What a buffer does
A buffer is a solution that resists changes in pH when small amounts of acid or base are added. It contains a weak acid (HA) and its conjugate base (A⁻) in comparable amounts: added H⁺ is taken up by A⁻, and added OH⁻ is neutralized by HA. Blood, cell culture media, enzyme assays, shampoos and swimming pools all rely on buffers.
The Henderson-Hasselbalch equation
- pH = pKa + log₁₀([A⁻] ÷ [HA])
- Ratio needed for a target pH = 10^(pH − pKa)
- Share in acid form = [HA] ÷ ([HA] + [A⁻])
The equation comes from rearranging the acid dissociation constant Ka = [H⁺][A⁻]/[HA] and taking logarithms.
Worked example
An acetate buffer contains 0.15 mol/L sodium acetate and 0.10 mol/L acetic acid; the pKa of acetic acid is 4.76.
- Ratio [A⁻]/[HA] = 0.15 ÷ 0.10 = 1.5.
- pH = 4.76 + log 1.5 = 4.76 + 0.176 = 4.94.
- 40% of the buffer is in the acid form.
- To reach pH 5.00 instead, you need a ratio of 10^0.24 = 1.74.
pH at other ratios (acetate, [HA] = 0.10 mol/L)
| [A⁻] (mol/L) | pH | Acid form |
|---|---|---|
| 0.01 | 3.76 | 90.9% |
| 0.05 | 4.46 | 66.7% |
| 0.10 | 4.76 | 50.0% |
| 0.20 | 5.06 | 33.3% |
| 1.00 | 5.76 | 9.1% |
Each tenfold change in the ratio shifts the pH by exactly one unit.
Common buffers
| Buffer | pKa (25 °C) | Useful pH range |
|---|---|---|
| Acetate | 4.76 | 3.8 to 5.8 |
| Bicarbonate | 6.35 | 5.4 to 7.4 |
| Phosphate (H₂PO₄⁻/HPO₄²⁻) | 7.21 | 6.2 to 8.2 |
| Tris | 8.07 | 7.1 to 9.1 |
| Ammonium | 9.25 | 8.3 to 10.3 |
Choose a buffer whose pKa is within one unit of the pH you want. Note that pKa values shift with temperature and ionic strength; Tris is especially sensitive, losing about 0.03 pH units per °C.
Blood pH
The bicarbonate buffer keeps blood at pH 7.35 to 7.45. In physiology, the equation is written pH = 6.1 + log([HCO₃⁻] ÷ (0.03 × PaCO₂)), with the pKa of 6.1 for dissolved CO₂ at body temperature and PaCO₂ in mmHg. With bicarbonate at 24 mmol/L and PaCO₂ at 40 mmHg, it gives pH 7.40.
Preparing a buffer
Mix the acid and its salt in the calculated ratio, or start from the acid and add a strong base until the pH meter reads the target. Higher total concentrations give more buffer capacity but more ionic strength.