pH = pKa is the 50/50 point
At pH = pKa, \([A^-]=[HA]\) and buffer capacity peaks—exactly the halfway point of a weak-acid titration curve.
Sweet spot
Buffer pH Calculator — Henderson–Hasselbalch Equation
Calculator inputs
Optional: pH after adding strong acid or base
Enter the initial total concentration and volume so component moles can be updated before applying the buffer equation.
Result
Ready to calculate
Choose a goal, enter the shown values, and select Calculate.
Calculated values
Composition
Effective buffer range
Estimated preparation
Preparation notes: This is a starting composition, not an exact lab recipe. pK depends on temperature and ionic strength; purity and hydrate form matter. Dissolve or mix below final volume, check with a calibrated pH meter at the working temperature, adjust if appropriate, then bring to final volume.
After strong acid/base addition
Calculation steps
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Inputs
required for calculations
or provide ratio
must be > 0
g·mol⁻¹
g·mol⁻¹
Results
Computed values
pKa: —
pH: —
[A⁻]/[HA]: —
Composition
[A⁻]: —
[HA]: —
Fractions — A⁻: —, HA: —
Recipe (if Ct & V provided)
—
Equation
\( \mathrm{pH} = \mathrm{p}K_a + \log_{10}\!\big(\frac{[A^-]}{[HA]}\big) \)
Worked example
Acetate buffer. pK\(_a\)=4.76, target pH=4.50, \(C_t=0.10\ \mathrm{M}\), \(V=1.00\ \mathrm{L}\).
- Ratio \(R=10^{\mathrm{pH}-\mathrm{p}K_a}=10^{4.50-4.76}\approx 0.55\).
- \([A^-]=\frac{R}{1+R}C_t\approx 0.0355\ \mathrm{M}\), \([HA]\approx 0.0645\ \mathrm{M}\).
- Moles at 1.00 L: \(n_{A^-}=0.0355\ \mathrm{mol}\), \(n_{HA}=0.0645\ \mathrm{mol}\).
- With NaOAc (82.03) and HOAc (60.05): ~2.91 g and ~3.87 g.
Understanding the Henderson–Hasselbalch Equation (Buffers)
The Henderson–Hasselbalch equation connects the pH of a buffer with its acid dissociation constant and the ratio of conjugate base to acid: \[ \mathrm{pH} = \mathrm{p}K_a + \log_{10}\!\left(\frac{[A^-]}{[HA]}\right). \] It follows from the definition \(K_a=\tfrac{[H^+][A^-]}{[HA]}\) by solving for \([H^+]\) and taking negative logarithms. In practice, it lets you think in ratios: every 1.0 increase in \(\log_{10}([A^-]/[HA])\) raises pH by 1.0.
When it works best
- Near pKa: Accuracy and buffer action are strongest within about ±1 pH unit of \(\mathrm{p}K_a\). At pH = pKa, \([A^-]=[HA]\).
- Moderate concentrations: The equation assumes activities \(\approx\) concentrations. At low to moderate ionic strength this is usually fine.
- Weak acid/base systems: It’s intended for weak acids and their salts (or weak bases and their conjugate acids via the analogous form with pKb/pOH).
Design logic in one page
- Choose a buffer system with \(|\mathrm{pH}_\text{target} - \mathrm{p}K_a| \lesssim 1\). This maximizes capacity and minimizes sensitivity to small composition errors.
- Compute the needed ratio \(R = [A^-]/[HA] = 10^{\mathrm{pH}-\mathrm{p}K_a}\).
- Set a total concentration \(C_t = [A^-] + [HA]\) guided by required capacity and compatibility with your experiment.
- Split the totals: \([A^-] = \tfrac{R}{1+R}C_t\), \([HA] = \tfrac{1}{1+R}C_t\). Multiply by volume to get moles; use molar masses to get grams.
