Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation (Henderson 1908, Hasselbalch 1916) is the fundamental formula for buffer pH from weak acid HA and conjugate base A-:

pH = pKa + log10([A-] / [HA])

Valid for dilute solutions with [HA], [A-] >> [H+], [OH-]. Derived from Ka = [H+][A-]/[HA] by taking -log10 of both sides.

Numerical example: acetate buffer

HA = CH3COOH (pKa = 4.76), A- = CH3COO-. For [HA] = [A-] = 0.1 M: pH = 4.76 + 0 = 4.76. For 1:3 ratio: pH = 5.24.

Buffer design

1. Choose weak acid with pKa within +/- 1 of target pH.
2. Calculate ratio [A-]/[HA] = 10^(pH - pKa).
3. Choose total concentration C_tot. Typical 0.05-0.5 M.
4. Compute masses of acid and salt for volume.
5. Verify with pH meter and adjust.

Buffer capacity (Van Slyke)

beta = dC_b/dpH = 2.303 * C_tot * fHA * fA-

Maximum at pH = pKa: beta_max = 0.576 * C_tot. Good buffer: beta = 0.05-0.2 mol/(L pH).

Useful range

pH = pKa +/- 1. Outside, ratio is too unbalanced (10:1 or 1:10), capacity drops below 30 % of max. pKa +/- 2: essentially ineffective.

Common biological buffers

• Carbonic acid/bicarbonate: pKa = 6.10. Blood pH 7.40.
• Phosphate (H2PO4-/HPO4^2-): pKa = 7.21.
• TRIS: pKa = 8.06.
• HEPES: 7.55. MOPS: 7.20. PIPES: 6.76 (Good buffers).
• Acetate: 4.76.
• Glycine: pKa1 = 2.34, pKa2 = 9.60.

Basic buffer (pKb form)

For base B / conjugate acid BH+: pOH = pKb + log10([BH+]/[B]). Equivalent to pH = pKa(BH+) + log10([B]/[BH+]) with pKa(BH+) = 14 - pKb. Example NH3/NH4+: pKb = 4.74, pKa(NH4+) = 9.26.

Limits

• Dilute solutions (activity ~ concentration).
• HA, A- > 10^-4 M.
• Strong acids: pKa outside 0-14.
• High ionic strength: apparent pKa shifts (Davies correction).
• T-dependence (Van t Hoff). Acetate pKa(25) = 4.76, pKa(37) = 4.65.
• Non-aqueous solvents: different pKa.

Thermodynamic derivation

Ka = [H+][A-]/[HA] -> -log10 Ka = -log10[H+] - log10([A-]/[HA]) -> pH = pKa + log10([A-]/[HA]). [HA] and [A-] are equilibrium concentrations.

Applications

• Biochemistry: enzyme/protein/DNA buffers.
• Physiology: blood acid-base balance.
• Pharma: drug stability, injectable formulations.
• Food: lactic acid, preservation.
• Cosmetics: skin pH 5.5.
• Analytical: titrations, colorimetry.
• Aquaria: natural buffers.
• Cells: cytoplasm 7.2, lysosomes 4.5.

History

Henderson 1908 (blood acid-base). Hasselbalch 1916 (logarithmic, clinical). Lewis-Sargent 1909 independent. Norman Good 1966 (Good buffers). Van Slyke 1922 (capacity).

Calculator modes

Five modes: pH from ratio; design ratio from target pH; pKb form for bases; Van Slyke capacity beta; from masses with MW and V. Output includes capacity, mole fractions, useful range pKa +/- 1.

Buffers in the blood: the bicarbonate system

The Henderson-Hasselbalch equation was born in physiology, and its most vital application is still the blood. Human plasma is kept near pH 7.4 chiefly by the bicarbonate buffer, a pair formed by carbonic acid and the bicarbonate ion. Written for this pair the equation becomes pH = 6.1 + log10([HCO3-]/[H2CO3]), and at the normal ratio of about 20 to 1 it yields exactly the 7.4 that arterial blood maintains. A deviation of a few tenths of a pH unit in either direction is life-threatening, which is why the body defends this value so vigorously.

What makes the bicarbonate system remarkable is that it is open: the carbonic-acid side is in equilibrium with dissolved carbon dioxide, which the lungs can expel, while the kidneys regulate the bicarbonate side. Breathing faster lowers CO2 and raises pH; the kidneys retain or excrete bicarbonate over hours to days. This dual respiratory and renal control lets an intrinsically modest buffer hold blood pH far more tightly than a closed system ever could, and clinicians read acidosis and alkalosis directly through the Henderson-Hasselbalch relation.

Choosing and preparing a buffer in the laboratory

Designing a buffer starts from a single rule that follows directly from the equation: pick a weak acid whose pKa lies within one unit of the target pH. At the midpoint, where conjugate acid and base are present in equal amounts, the ratio term vanishes and pH equals pKa, and it is precisely there that the buffer capacity beta reaches its maximum of about 0.576 times the total concentration. Straying more than one pH unit from pKa collapses that capacity, because a small addition of acid or base then shifts the ratio steeply.

For biological work the classic choices are Good's buffers, introduced by Norman Good in 1966: MES, HEPES, MOPS and Tris span the physiological range with low toxicity and minimal metal binding. Two practical warnings follow from the theory. First, pKa depends on temperature and ionic strength, so a buffer titrated at room temperature drifts when cooled or diluted, an effect especially large for Tris. Second, capacity scales with the total concentration, so a dilute buffer resists pH change poorly no matter how well its pKa is matched. Preparing a buffer well means matching pKa, fixing the ratio for the target pH, and choosing a concentration high enough to absorb the expected acid or base load.

Updated July 2026