Buffer Solution pH Calculator (Henderson-Hasselbalch)

The Henderson-Hasselbalch Equation

A buffer solution resists changes in pH when small amounts of acid or base are added. Buffers are essential in chemistry, biochemistry, medicine, and industrial processes. They work by containing a weak acid and its conjugate base (or a weak base and its conjugate acid) in equilibrium.

The Henderson-Hasselbalch equation:

pH = pKa + log₁₀([A⁻] / [HA])

Where:

• pH = the acidity/alkalinity of the solution (scale 0–14)
• pKa = the acid dissociation constant of the weak acid (lower pKa = stronger acid)
• [A⁻] = molar concentration of the conjugate base (the deprotonated form)
• [HA] = molar concentration of the weak acid (the protonated form)

What pKa means: pKa = -log₁₀(Ka). When [A⁻] = [HA] (equal concentrations), log(1) = 0, so pH = pKa exactly. This is the half-equivalence point, and it is also the centre of the buffer’s effective range.

Effective buffer range: A buffer works effectively within pKa ± 1 pH unit. Outside this range, one component dominates and the buffer loses its capacity to resist pH changes.

Common buffers and their pKa values:

Every range above is simply pKa ± 1, except citrate, which has three pKa values and so covers a wider span than any single one of them would.

Blood pH regulation: Human blood is maintained at pH 7.35–7.45 primarily through the bicarbonate buffer system (pKa 6.35), combined with respiratory control of CO₂ and kidney regulation of bicarbonate reabsorption.

Look at that against the table and it seems impossible: 7.4 sits right at the top edge of bicarbonate’s window, where a sealed buffer has almost no capacity left. Blood gets away with it because it is not a closed system. The lungs keep blowing off CO₂, which resets the acid side of the equilibrium continuously, so the working capacity is far higher than Henderson-Hasselbalch predicts for a beaker. If you enter blood’s numbers below, the calculator will correctly tell you the ratio is near the edge of the effective range. That answer is right for glassware and wrong for a living person, and the difference is the open system.

Worked example: an acetate buffer with pKa = 4.76, [A⁻] = 0.2 mol/L and [HA] = 0.1 mol/L: pH = 4.76 + log(0.2/0.1) = 4.76 + log(2) = 4.76 + 0.301 = 5.06

What the equation quietly assumes

Henderson-Hasselbalch is an approximation, and it is worth knowing where it stops being a good one. It treats [A⁻] and [HA] as the amounts you weighed out, ignoring the small extra ionization of the acid itself. That is fine when both concentrations are well above the Ka, which covers essentially every buffer anyone actually prepares, and it starts to drift when either component is very dilute or the ratio is extreme.

It also assumes ideal behaviour, so it works with concentrations rather than activities. In a buffer that also carries a lot of salt, the measured pH can sit a couple of tenths away from the calculated one. For work where that matters, mix the buffer by calculation and then adjust it on a meter.

Ratio, not amount

Notice what is missing from the equation: the total concentration. A buffer made from 0.2 M and 0.1 M has the same pH as one made from 0.02 M and 0.01 M, because only the ratio appears. What the total concentration changes is capacity, meaning how much acid or base the buffer can absorb before the pH moves. Two buffers can sit at exactly the same pH and behave completely differently when you add something to them.