Buffer capacity (qualitative)
Capacity is the resistance to pH change upon adding acid or base. It is largest when \([A^-]\approx[HA]\) and when the overall buffer concentration is higher. Two practical levers therefore are: pick a system with pKa close to your target pH, and use a sufficient total concentration (balanced with solubility, ionic strength, and biological compatibility).
Common pitfalls and limitations
- Activities vs. concentrations: At high ionic strength, activity coefficients deviate from 1.0 and pH predictions can drift. If precision is critical, account for activity or use a calibration curve.
- Dilution effects: Diluting a buffer changes both ionic strength and concentrations; pH may shift slightly even if the ratio stays fixed.
- Strong acid/base additions: If you titrate to pH using strong reagents, first update the stoichiometry (convert HA⇌A⁻ accordingly), then apply Henderson–Hasselbalch. Large additions can move the system outside the buffer region.
- Polyprotic acids: Systems like phosphate or citrate have multiple pKa values. Use the pair bracketing your target pH and treat that step independently, noting that other equilibria can contribute at the edges.
- Temperature: pKa values are temperature dependent. If your work is sensitive, use pKa at your working temperature.
- CO₂ uptake and volatility: Open containers can drift in pH over time (e.g., carbonate formation). Seal and equilibrate appropriately.
Quick reading of the ratio
Rules of thumb: if pH = pKa ± 0.30, then the ratio is about 2:1 or 1:2; at ±1.0, it’s ~10:1 or 1:10. These mental anchors help during rough planning and sanity checks.
Workflow tips
- Prepare slightly below volume, dissolve, adjust pH, then bring to final volume.
- Record the buffer system, pKa, temperature, final pH, and ionic components for reproducibility.
- For biological work, consider compatibility (e.g., metal chelation, enzyme inhibition, buffering range).
Bottom line: Henderson–Hasselbalch turns buffer planning into a clean ratio problem. Stay near pKa, keep total concentration appropriate, and validate with a pH meter for final adjustments.
Equations and calculation guidance
An acid buffer uses weak acid HA and conjugate base A⁻:
Plain text: pH = pKa + log10([A−]/[HA])
A base buffer uses weak base B and conjugate acid BH⁺. The calculator finds pOH, then converts it with temperature-dependent pKw:
Plain text: pOH = pKb + log10([BH+]/[B]); pH = pKw − pOH
- Choose the conjugate pair with its pK near the target; the usual effective range is approximately one pH unit either side of the buffer center.
- Use R to split total concentration: numerator fraction = R/(1 + R), denominator fraction = 1/(1 + R).
- For a recipe, convert concentration and volume to moles, then moles to stock volume or mass using the actual reagent form.
Common buffer reference
Preset values are approximate references, mostly at 25 °C. They stay editable because ionic strength, concentration, solvent, and temperature can shift them.
| System | Pair used | Reference value | Approx. range |
|---|---|---|---|
| Acetate | CH₃COOH / CH₃COO⁻ | pKa 4.76 at 25 °C | 3.76–5.76 |
| Phosphate | H₂PO₄⁻ / HPO₄²⁻ | pKa₂ 7.21 at 25 °C | 6.21–8.21 |
| Citrate | H₂Cit⁻ / HCit²⁻ | pKa₂ 4.76 at 25 °C | 3.76–5.76 |
| MES | MES-H / MES⁻ | pKa 6.10 at 25 °C | 5.10–7.10 |
| PIPES | PIPES-H / PIPES⁻ | pKa 6.76 at 25 °C | 5.76–7.76 |
| HEPES | HEPES-H / HEPES⁻ | pKa 7.48 at 25 °C | 6.48–8.48 |
| Tris | Tris-H⁺ / Tris | pKa 8.06 at 25 °C | 7.06–9.06 |
| Borate | B(OH)₃ / B(OH)₄⁻ | pKa 9.24 at 25 °C | 8.24–10.24 |
| Ammonia/ammonium | NH₃ / NH₄⁺ | pKb 4.751 at 25 °C | pH ≈ 8.25–10.25 |
| Bicarbonate | H₂CO₃ / HCO₃⁻ | pKa₁ 6.35 at 25 °C | 5.35–7.35 |
Methodology, limitations, and references
This tool applies the concentration form of Henderson–Hasselbalch. In base mode, pKw is estimated for pure liquid water at ambient pressure from 0–100 °C with a compact temperature correlation; high-accuracy or non-ambient work should use the full IAPWS formulation. Strong-acid/base stress uses complete 1:1 stoichiometric conversion before reapplying the buffer equation.
