About

Buffer capacity (β) quantifies the resistance of a solution to pH change upon addition of strong acid or base. It is defined as the moles of strong acid or base required to shift the pH of 1 L of buffer by one pH unit. The Van Slyke equation models β as a function of total buffer concentration C and the ratio of the acid dissociation constant K_a to the hydronium concentration. Miscalculating buffer capacity in pharmaceutical formulation or enzyme assay design leads to pH drift, protein denaturation, and unreliable kinetic data. This tool computes β, pH from the Henderson-Hasselbalch equation, and maximum theoretical capacity β_max = 0.576 × C. Note: calculations assume ideal dilute aqueous solutions at 25 °C with activity coefficients of unity. Ionic strength corrections (Debye-Hückel) are not applied.

Formulas

The Henderson-Hasselbalch equation gives the pH of a buffer solution:

pH = pK_a + log₁₀ [A⁻][HA]

The Van Slyke equation defines buffer capacity β (mol/L per pH unit):

β = 2.303 × C × K_a ⋅ [H⁺](K_a + [H⁺])²

Maximum buffer capacity occurs when pH = pK_a (equal concentrations of acid and conjugate base):

β_max = 0.576 × C

Where C = total buffer concentration [HA] + [A⁻] in mol/L, K_a = acid dissociation constant, [H⁺] = hydronium ion concentration = 10^−pH. The pK_a = −log₁₀(K_a).

Reference Data

Buffer System	Conjugate Pair	pK_a	Effective pH Range	Temp. Coefficient (ΔpK_a/°C)	Common Use
Acetate	CH₃COOH / CH₃COO⁻	4.76	3.76 - 5.76	+0.0002	Protein purification, histology
Phosphate (pK_a2)	H₂PO₄⁻ / HPO₄²⁻	7.20	6.20 - 8.20	−0.0028	Biological assays, cell culture (PBS)
Tris	Tris-H⁺ / Tris	8.07	7.07 - 9.07	−0.028	Molecular biology, gel electrophoresis
Bicarbonate	H₂CO₃ / HCO₃⁻	6.35	5.35 - 7.35	−0.0055	Blood plasma, CO₂ equilibrium
Citrate (pK_a2)	H₂Cit⁻ / HCit²⁻	4.76	3.00 - 6.40	+0.0002	Food chemistry, anticoagulant
Borate	H₃BO₃ / B(OH)₄⁻	9.24	8.24 - 10.24	−0.008	Electrophoresis, enzyme kinetics
HEPES	HEPES-H⁺ / HEPES	7.55	6.55 - 8.55	−0.014	Cell culture, physiological studies
Glycine (pK_a1)	Gly-H⁺ / Gly	2.35	1.35 - 3.35	+0.001	SDS-PAGE, low-pH buffers
MES	MES-H⁺ / MES	6.15	5.15 - 7.15	−0.011	Plant biology, organelle isolation
MOPS	MOPS-H⁺ / MOPS	7.20	6.20 - 8.20	−0.013	Running buffer, protein studies
PIPES	PIPES-H⁺ / PIPES	6.76	5.76 - 7.76	−0.0085	Fixation buffers, electron microscopy
Glycylglycine	GlyGly-H⁺ / GlyGly	8.40	7.40 - 9.40	−0.028	Metal-ion studies
CAPS	CAPS-H⁺ / CAPS	10.40	9.40 - 11.40	−0.032	High-pH electrophoresis
Ammonia	NH₄⁺ / NH₃	9.25	8.25 - 10.25	−0.031	Nesslerization, cleaning
Formate	HCOOH / HCOO⁻	3.75	2.75 - 4.75	+0.0002	HPLC mobile phase

Frequently Asked Questions

At pH = pKa, the concentrations of weak acid [HA] and conjugate base [A⁻] are equal. The Van Slyke equation's numerator Ka·[H⁺] reaches its maximum relative to the denominator (Ka + [H⁺])² when Ka = [H⁺], i.e., pH = pKa. At this point, the buffer has the greatest reservoir of both proton donors and acceptors, maximizing resistance to pH change.

A buffer is considered effective within ±1 pH unit of its pKa value. Outside this range, the ratio [A⁻]/[HA] exceeds 10:1 or falls below 1:10, and buffer capacity drops below approximately 33% of βmax. For critical applications such as enzyme assays, a narrower window of ±0.5 pH units is recommended to maintain capacity above 73% of maximum.

Temperature shifts the pKa of the buffer system. Tris buffer has a large temperature coefficient of −0.028 pKa units per °C, meaning a solution prepared at 25 °C with pH 8.07 will read approximately pH 7.51 at 37 °C. Phosphate buffers are far more stable with a coefficient of −0.0028 per °C. Always calibrate pH at the working temperature.

Yes. This calculator assumes ideal solutions (activity coefficients = 1). At ionic strengths above 0.1 M, activity coefficients deviate significantly from unity, altering the effective Ka. The Davies equation or extended Debye-Hückel model can correct for this. In practice, high salt concentrations compress buffer capacity by 5-15% compared to ideal predictions.

Buffer capacity β is always ≥ 0 for a real buffer solution. It approaches zero as the ratio [A⁻]/[HA] becomes extremely large or small (far from pKa). Pure water has β ≈ 0 except at very low or very high pH where autoprotolysis contributions from H₂O dominate. A computed β of zero means the solution provides no buffering and behaves like an unbuffered system.

The buffer is overwhelmed when the moles of added strong acid exceed the moles of conjugate base [A⁻] present. At that point, all A⁻ has been converted to HA, excess H⁺ accumulates freely, and pH drops sharply. This is the buffer's capacity limit. Design buffers so that the expected acid/base load does not exceed approximately 75% of the limiting conjugate component.