Henderson–Hasselbalch — Buffer pH Calculator

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 pK_a: Accuracy and buffer action are strongest within about ±1 pH unit of \(\mathrm{p}K_a\). At pH = pK_a, \([A^-]=[HA]\).
• 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 pK_b/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 pK_a 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 pK_a values. Use the pair bracketing your target pH and treat that step independently, noting that other equilibria can contribute at the edges.
• Temperature: pK_a values are temperature dependent. If your work is sensitive, use pK_a 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 = pK_a ± 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, pK_a, 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 pK_a, keep total concentration appropriate, and validate with a pH meter for final adjustments.