Buffer Capacity Formula
Quantify how much acid or base a buffer can absorb per pH change
Definition
beta = delta n / delta pH
delta n = moles of strong acid or base added
Units are typically mol per pH unit per liter of buffer (mol/L·pH).
How to Determine beta
- Measure initial pH of the buffer (pH1).
- Add a known small amount of strong acid or base (delta n, in moles).
- Measure new pH (pH2).
- Compute delta pH = |pH2 - pH1|.
- beta = delta n / delta pH.
For theoretical estimates near pKa: beta ≈ 2.303 * C_total * (Ka*[H+] / (Ka + [H+])^2)
Example
Problem: A 0.20 L buffer shows pH drop from 7.40 to 7.20 after adding 0.0010 mol HCl. Find beta (per liter).
1) delta pH = 0.20
2) beta (for the sample) = 0.0010 mol / 0.20 = 0.0050 mol per pH unit
3) Per liter: divide by volume 0.20 L → 0.025 mol/(L·pH)
Answer: beta ≈ 0.025 mol per liter per pH unit
Common Pitfalls
Too large additions
Adding too much acid/base invalidates linear approximation; use small delta pH.
Not normalizing to volume
Report capacity per liter so buffers can be compared.
Ignoring temperature
Buffer pKa and capacity shift with temperature; note conditions.
Far from pKa
Capacity is maximum near pH ≈ pKa; drops when pH is far from pKa.
FAQ
Does buffer capacity differ for acid vs base additions?
Yes, but near pKa the capacity is similar; away from pKa it can be asymmetric.
How to increase capacity?
Increase buffer concentration and keep pH close to pKa.
What about polyprotic buffers?
Consider the relevant pKa near your working pH; capacity will vary between pKa values.