Preparing a reliable buffer solution is one of the most fundamental tasks in analytical, biological, and pharmaceutical chemistry. Whether you are stabilising an enzymatic assay at physiological pH or designing a mobile phase for HPLC, the Henderson-Hasselbalch equation is the governing relationship that dictates the composition of your mixture.
This calculator removes the logarithmic arithmetic from bench work. It solves for pH, pKa, the conjugate base-to-acid ratio, or either absolute concentration — delivering derived quantities such as $[H^+]$, $[OH^-]$, pOH, and $K_a$ in a single pass.
Required Solution Parameters
To obtain a valid result, the following variables must be defined. The solver will treat one of them as the unknown based on the selected calculation mode:
- Solution pH — the target or measured acidity of the buffer, typically between 0 and 14.
- pKa — the negative base-10 logarithm of the acid dissociation constant $K_a$ of the weak acid.
- Conjugate Base [A⁻] — the molar concentration (M) of the deprotonated species, usually supplied as a soluble salt.
- Weak Acid [HA] — the molar concentration (M) of the protonated, weakly ionising acid.
- Ratio [A⁻]/[HA] — used when only the proportional composition is known, independent of absolute molarity.
Theoretical Foundation & Formulas
The Governing Equation
The Henderson-Hasselbalch relation expresses the pH of a buffered solution as a function of the acid dissociation constant and the concentration ratio of the conjugate pair:
$$pH = pK_a + \log_{10}\left(\frac{[A^-]}{[HA]}\right)$$
It is formally an approximation, valid when the equilibrium concentrations can be replaced by the analytical (formal) concentrations — a condition that holds for most bench-scale buffers.
Derivation from the Acid Dissociation Constant
For a generic monoprotic weak acid HA dissociating in aqueous solution as $HA \rightleftharpoons H^+ + A^-$, the equilibrium constant is:
$$K_a = \frac{[H^+][A^-]}{[HA]}$$
Solving for $[H^+]$ and applying the negative logarithm to both sides yields:
$$-\log[H^+] = -\log K_a - \log\frac{[HA]}{[A^-]}$$
Substituting the Sørensen convention ($pH = -\log[H^+]$, $pK_a = -\log K_a$) and inverting the fraction produces the final form used by the solver.
Derived Quantities
From the primary result, the calculator propagates four auxiliary values:
$$[H^+] = 10^{-pH} \qquad [OH^-] = 10^{-(14-pH)}$$
$$pOH = 14 - pH \qquad K_a = 10^{-pK_a}$$
The mole fraction of each species is computed from the ratio $r = [A^-]/[HA]$ as $\chi_{A^-} = r/(1+r)$, which drives the composition visualisation.
Reference Data: Common Weak Acid Systems
Selecting a buffer begins with matching the target pH to a weak acid whose pKa falls within one unit of that value. The table below lists widely used systems at 25 °C.
| Buffer System | Weak Acid | pKa (25 °C) | Useful pH Range | Typical Application |
|---|---|---|---|---|
| Acetate | Acetic acid (CH₃COOH) | 4.76 | 3.76 – 5.76 | Protein crystallography, electrophoresis |
| Phosphate (H₂PO₄⁻/HPO₄²⁻) | Dihydrogen phosphate | 7.20 | 6.20 – 8.20 | Cell culture, PBS, enzymology |
| Tris-HCl | Tris(hydroxymethyl)aminomethane | 8.06 | 7.06 – 9.06 | Molecular biology, PAGE |
| Carbonate / Bicarbonate | Carbonic acid (apparent) | 6.35 | 5.35 – 7.35 | Blood plasma modelling |
| Citrate (second) | Dihydrogen citrate | 4.76 | 3.76 – 5.76 | Food chemistry, pharmaceuticals |
| Ammonium | Ammonium ion (NH₄⁺) | 9.25 | 8.25 – 10.25 | Alkaline organic synthesis |
| HEPES | — | 7.55 | 6.80 – 8.20 | Biological "Good's" buffer |
| Formate | Formic acid (HCOOH) | 3.75 | 2.75 – 4.75 | Mass spectrometry eluents |
Engineering Analysis & Real-World Application
The Isohydric Point and Maximum Capacity
When $[A^-] = [HA]$, the logarithmic term collapses to zero and pH equals pKa exactly. This is the point of maximum buffer capacity ($\beta$), where the solution most effectively resists changes in pH upon addition of strong acid or base. Practitioners should therefore select a weak acid whose pKa is as close as possible to the desired operational pH.
Effective Buffering Range
The accepted working envelope of a buffer is $pK_a \pm 1$. Outside this interval, the ratio $[A^-]/[HA]$ exceeds 10:1 or falls below 1:10, at which point the buffer can neutralise only limited quantities of titrant before the pH drifts sharply.
Dilution Behaviour
Because the equation depends on a ratio, not absolute concentrations, dilution with pure solvent theoretically does not shift pH. In practice, deviations arise from changes in ionic strength, activity coefficients, and temperature — the equation assumes ideal behaviour and neglects water autoionisation.
Known Limitations
The approximation breaks down under several conditions:
- When the buffer concentration approaches $10^{-7}$ M, where water self-dissociation becomes non-negligible.
- At the extreme ends of a titration curve, where $[A^-]/[HA]$ departs from the 0.1 – 10 window.
- For polyprotic acids where consecutive pKa values differ by less than three units.
- With solutions of very high ionic strength, where activity differs markedly from concentration.
Frequently Asked Questions
The equation uses formal concentrations and assumes unit activity coefficients. Real solutions — particularly at high ionic strength, in non-aqueous media, or at temperatures deviating from 25 °C — exhibit non-ideal thermodynamic behaviour.
Additionally, the pKa itself is temperature-dependent; Tris, for instance, shifts by roughly −0.028 units per °C. For precision work, always calibrate against a measured pKa at the operating temperature rather than a handbook value.
Yes, with a simple substitution. Enter the pKa of the conjugate acid (for example, pKa of $NH_4^+$ = 9.25 rather than pKb of $NH_3$ = 4.75). The ratio then becomes $[B]/[BH^+]$, i.e. base over its protonated form.
Alternatively, calculate using the symmetric form $pOH = pK_b + \log_{10}([BH^+]/[B])$ and convert via $pH = 14 - pOH$. Both approaches yield identical results because $pK_a + pK_b = pK_w = 14$.
First, choose a weak acid whose pKa lies within ±1 of the target pH. Select a total buffer concentration — typically 10 to 100 mM for biological work — and use the solver in "Ratio" mode to obtain the required $[A^-]/[HA]$.
Dissolve the calculated masses of acid and conjugate salt in roughly 90% of the final volume, then fine-tune with a calibrated pH meter using small additions of strong acid or base. Bring to final volume only after the pH has stabilised, since dilution shifts ionic strength.
Professional Conclusion
The Henderson-Hasselbalch equation is simultaneously one of the simplest and most powerful expressions in aqueous chemistry. Manual evaluation is error-prone — base-10 logarithms, inversion of ratios, and sign management of pKa all invite mistakes that propagate into wasted reagents and failed experiments.
Automated computation eliminates this arithmetic overhead and, more importantly, surfaces derived quantities ($[H^+]$, $[OH^-]$, pOH, $K_a$, mole fractions) that manual workflows typically omit. For any researcher designing buffered systems, instrumented calculation is not a convenience — it is a standard of rigour.