How Buffer Capacity Is Calculated
Buffer capacity (beta, also written as beta) quantifies how effectively a buffer resists pH changes. It was first defined by Van Slyke (1922) as the ratio of the small amount of strong base (or acid) added to the resulting pH change:
beta = dB / dpH
For a simple weak acid (HA) / conjugate base (A-) buffer, the Van Slyke equation gives:
beta = 2.303 x C x (Ka x [H+]) / (Ka + [H+])^2
Where C is the total molar concentration of the buffer (C = [HA] + [A-]), Ka is the acid dissociation constant (Ka = 10^(-pKa)), and [H+] is the hydrogen ion concentration (= 10^(-pH)).
Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation relates solution pH, pKa, and the ratio of conjugate base to weak acid:
pH = pKa + log([A-] / [HA])
Rearranged: [A-] / [HA] = 10^(pH - pKa). The individual concentrations are:
- [A-] = C x 10^(pH - pKa) / (1 + 10^(pH - pKa))
- [HA] = C / (1 + 10^(pH - pKa))
Maximum Buffer Capacity
Buffer capacity is greatest when pH = pKa, meaning [A-] = [HA] (equal concentrations of acid and conjugate base). At this point the Van Slyke equation simplifies to:
beta_max = 2.303 x C / 4 = 0.5756 x C
For example, a 0.1 mol/L acetate buffer at pH 4.76 (its pKa) has a maximum beta of approximately 0.0576 mol/L per pH unit. Moving the pH one unit away from the pKa reduces beta to about 23% of its maximum value.
Effective Buffer Range
A buffer is considered effective within the range of pKa plus or minus 1 pH unit. Within this range, both acid and base components are present in concentrations above about 9% of the total, providing meaningful resistance to pH change in both directions. Common laboratory buffers are chosen so that the desired working pH falls within this range.
Worked Example (Default Values)
Using a 0.1 mol/L acetic acid / acetate buffer at pH 4.76 (the pKa of acetic acid):
- pKa = 4.76, so Ka = 10^(-4.76) = 1.738 x 10^(-5) mol/L
- [H+] = 10^(-4.76) = 1.738 x 10^(-5) mol/L
- Because pH = pKa, Ka = [H+], so Ka x [H+] = (1.738 x 10^(-5))^2 = 3.021 x 10^(-10)
- (Ka + [H+])^2 = (2 x 1.738 x 10^(-5))^2 = (3.476 x 10^(-5))^2 = 1.208 x 10^(-9)
- beta = 2.303 x 0.1 x 3.021 x 10^(-10) / 1.208 x 10^(-9) = 0.2303 x 0.25 = 0.0576 mol/L/pH unit
This matches the simplified maximum formula: 2.303 x 0.1 / 4 = 0.0576. This is the highest possible buffer capacity for a 0.1 mol/L acetate buffer, achieved at pH = pKa = 4.76.
Common Buffer Systems
| Buffer System | pKa | Useful pH Range | Common Use |
|---|
| Acetic acid / Acetate | 4.76 | 3.8 to 5.8 | Food chemistry, electrochemistry |
| Citric acid / Citrate (pKa2) | 4.76 | 3.0 to 6.2 | Food, pharmaceuticals |
| MES | 6.15 | 5.5 to 6.7 | Biochemistry |
| Phosphate (H2PO4- / HPO4-2) | 7.21 | 6.2 to 8.2 | Biochemistry, cell culture |
| HEPES | 7.55 | 6.8 to 8.2 | Cell biology, molecular biology |
| Tris | 8.06 | 7.0 to 9.0 | Molecular biology, electrophoresis |
| Ammonium / Ammonia | 9.25 | 8.3 to 10.3 | Analytical chemistry |
| Carbonate (HCO3- / CO3-2) | 10.33 | 9.3 to 11.3 | Biochemistry, photography |
Related Calculators
Sources and method: Van Slyke DD (1922) "On the measurement of buffer values and on the relationship of buffer value to the dissociation constant of the buffer and the concentration and reaction of the buffer solution." Journal of Biological Chemistry 52:525-570. Henderson-Hasselbalch equation as used in analytical and biochemistry curricula. Standard thermodynamic values at 25 degrees Celsius.
This calculator uses the Van Slyke equation for a simple monoprotic weak acid buffer. Polyprotic acids, mixed buffers, and ionic strength effects are not included. Results are approximate and suitable for teaching and preliminary experimental planning. Always verify buffer performance experimentally for critical applications.
