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Buffer Capacity Calculator

Calculate the buffer capacity of a weak-acid buffer at a given pH, its maximum at the pKa, and the pH after you add a known amount of strong acid or base.

Formula

β=2.303[C Ka[H+](Ka+[H+])2+[H+]+Kw[H+]]\beta = 2.303\left[\dfrac{C\,K_{\mathrm{a}}[\mathrm{H}^+]}{(K_{\mathrm{a}} + [\mathrm{H}^+])^2} + [\mathrm{H}^+] + \dfrac{K_{\mathrm{w}}}{[\mathrm{H}^+]}\right]
βmax⁡=2.303 C4=0.576 Cat pH=pKa\beta_{\max} = \dfrac{2.303\,C}{4} = 0.576\,C\quad\text{at } \mathrm{pH} = \mathrm{p}K_{\mathrm{a}}
β\beta
buffer capacity: moles of strong acid or base per litre needed to change the pH by one unit
CC
total buffer concentration

How it works

A buffer's capacity is how much strong acid or base it can absorb before its pH changes by a unit. It depends on the concentration of the buffer, and on how close the pH is to the pKa: it is greatest at the pKa, where the acid and base forms are equal, and falls to about a third at one unit away and a tenth at two. Van Slyke gave the expression for it in 1922.

From the capacity you can see why a buffer is chosen for a pH near its pKa, and why a more concentrated buffer resists larger additions. The page also solves exactly what happens when you add a given amount of strong acid or base to a volume of buffer, from the charge balance, without the small-change approximation.

Worked example

100 mL of 100 mM acetate buffer at pH 4.76 (its pKa), to which 1 mmol of NaOH is added.

  1. β = 2.303 × 0.1 / 4 = 0.0576 mol/L per pH unit, which is 57.6 mmol/L per unit.
  2. Adding 1 mmol to 100 mL is 10 mmol/L, which shifts the pH by about 10 / 57.6 = 0.17; solved exactly, the new pH is 4.94.

β = 57.6 mmol/L per pH unit, and the pH rises by 0.18 to 4.94.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • A single monoprotic buffer; real mixtures with several buffering species have broader capacity.
  • Ideal solution, with activity coefficients of one, and no change in volume on adding the reagent.
  • The added acid or base is strong and fully dissociated.

Common mistakes

  • Choosing a buffer whose pKa is more than a unit from the working pH, where it has little capacity.
  • Expecting a dilute buffer to hold the pH when acid is produced in the reaction.
  • Quoting capacity without the pH at which it applies.

Related tools

Henderson-Hasselbalch CalculatorBuffer pH, base-to-acid ratio, or pKaOpen calculatorTitration Curve CalculatorpH against volume for a weak, strong or polyprotic acid titrated with baseOpen calculatorAcetate Buffer CalculatorAcetic acid and sodium acetate for a buffer at pH 3.8 to 5.8Open calculatorPhosphate Buffer Calculator (Sodium and Potassium)Masses of the mono- and dibasic salts for a phosphate buffer at a target pHOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.