Chemkit

Buffer Calculator — Henderson-Hasselbalch pH

Buffers hold pH constant against small additions of strong acid or base. The Henderson-Hasselbalch equation tells you the pH of a buffer from the ratio of its conjugate-base form to its weak-acid form and the acid’s pKa. Pick a common buffer from the dropdown to auto-load its pKa, or enter a custom pKa.

Buffer Calculator

Henderson-Hasselbalch. Pick a common buffer to load its pKa, or enter a custom pKa.

Solve for

Equations used

The equation

For a weak acid HA with dissociation constant Ka:

pH=pKa+log⁡10 ⁣([A−][HA])\mathrm{pH} = \mathrm{p}K_a + \log_{10}\!\left(\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}\right)

At [A⁻] = [HA] (equimolar), pH = pKa exactly — this is the buffer’s point of maximum capacity. Every buffer works best within pKa ± 1 pH unit; farther than that, the ratio becomes extreme (above 10:1 or below 1:10) and small acid/base additions swing the pH.

The reverse direction — pick a target pH and calculate the ratio you need:

[A−][HA]=10pH−pKa\frac{[\mathrm{A^-}]}{[\mathrm{HA}]} = 10^{\mathrm{pH} - \mathrm{p}K_a}

Which buffer for which pH range

Rule of thumb: choose a buffer whose pKa is within ±1 pH unit of your target. Common lab buffers, ordered by pKa (25 °C):

BufferpKaUsable pH range
Acetate4.763.8 – 5.8
MES6.155.2 – 7.2
Bis-Tris6.465.8 – 7.2
PIPES6.806.1 – 7.5
MOPS7.206.5 – 7.9
Phosphate (pKa₂)7.206.2 – 8.2
HEPES7.556.8 – 8.2
Tris8.067.0 – 9.0 (temp-sensitive)
TAPS8.407.7 – 9.1
CHES9.558.6 – 10.5
Carbonate (pKa₂)10.339.3 – 11.3

Common pitfalls

  • Temperature matters, especially for Tris. Tris pKa drops by ~0.028 per °C. A “pH 8.0 Tris” prepared at 25 °C is actually pH 7.75 at 37 °C. Adjust pH at your working temperature.
  • Concentration ≠ activity. Henderson-Hasselbalch uses concentrations, ignoring the activity coefficient. For high-salt buffers or biological media the true pH can differ by 0.1–0.2 units. Measure with a meter for precise work.
  • Watch out for ionic strength. High-conductivity buffers (>100 mM) can shift pKa’s noticeably; the tabulated pKa values assume dilute aqueous conditions.
  • Pick your buffer for the target pH, not the reverse. Trying to force a HEPES buffer to hold pH 5.0 needs a 3500:1 ratio and has near-zero capacity. Use MES or acetate instead.

Practice problems

Attempt each on paper, then expand the worked solution to check your arithmetic and sig-figs.

Problem 1 Easy You mix 100 mM Tris base with 100 mM Tris-HCl in a 2:1 ratio (base:acid). What is the pH? (Tris pKa = 8.06)

Answer: pH 8.36

Solve for pH given ratio
pKa
8.06 (Tris at 25 °C)
[A⁻]/[HA]
2 (base:acid = 2:1)
  1. Formula
  2. Substitute
  3. Note

    At 25 °C. If you use this buffer at 37 °C, the actual pH drops by about 0.028 × 12 ≈ 0.34 units to pH 8.03 — measure and adjust at working temperature.

  4. Result
Problem 2 Easy You need a phosphate buffer at pH 7.40. Phosphate pKa₂ = 7.20. What [HPO₄²⁻]/[H₂PO₄⁻] ratio do you use?

Answer: 1.58 (about 3:2)

Solve for ratio given target pH
pKa₂
7.20 (H₂PO₄⁻ / HPO₄²⁻)
Target pH
7.40
  1. Formula
  2. Substitute
  3. Note

    So HPO₄²⁻ / H₂PO₄⁻ ≈ 1.58. Physiologically, most 'PBS' recipes hit ~pH 7.4 by using ~2 mM K₂HPO₄ and ~1.4 mM KH₂PO₄ (plus NaCl for isotonicity).

  4. Result
Problem 3 Intermediate You want a MES buffer at pH 6.15 (which equals its pKa). What is the fractional composition [A⁻]/([A⁻]+[HA])?

Answer: 50 % A⁻ (equimolar)

At pH = pKa the buffer is 50:50
pKa (MES)
6.15
Target pH
6.15
  1. Formula
  2. Substitute
  3. Note

    This is where a buffer resists pH change most effectively — small additions of strong acid or base move the ratio only slightly. Every buffer preparation targets pH within ±1 of its pKa for this reason.

  4. Result
Problem 4 Hard You need pH 5.0 and are stuck with HEPES (pKa 7.55). Estimate the [A⁻]/[HA] ratio. Should you use this buffer?

Answer: ≈ 0.00028 (1:3500) — no, use MES or acetate instead

Ratio when target is far from pKa
pKa (HEPES)
7.55
Target pH
5.00
  1. Formula
  2. Substitute
  3. Note

    That's basically all HA and essentially no conjugate base. A tiny addition of strong base pushes the pH up rapidly — the buffer has almost no capacity here. Use MES (pKa 6.15) or acetate (pKa 4.76) for pH 5.0.

  4. Result

Frequently asked questions

What is the Henderson-Hasselbalch equation?
pH = pKa + log10([A⁻] / [HA]). It tells you the pH of a buffered solution given the ratio of the conjugate base to the weak acid form and the acid's pKa. A ratio of 1 (equimolar) gives pH = pKa — the point of maximum buffering capacity.
Which buffer should I pick for my target pH?
The rule is: choose a buffer whose pKa is within ±1 unit of your target pH. At pH = pKa the buffer has maximum capacity; beyond ±1 unit the ratio becomes extreme (>10:1) and small acid or base additions swing the pH more. This calculator warns you when your target lies outside the pKa ± 1 window.
Do I need to correct pKa for temperature?
For most buffers, no — the ΔpKa/°C is small enough that a value measured at 25 °C is fine anywhere from 4 °C to 37 °C. The big exception is Tris, whose ΔpKa/°C ≈ -0.028, meaning a pH-8.0 Tris buffer prepared at 25 °C is actually pH 7.75 at 37 °C or pH 8.3 at 4 °C. Adjust the pH at the temperature you'll actually use the buffer at.
What about ionic strength and activity corrections?
Henderson-Hasselbalch uses concentration in place of activity. For low ionic strength buffers (< 0.1 M) the error is under 0.1 pH unit; for high-salt buffers or biological media the actual pH can differ by 0.2 pH or more. For precise work (enzyme assays, protein crystallography) measure pH at working conditions with a calibrated meter.

Sources

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