The Van Slyke equation
Buffer capacity β is how many moles of acid or base you must add to one litre to shift the pH by one unit. The Van Slyke formula gives it directly from the buffer concentration and where the pH sits relative to pKa.
C is total buffer concentration in mol/L. A full treatment adds a water term, 2.303 ([H+] + [OH−]), which is negligible except in very dilute or very acidic/basic solutions.
Capacity peaks at pH = pKa
- Maximum. At pH = pKa the buffer term simplifies to βmax ≈ 0.576 · C. A 0.1 M buffer tops out near 0.058 mol/(L·pH).
- Scales with concentration. Double C and you double the capacity. A 1.0 M buffer is ten times stronger than a 0.1 M one at the same pH.
- Falls off fast. One pH unit either side of pKa, capacity is already down to about 25 percent of the peak.
- The ratio at the peak. [A−]/[HA] = 1, equal parts acid and conjugate base.
Common buffers and their working range
| Buffer | pKa | Useful pH range | Typical use |
|---|---|---|---|
| Acetate | 4.76 | 3.6 – 5.6 | Mildly acidic |
| MES | 6.15 | 5.5 – 6.7 | Plant biology |
| Phosphate | 6.86 | 6.4 – 7.4 | Physiological |
| Tris | 8.06 | 7.0 – 9.0 | Molecular biology |
pKa and Kw both shift with temperature, so capacity is temperature-specific — compute it at your working temperature, not 25 °C by default.
Common questions
Why is buffer capacity highest when pH equals pKa?
At pH = pKa the acid and its conjugate base are present in equal amounts, so the buffer holds the largest reserve of both. It can soak up added acid or added base equally well, which is where the Van Slyke term peaks.
What is the usable pH range of a buffer?
Roughly pKa plus or minus 1. At the edges of that band the capacity has already fallen to about a quarter of its maximum, and beyond it the buffer resists change poorly.
How do I pick a buffer for a target pH?
Choose one whose pKa is within 1 unit of your target pH, and as close to it as you can get. For pH near 7 use phosphate (pKa 6.86); for mildly acidic work use acetate (pKa 4.76).
