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Phosphate Buffer Calculator (Sodium and Potassium)

Calculate how much monobasic and dibasic sodium or potassium phosphate to weigh for a phosphate buffer at a target pH and concentration, with a choice of hydrate.

Formula

pH=pKa2+log⁡10[HPO42−][H2PO4−],pKa2=7.198\mathrm{pH} = \mathrm{p}K_{a2} + \log_{10}\dfrac{[\mathrm{HPO_4^{2-}}]}{[\mathrm{H_2PO_4^{-}}]},\quad \mathrm{p}K_{a2} = 7.198
m=C×V×MWsalt as suppliedm = C \times V \times \mathrm{MW}_{\text{salt as supplied}}
pKa2\mathrm{p}K_{\mathrm{a}2}
second dissociation constant of phosphoric acid, 7.198 at 25 °C
MW\mathrm{MW}
molecular weight of the exact salt and hydrate on the bottle

How it works

Phosphate buffers are made from two salts: the monobasic salt (NaH₂PO₄ or KH₂PO₄), which supplies the acid form, and the dibasic salt (Na₂HPO₄ or K₂HPO₄), which supplies the base. Their ratio sets the pH. The page solves the full charge balance for phosphoric acid, using all three pKa values, which is exact for an ideal solution.

The mass of each salt depends on its hydrate. Disodium phosphate is sold anhydrous and as the dihydrate, heptahydrate and dodecahydrate, with molecular weights from 142 to 358, so the bottle label decides the mass to weigh. Phosphate buffers work best from about pH 5.8 to 8.0, centred on pKa₂.

Worked example

1 L of 100 mM sodium phosphate at pH 7.4, from disodium phosphate heptahydrate and monosodium phosphate monohydrate.

  1. At pH 7.4 the solution is 61.42 mM dibasic and 38.58 mM monobasic, a ratio of 1.59 : 1.
  2. Na₂HPO₄·7H₂O: 0.06142 mol × 268.06 g/mol = 16.47 g.
  3. NaH₂PO₄·H₂O: 0.03858 mol × 137.99 g/mol = 5.323 g.

Weigh 16.47 g of the dibasic heptahydrate and 5.323 g of the monobasic monohydrate, dissolve them in less than a litre of water, check the pH, and make up to 1 L.

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

Assumptions

  • An ideal solution at 25 °C with no activity correction.
  • The pKa values are those entered; the defaults are the 25 °C thermodynamic values.
  • The salts are pure and the hydrate is as stated.

Common mistakes

  • Using the anhydrous molecular weight for a hydrated salt, which gives a far weaker buffer.
  • Mixing sodium and potassium salts when one cation is required.
  • Adding calcium or magnesium to phosphate buffer, which precipitates the phosphate.

Related tools

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Related equipment

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