Article — Buffer pH Calculator
Buffer pH Calculator: Henderson-Hasselbalch Equation for Acid-Base Buffers
The buffer pH formula is pH = pKa + log10([A⁻]/[HA]). When the conjugate base [A⁻] equals the weak acid [HA], the log term is zero and pH equals pKa. For acetic acid (pKa 4.74), a 1:1 acetate/acetic-acid mixture buffers at pH 4.74. To reach pH 5.74 you need 10× more acetate than acetic acid; pH 6.74 needs 100× more. Buffers work effectively in the pKa ± 1 range — outside it, the protonation state is dominated by one form and capacity collapses. Phosphate (pKa2 = 7.21) is the classic choice for pH near 7; Tris (8.06) for pH 7.5 to 9; acetate (4.74) for pH 4 to 5.5.
This calculator runs in three modes. Mode 1 computes the pH from pKa, [A⁻], and [HA]. Mode 2 returns the [A⁻]/[HA] ratio needed for a target pH. Mode 3 splits a chosen total concentration C into [HA] and [A⁻] amounts to hit a target pH — useful when preparing buffers from stock solutions.
What is a buffer pH
A buffer pH is the steady-state pH of an aqueous solution that contains a weak acid and its conjugate base in significant amounts. The buffer resists pH changes when small amounts of strong acid or strong base are added because either component can react with the addition. Most biological systems, soils, oceans, and laboratory chemistry operate inside buffered solutions.
Common buffer pH ranges: acetate (3.7–5.8), MES (5.5–6.7), carbonate (5.3–7.3), phosphate (6.2–8.2), HEPES (6.8–8.2), Tris (7.0–9.0), ammonium (8.2–10.2). Each system spans about two pH units around its pKa.
The carbonic acid / bicarbonate buffer that keeps blood pH near 7.40 has a pKa of only 6.35 — well outside the usual pKa ± 1 effective range. It still works because it is an open system: the lungs continuously remove CO₂ and the kidneys excrete or reabsorb HCO₃⁻. This active management gives blood a much higher effective buffer capacity than the static Henderson-Hasselbalch prediction suggests.
Buffer pH formula (Henderson-Hasselbalch)
The buffer pH formula from Henderson (1908) and Hasselbalch (1916) is pH = pKa + log10([A⁻]/[HA]). It is a rearrangement of the acid dissociation expression Ka = [H⁺][A⁻]/[HA]. Take −log of both sides, define pH = −log[H⁺] and pKa = −log(Ka), rearrange, and you get the buffer equation.
The equation assumes equilibrium has been reached, the buffer is dilute enough that activity coefficients are about 1, and the acid is weak enough that its dissociation does not dominate the calculation. These assumptions are good for 10 mM to 500 mM buffers at modest ionic strength.
pH = pKa 1:1 ratiopH = pKa + 1 10:1 A⁻:HApH = pKa − 1 1:10 A⁻:HAPhosphate pKa2 7.21HEPES pKa 7.48Calculating buffer pH from concentrations
To calculate buffer pH from concentrations, plug the values into the Henderson-Hasselbalch equation. Example: an acetate buffer containing 80 mM sodium acetate and 20 mM acetic acid. The ratio [A⁻]/[HA] = 80/20 = 4. log10(4) = 0.602. pH = 4.74 + 0.602 = 5.34. That buffer holds steady at pH 5.34 — within ±1 of the pKa, so it has decent capacity (~33% of peak).
For a 1:1 ratio of [A⁻]:[HA], the log term vanishes and pH = pKa exactly. This is the half-equivalence point in a titration and the point of maximum buffer capacity. Most buffer recipes target a ratio between 1:10 and 10:1, corresponding to pH inside ±1 of the pKa.
Preparing a buffer at a target pH
To prepare a buffer at a target pH, work backwards from the equation. Required ratio [A⁻]/[HA] = 10^(pH − pKa). For pH 7.0 phosphate buffer (pKa2 = 7.21), the ratio is 10^(7.0 − 7.21) = 10^(−0.21) = 0.617. So you need 0.617 mol of Na₂HPO₄ per mol of NaH₂PO₄. For 100 mM total: [HA] = 100 / (1 + 0.617) = 61.9 mM, [A⁻] = 38.1 mM.
Method 1: mix the two salts in the calculated ratio. Method 2: dissolve the conjugate acid (NaH₂PO₄) and titrate with NaOH until the pH meter reads the target. Method 2 is the gold standard because it accounts for impurities and small temperature effects.
Choosing the right buffer for your pH
Choosing the right buffer for your target pH means picking a system whose pKa is within 1 unit of where you want to work. For pH 7.0–7.5 (physiological), choose phosphate or HEPES. For pH 8.0 (molecular biology), Tris is standard but watch the temperature drift. For acidic conditions (pH 4–5), acetate or formate. For alkaline conditions (pH 9–10), ammonium or borate.
Buffer pH vs temperature and dilution
Buffer pH depends on temperature because pKa is temperature-dependent. Tris is the worst offender — pKa shifts by 0.028 per °C, so a Tris buffer made at 25 °C and used at 4 °C reads 0.6 pH units higher. Phosphate is much more stable (~0.003 per °C). Always prepare and measure buffers at the working temperature.
If your protocol calls for "Tris pH 8.0 at 4 °C," prepare it at 4 °C and let it equilibrate before pH adjustment. Pre-making at room temperature and chilling later will give a pH closer to 8.6. Always note the temperature on buffer labels.
Physiological buffers in the body
Physiological buffers in the body keep blood pH between 7.35 and 7.45 — a range of just 0.1 units despite constant metabolic acid production. The main buffer is bicarbonate (H₂CO₃ / HCO₃⁻) at ~25 mM in plasma. Phosphate (~1 mM in plasma, much higher in cells), protein side chains (especially histidine, with pKa 6.0), and ammonia (in renal tubules) contribute too. The bicarbonate buffer succeeds despite its pKa being well off pH 7.4 only because the body actively regulates CO₂ via breathing.
Common buffer pH mistakes
The most common mistake is forgetting to verify pH with a calibrated meter after mixing. The Henderson-Hasselbalch equation gives a theoretical pH that ignores activity coefficients, impurities, and CO₂ uptake. Always check. Second mistake: assuming dilution preserves pH. Diluting a buffer changes its ionic strength and slightly shifts pH; the shift is small (~0.05) for moderate dilutions but real. Third: ignoring temperature, especially with Tris.
Buffers exposed to air absorb CO₂, which dissolves to carbonic acid and shifts pH downward. Tris and ammonium buffers are particularly vulnerable. Store buffers tightly sealed at 4 °C, and equilibrate to working temperature before pH measurement. Filter-sterilise rather than autoclave for heat-sensitive buffers.