Henderson–Hasselbalch — Buffer pH Calculator

Compute pH, the ratio \([A^-]/[HA]\), or a buffer recipe. Private by design—everything runs locally in your browser.

Inputs

required for calculations
or provide ratio
must be > 0
optional
optional
for recipe
for recipe
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, \(C_t=0.10\ \mathrm{M}\), \(V=1.00\ \mathrm{L}\).

  1. Ratio \(R=10^{\mathrm{pH}-\mathrm{p}K_a}=10^{4.50-4.76}\approx 0.55\).
  2. \([A^-]=\frac{R}{1+R}C_t\approx 0.0355\ \mathrm{M}\), \([HA]\approx 0.0645\ \mathrm{M}\).
  3. Moles at 1.00 L: \(n_{A^-}=0.0355\ \mathrm{mol}\), \(n_{HA}=0.0645\ \mathrm{mol}\).
  4. 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

  1. 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.
  2. Compute the needed ratio \(R = [A^-]/[HA] = 10^{\mathrm{pH}-\mathrm{p}K_a}\).
  3. Set a total concentration \(C_t = [A^-] + [HA]\) guided by required capacity and compatibility with your experiment.
  4. 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.

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