⚗️ Henderson–Hasselbalch Calculator – Calculate Buffer pH Instantly
The Henderson–Hasselbalch equation is the cornerstone formula for calculating the pH of a buffer solution. Whether you are preparing biological buffers in a lab, studying acid–base equilibria, or designing pharmaceutical formulations, this equation lets you determine the exact pH from just three values: the pKa of the weak acid and the molar concentrations of the acid and its conjugate base.
The Henderson–Hasselbalch Formula Explained
The equation is elegantly simple:
pH = pKa + log₁₀([A⁻] / [HA])Where each term means:
- pH — the measure of acidity or basicity of the solution (dimensionless, 0–14 for most aqueous solutions).
- pKa — the negative logarithm of the acid dissociation constant Ka; a lower pKa means a stronger acid.
- [A⁻] — molar concentration of the conjugate base (e.g., acetate CH₃COO⁻ for acetic acid buffers).
- [HA] — molar concentration of the weak acid (e.g., acetic acid CH₃COOH).
How Buffer Solutions Work
A buffer resists changes in pH when small amounts of acid or base are added. It is prepared by mixing a weak acid with its conjugate base (or a weak base with its conjugate acid) in the same solution. When an acid is added, the conjugate base neutralises it; when a base is added, the weak acid neutralises it — keeping the pH nearly constant.
The Henderson–Hasselbalch equation makes it straightforward to predict the pH of any such mixture. Because it is a logarithmic relationship, changing the ratio of conjugate base to acid has a predictable, measurable effect on pH.
Effective Buffer Range and the 1:1 Rule
The most important rule in buffer chemistry: a buffer is effective only when the pH stays within ±1 unit of its pKa. This corresponds to a [A⁻]/[HA] ratio between 0.1 and 10. Outside this range the buffer loses capacity rapidly. The optimal point — where buffering capacity is at its maximum — is when the ratio equals 1 (i.e., [A⁻] = [HA]), giving pH = pKa.
This calculator shows an effectiveness indicator so you can instantly tell whether your chosen concentrations produce a reliable buffer.
Common Buffer Systems and Their pKa Values
| Weak Acid / System | pKa | Useful pH Range | Common Use |
|---|---|---|---|
| Acetic acid (CH₃COOH) | 4.76 | 3.8 – 5.8 | Food & analytical chemistry |
| Formic acid (HCOOH) | 3.75 | 2.8 – 4.8 | HPLC mobile phases |
| Lactic acid | 3.86 | 2.9 – 4.9 | Biological & food systems |
| Citric acid (pKa₁) | 3.13 | 2.1 – 4.1 | Food preservation |
| Carbonic acid (pKa₁) | 6.35 | 5.4 – 7.4 | Physiological buffering |
| Dihydrogen phosphate | 7.20 | 6.2 – 8.2 | Biological/PBS buffers |
| H₂S (pKa₁) | 7.00 | 6.0 – 8.0 | Environmental chemistry |
| Boric acid | 9.24 | 8.2 – 10.2 | Ophthalmic solutions |
| Ammonium (NH₄⁺) | 9.25 | 8.3 – 10.3 | Analytical chemistry |
| Bicarbonate (HCO₃⁻) | 10.33 | 9.3 – 11.3 | Alkaline solutions |
Worked Example
Problem: Prepare a buffer at pH 5.06 using acetic acid (pKa = 4.76) with 0.20 M sodium acetate and 0.10 M acetic acid.
pH = pKa + log₁₀([A⁻] / [HA])
pH = 4.76 + log₁₀(0.20 / 0.10)
pH = 4.76 + log₁₀(2.00)
pH = 4.76 + 0.3010
pH = 5.06
The ratio of 2:1 (conjugate base to acid) shifts the pH 0.30 units above the pKa. This is well within the ±1 effective range.
Real-World Applications
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Biochemistry
PBS and TRIS buffers maintain enzyme and cell culture conditions.
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Pharmaceuticals
Buffer pH controls drug solubility, stability, and bioavailability.
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Food Science
Citrate and acetate buffers control preservation and flavour stability.
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Medicine
Blood plasma is buffered at pH 7.4 by the carbonate/bicarbonate system.
How to Use This Calculator
- Select a preset from the dropdown (e.g., Acetic acid) to automatically fill in a pKa value, or enter your own custom pKa.
- Enter the molar concentration of the conjugate base [A⁻] in mol/L (e.g., 0.20 for 0.20 M sodium acetate).
- Enter the molar concentration of the weak acid [HA] in mol/L (e.g., 0.10 for 0.10 M acetic acid).
- Click Calculate pH to get the result, a full summary, a buffer effectiveness rating, and the step-by-step derivation.
Assumptions and Limitations
The Henderson–Hasselbalch equation assumes ideal behaviour: it is most accurate for dilute aqueous solutions (typically 0.001–1 M) at room temperature where activity coefficients are close to 1. For very concentrated buffers, high ionic strength solutions, or non-aqueous systems, the effective pKa may shift and a more rigorous treatment using activity-corrected concentrations is advised. The equation also assumes that the acid/base dissociation does not significantly change the starting concentrations — which holds when both concentrations are much larger than √Ka.