- Concentrations approximate activities, so high ionic strength and very dilute solutions can differ materially.
- The pK ± 1 convention is a useful composition range, not a guarantee of capacity or accuracy.
- For polyprotic systems, select the dissociation pair bracketing the target pH.
- Presets are lookup aids, not certificates for a lot, formulation, solvent, or temperature.
References
- IUPAC Gold Book: Henderson–Hasselbalch equation
- OpenStax Chemistry 2e, section 14.6: Buffers
- IAPWS revised release on the ionization constant of water
- Sigma-Aldrich Buffer Reference Center
- PubChem: acetic acid, boric acid, and ammonia dissociation data
No reviewed-by attribution is shown because this page does not document an identifiable qualified reviewer and review process.
Frequently asked questions
How do I calculate the pH of a buffer?
For an acid buffer, use pH = pKa + log10([A−]/[HA]). For a base buffer, first calculate pOH = pKb + log10([BH+]/[B]), then use pH = pKw − pOH at the selected temperature.
How do I find pKa or the required buffer ratio?
Rearrange the same equation: pKa = pH − log10([A−]/[HA]), or [A−]/[HA] = 10^(pH − pKa). The base-buffer forms use pOH, pKb, and [BH+]/[B].
Why does pH equal pKa at a 1:1 ratio?
The base-10 logarithm of 1 is zero, so equal conjugate-base and acid concentrations make the Henderson–Hasselbalch equation reduce to pH = pKa.
What is the difference between acid and base buffers?
An acid buffer contains a weak acid and its conjugate base. A base buffer contains a weak base and its conjugate acid; its equation is commonly written for pOH and converted to pH with pKw.
Does dilution change buffer pH?
Ideal dilution leaves the component ratio unchanged, so the calculated pH is unchanged, but buffer capacity falls. Real solutions can shift because activities and ionic strength change.
How does temperature affect a buffer?
Temperature can change pKa, pKb, pKw, and activity coefficients. Use dissociation data measured near the working temperature and verify the prepared solution at that temperature.
How do I handle a polyprotic buffer such as phosphate or citrate?
Choose the conjugate pair whose pKa brackets the target pH and treat that dissociation step as the buffer pair. Other equilibria may matter near overlapping pKa values.
Why can a calculated buffer recipe differ from measured pH?
Henderson–Hasselbalch uses concentrations as activity approximations. Temperature, ionic strength, reagent purity, hydrate form, carbon dioxide uptake, calibration, and volume adjustment can all change the measured pH.
5 Fun Facts about Buffers & pH
Log math makes quick ratios
Every 1.0 pH unit away from pKa is a 10× ratio shift; 0.30 pH is about a 2× shift—handy for mental checks.
Head math
Blood runs Henderson–Hasselbalch
Your blood stays near pH 7.4 because bicarbonate buffers at a ~20:1 base:acid ratio (pKa ≈ 6.1) aided by CO₂ breathing.
Living buffer
Dilution hides in the capacity
Keeping the ratio fixed means pH barely moves when you dilute, but the capacity halves if you halve total concentration—less moles to soak up acid/base.
Stealth effect
pKa drifts with temperature
Many pKa values shift by 0.01–0.03 per °C; a 10 °C swing can nudge pH by ~0.1–0.3 at constant ratio.
Temperature twist