cold room can therefore change whether, and how strongly, a protein binds. Make the buffer at the temperature you will run at, or correct for the shift.

Sources and scope

• Goldberg, Kishore and Lennen (2002), Thermodynamic quantities for the ionization reactions of buffers, Journal of Physical and Chemical Reference Data 31, 231–370. Critical compilation from NIST. Source of every pKa, ΔrH°, ΔrCp° and evaluation code above (Section 8 and Tables 7.2, 7.13, 7.22, 7.31, 7.36, 7.41, 7.44, 7.48, 7.51 and 7.68), of the van ’t Hoff relation (eq. 11), the temperature model (eq. 12), the uncertainty codes and the activity model with its zero correction for charge-symmetric reactions. Read in full (copy hosted by NIST).
• Bates and Hetzer (1961), Dissociation constant of the protonated acid form of Tris and related thermodynamic quantities from 0 to 50°, Journal of Physical Chemistry 65, 667–671. Primary measurement of Tris pKa against temperature. Values quoted here as tabulated in Goldberg et al., Table 7.68; the original was not read.
• Cytiva™, Ion Exchange Chromatography: Principles and Methods (handbook; read 2026-11-07). Net surface charge depends on pH; proteins often begin to dissociate about 0.5 pH units from their pI at an ionic strength around 100 mM; select buffers with a suitable pKa for the working temperature and prepare them at the temperature of use; Appendix 2 lists citric acid (pKa 3.13) for pH 2.6–3.6 and the coefficients compared above.
• HORIBA, Automatic temperature compensation in pH measurement (technical tip, 2018; read 2026-11-07). Temperature compensation corrects the electrode slope, not the sample’s pH; calibrate with buffers at the sample temperature and record the temperature with the pH.
• Good et al. (1966), Hydrogen ion buffers for biological research, Biochemistry 5, 467–477. Cited by Goldberg et al. as the origin of the “Good” buffers. Cited for history only; not read, and no value on this page is taken from it.

The coefficients, the worked example and the comparison with the curved model are our arithmetic from the sources above. The page text is original. Nothing you enter is saved or sent.