Choosing and weighing a buffer that must hold pH at 37 °C, not on the bench
A teaching laboratory must prepare 500 mL of a 0.10 M buffer at pH 7.20 for an enzyme kinetics assay. The enzyme keeps full activity only between pH 6.90 and 7.50, and the assay is later scaled up and run at 37 °C, not at the 25 °C at which the buffer is made up. The store holds HEPES free acid (pKa 7.55 at 25 °C, molar mass 238.3 g/mol), HEPES sodium salt (molar mass 260.3 g/mol), MES (pKa 6.15), Tris (pKa 8.06), acetic acid (pKa 4.76), and stock 1 M NaOH and HCl. The technician proposes Tris because it is the standard biological buffer and plans to titrate to pH 7.20 with HCl. The supervisor objects that Tris drifts with temperature and asks for a defensible choice, the masses to weigh out, and a check that the buffer will still hold pH when the assay runs hot.
1. Select the buffer with a quantitative justification, then compute the conjugate base to acid ratio and the masses to weigh for 500 mL of 0.10 M solution.
Read the worked answer
Choice. Buffer capacity peaks at pH = pKa and falls roughly tenfold per pH unit away, so pick the acid whose pKa is nearest 7.20. Distances: HEPES 7.55 → 0.35; Tris 8.06 → 0.86; MES 6.15 → 1.05; acetate 4.76 → 2.44. Choose HEPES.
Ratio. pH = pKa + log([A⁻]/[HA]): 7.20 = 7.55 + log r → log r = −0.35 → r = 0.447.
Moles. Total = 0.10 mol/L × 0.500 L = 0.0500 mol. With HA + A⁻ = 0.0500 and A⁻ = 0.447 HA: HA = 0.0500 / 1.447 = 0.0346 mol; A⁻ = 0.0154 mol.
Masses. HEPES free acid = 0.0346 × 238.3 = 8.24 g; HEPES sodium salt = 0.0154 × 260.3 = 4.02 g.
Procedure note. Dissolve both solids in about 400 mL of water, confirm with a calibrated electrode, then make up to 500 mL. Do not add NaOH on top of the sodium salt - the salt already supplies the conjugate base, and adding both would push the ratio above 0.447 and the pH above 7.20.
2. The assay is run at 37 °C. Using a HEPES pKa temperature coefficient of about −0.014 per °C, what pH will the batch actually have, and is it acceptable?
Read the worked answer
The composition is fixed by the weighing, so only the pKa moves:
pKa(37) = 7.55 − 0.014(37 − 25) = 7.55 − 0.168 = 7.38. pH(37) = pKa + log r = 7.38 + log(0.447) = 7.38 − 0.35 = 7.03.
Verdict. 7.03 lies inside the 6.90–7.50 activity window, so the batch is usable. But it sits 0.17 units below the nominal 7.20 and consumes more than half of the tolerance below the set point, which is poor practice for an assay that will be scaled up.
If pH 7.20 is required at 37 °C, weigh for the hot pKa instead: log r = 7.20 − 7.38 = −0.18 → r = 0.66; HA = 0.0500/1.66 = 0.0302 mol (7.19 g), A⁻ = 0.0198 mol (5.16 g). The same solution then reads 7.37 at 25 °C, still acceptable at make-up, so the buffer satisfies both temperatures.
General point. pH is defined at the temperature of measurement; a buffer certified on a 25 °C bench is not automatically correct in a 37 °C block.
3. Quantify how badly the technician's Tris proposal would fail, and state the final recommendation.
Read the worked answer
Tris pKa is 8.06 at 25 °C with a coefficient near −0.028 per °C.
At 25 °C the titration would appear to work: log r = 7.20 − 8.06 = −0.86 → r = 0.138, so only 12% of the Tris is in the basic form. The pH is right on paper, but capacity is poor that far from pKa and the value is hypersensitive to small acid errors.
At 37 °C it collapses: pKa = 8.06 − 0.028(12) = 7.72, so pH = 7.72 + log(0.138) = 7.72 − 0.86 = 6.86. That is below the 6.90 floor, so the enzyme assay fails on the day it is scaled up although the buffer was correct on the bench.
Why titration does not rescue it. Titrating with HCl fixes the composition once and for all; it cannot compensate for a pKa that shifts with temperature. The error would surface only when the plate is read.
Recommendation. Reject Tris. Use HEPES at r = 0.447 and accept pH 7.03 at 37 °C, or re-weigh at r = 0.66 if the hot pH must be exactly 7.20. Finally, note that dilution during make-up changes capacity but not the ratio, so a few mL of volume error is not the risk here - temperature is.