A buffer keeps pH nearly constant when acid or base is added, but only up to a point. Buffer capacity β puts a number on that resistance: it is the amount of strong acid or base, in moles per litre of buffer, needed to change the pH by one unit. A buffer with β = 0.1 mol/(L·pH) shifts by about 0.1 pH unit when you add 0.01 mol of HCl or NaOH to a litre.
Capacity depends on two things. The first is total concentration: doubling the amount of weak acid and conjugate base doubles the capacity. The second is the ratio of the two: capacity peaks when pH = pKa (equal amounts of acid and base) at about 0.576 times the total concentration, and drops to about a third of that one pH unit away. That is why buffers are chosen with a pKa within ±1 of the working pH.
This calculator gives three views: the practical definition from a measured experiment, the exact theoretical capacity from Van Slyke’s equation (which also includes the small contribution of water itself), and a prediction of the final pH after adding a known amount of strong acid or base.
How to use the Buffer Capacity Calculator
- Calculate
- Amount of strong acid or base added
- Buffer volume
- Initial pH
- Final pH
- Total buffer concentration (acid + conjugate base)
- pKa of the weak acid
- pH of the buffer
- Weak acid concentration [HA]
- Conjugate base concentration [A⁻]
- Buffer volume
- Added
- Amount added
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
In the measured mode β is the moles of acid or base added per litre divided by the size of the pH change. In the theoretical mode the Van Slyke equation is evaluated at your pH. In the prediction mode the added strong acid converts conjugate base into weak acid (or strong base does the reverse), and the Henderson–Hasselbalch equation gives the pH before and after.
Worked example
One litre of buffer contains 0.10 M acetic acid and 0.10 M sodium acetate (pKa 4.76), so its pH is 4.76. Adding 0.010 mol HCl turns 0.010 mol acetate into acetic acid: 0.090 mol A⁻ and 0.110 mol HA remain. The new pH = 4.76 + log₁₀(0.090/0.110) = 4.76 − 0.087 = 4.673. The average capacity is 0.010 / (1 × 0.087) ≈ 0.115 mol/(L·pH), which matches the Van Slyke value at pH 4.76 for C = 0.20 M: 2.303 × 0.20/4 ≈ 0.115.
The same acid added to 1 L of unbuffered water would drop the pH from 7 to 2.
How capacity changes with pH
| pH − pKa | Base : acid ratio | β as % of maximum |
|---|---|---|
| 0 | 1 : 1 | 100% |
| ±0.5 | 3.16 : 1 | 73% |
| ±1 | 10 : 1 | 33% |
| ±1.5 | 31.6 : 1 | 12% |
| ±2 | 100 : 1 | 3.9% |
Tips
- Use the final volume of the solution, not the volume of solvent added, for molarity.
- For dilutions, C₁V₁ = C₂V₂ only holds when both concentrations use the same unit.
- Add acid to water, never water to acid.
- Everything is calculated in your browser.
Common mistakes to avoid
- Mixing w/w, w/v and v/v percentages.
- Forgetting that pH is logarithmic – one unit is a tenfold change in [H⁺].
- Using pKa where Ka is asked for (or the other way round).
Inputs explained
| Field | What to enter |
|---|---|
| Calculate | Choose one: From a measured pH change, From the buffer composition (Van Slyke), Predict the pH change after adding acid or base |
| Amount of strong acid or base added | Units: mol, mmol, µmol, nmol, kmol |
| Buffer volume | Units: L, mL, µL, m³, dm³, cm³ … |
| Initial pH | A number |
| Final pH | A number |
| Total buffer concentration (acid + conjugate base) | Units: mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³ |
| pKa of the weak acid | A number |
| pH of the buffer | A number |
| Weak acid concentration [HA] | Units: mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³ |
| Conjugate base concentration [A⁻] | Units: mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³ |
| Buffer volume | Units: L, mL, µL, m³, dm³, cm³ … |
| Added | Choose one: Strong acid (e.g. HCl), Strong base (e.g. NaOH) |
| Amount added | Units: mol, mmol, µmol, nmol, kmol |
What each result means
- Initial pH = [pKa of the weak acid] + log10([Conjugate base concentration [A⁻]]÷[Weak acid concentration [HA]])
- Buffer capacity β = [Amount of strong acid or base added]÷([Buffer volume]×abs([pH change]))
- Average buffer capacity over the change = [Amount added]÷([Buffer volume]×abs([pH change]))
- Maximum possible capacity (at pH = pKa) = 2.302585092994046×[Total buffer concentration (acid + conjugate base)]÷4
- Capacity relative to the maximum = ([Buffer capacity β]÷[Maximum possible capacity (at pH = pKa)])×100
Formula
β = n ÷ (V·|ΔpH|) · Van Slyke: β = ln 10·(Kw/[H⁺] + [H⁺] + C·Ka·[H⁺] ÷ (Ka + [H⁺])²) · β_max = ln 10 · C ÷ 4 ≈ 0.576·C at pH = pKa · pH = pKa + log₁₀(n_A⁻ ÷ n_HA)Worked example
Inputs — Calculate: Predict the pH change after adding acid or base; pKa of the weak acid: 4.76; Weak acid concentration [HA]: 0.1 mol/L (M); Conjugate base concentration [A⁻]: 0.1 mol/L (M); Buffer volume: 1 L; Added: Strong acid (e.g. HCl); Amount added: 0.01 mol.
Results — Initial pH = 4.76; Final pH = 4.673; pH change = -0.0872; Average buffer capacity over the change = 0.1147 mol/(L·pH); Buffer status = Still buffering – pH within ±1 of pKa.
Key terms
- Buffer capacity (β)
- dn/dpH – moles of strong acid or base per litre needed per unit change in pH.
- Van Slyke equation
- Exact expression for the capacity of a weak-acid buffer, published by D. D. Van Slyke in 1922.
- Buffer range
- pH interval, about pKa ± 1, where a buffer works effectively.
- Conjugate base
- The species left when a weak acid gives up a proton (A⁻ for HA).
Frequently asked questions
What is buffer capacity?
The amount of strong acid or base (mol per litre of buffer) needed to change the pH by one unit. Higher β means a more robust buffer.
How do I calculate buffer capacity from an experiment?
Divide the moles of acid or base added per litre by the pH change. Adding 0.005 mol NaOH to 0.5 L and raising the pH from 7.20 to 7.32 gives β = 0.01 / 0.12 ≈ 0.083 mol/(L·pH).
At what pH is buffer capacity highest?
At pH = pKa, where the weak acid and its conjugate base are present in equal amounts. The maximum is about 0.576 × the total buffer concentration.
How does concentration affect buffer capacity?
Capacity is proportional to the total buffer concentration – a 0.2 M acetate buffer resists twice as much acid as a 0.1 M one at the same pH.
What is the useful range of a buffer?
Roughly pKa ± 1. One unit away, capacity falls to about a third of its maximum; two units away to about 4%.
Why is the measured capacity an average?
β changes with pH, so a finite addition gives the average over the pH interval. For small additions it approaches the exact (differential) Van Slyke value.
Does water contribute to buffer capacity?
Yes, slightly: the terms Kw/[H⁺] and [H⁺] in the Van Slyke equation. They matter only below pH ~3 or above pH ~11, where strong acid or base itself "buffers".