Buffer pH Calculator

The Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation expresses the pH of a buffer solution in terms of the pKa of the weak acid and the ratio of the concentrations of conjugate base to weak acid:

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

Where:

• pKa is the negative base-10 logarithm of the acid dissociation constant (Ka)
• [A-] is the molar concentration of the conjugate base (the deprotonated form)
• [HA] is the molar concentration of the weak acid (the protonated form)

The equation is derived from the equilibrium expression for the dissociation of the weak acid (HA) into H+ and A-. It is an excellent approximation when the concentrations of acid and base are both substantially greater than the H+ concentration (typically above about 1 mmol/L) and the ratio [A-]/[HA] is between 0.1 and 10.

How Buffer Solutions Work

A buffer solution resists changes in pH when small amounts of acid or base are added. It does this through two reactions:

• Added acid: H+ is consumed by the conjugate base: A- + H+ → HA
• Added base: OH- is consumed by the weak acid: HA + OH- → A- + H2O

The buffer is most effective at resisting pH change when both [A-] and [HA] are present in substantial amounts. A buffer is essentially exhausted when one component is fully consumed.

Effective Buffering Range

The Henderson-Hasselbalch equation shows that the buffer pH equals pKa when [A-] = [HA] (since log(1) = 0). As the ratio moves away from 1, the pH moves away from pKa. At a ratio of 10:1 (base:acid), pH = pKa + 1. At a ratio of 1:10 (base:acid), pH = pKa - 1. Outside the range pKa ± 1, the buffer loses much of its capacity to resist pH change, and a different buffer with a more appropriate pKa should be selected.

Common Buffer Systems

Preparing a Buffer at a Target pH

To prepare a buffer at a specific target pH, rearrange the Henderson-Hasselbalch equation to find the required ratio of conjugate base to weak acid:

[A-] / [HA] = 10^(pH - pKa)

For example, to prepare a phosphate buffer at pH 7.40 using the H2PO4-/HPO42- pair (pKa 7.20):

• Ratio = 10^(7.40 - 7.20) = 10^0.20 = 1.585
• So you need approximately 1.585 parts of HPO42- (dibasic) to every 1 part of H2PO4- (monobasic)

Limitations of the Henderson-Hasselbalch Equation

The equation assumes ideal solution behaviour and that the autoionisation of water is negligible compared to the concentrations of the buffer components. It becomes less accurate at very low concentrations (below about 1 mmol/L), at extreme pH values (below 3 or above 11), or when the ratio [A-]/[HA] is outside the range 0.01 to 100. For high-precision work, activity coefficients and the contribution of water autoionisation should be accounted for.

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Sources and method: Henderson-Hasselbalch equation as derived from the weak acid equilibrium expression (Lawrence J. Henderson, 1908; Karl A. Hasselbalch, 1917). Atkins' Physical Chemistry (Oxford University Press). Chang, R., Chemistry (McGraw-Hill). pKa values from the NIST Chemistry WebBook and standard biochemistry references.

This calculator provides theoretical pH values based on the Henderson-Hasselbalch approximation. It assumes ideal behaviour and that concentrations are well above the ionisation of water. For high-precision laboratory work, verify against measured pH using a calibrated pH meter.