Monosodium Phosphate Buffer Calculator: NaH2PO4 and Na2HPO4 for a Target pH

This calculator splits a phosphate buffer into its two salts. Enter the target pH, total phosphate concentration, volume, pK_a2 and the two molar masses; you get the grams of monosodium phosphate (NaH₂PO₄, the acid), the grams of disodium phosphate (Na₂HPO₄, the base) and their mole ratio.

Formula

From pH = pK_a2 + log₁₀([HPO₄²⁻] ÷ [H₂PO₄⁻]): r = 10^{(pH − pKa2)}, n_total = C × V, n_acid = n_total ÷ (1 + r), n_base = n_total × r ÷ (1 + r); grams = moles × molar mass.

pK_a2 ≈ 7.20 at 25 °C and low ionic strength
C: total phosphate in mol/L (mM ÷ 1000); V: volume in L
Molar masses (anhydrous): NaH₂PO₄ = 22.990 + 2 × 1.008 + 30.974 + 4 × 15.999 = 119.98 g/mol; Na₂HPO₄ = 2 × 22.990 + 1.008 + 30.974 + 4 × 15.999 = 141.96 g/mol

Worked Example

500 mL (0.5 L) of 100 mM sodium phosphate buffer, pH 7.4.

r = 10^{(7.4 − 7.20)} = 10^0.2 = 1.585
Total phosphate: 0.100 mol/L × 0.5 L = 0.05 mol
NaH₂PO₄: 0.05 ÷ 2.58489 = 0.019343 mol; × 119.98 = 2.321 g
Na₂HPO₄: 0.05 − 0.019343 = 0.030657 mol; × 141.96 = 4.352 g

Assumptions

The salts are anhydrous. Hydrates are heavier: use the molar mass printed on your container (monohydrate, dihydrate, heptahydrate and so on).
Concentrations stand in for activities; at 100 mM the ionic strength lowers the effective pKa2, so the mix usually reads below the target.
The target pH lies within about pKa2 ± 1 (6.2 to 8.2), where the equation and the buffer work well.

How to read the result

At pH = pKa2 the two salts are present in equal moles; above it there is more Na₂HPO₄. Dissolve both in about 80% of the volume, adjust the pH, then make up to volume. The calculated pH is a starting point: the reading of a calibrated pH meter is the real check, and pH depends on temperature and ionic strength, so adjust with small additions of acid or base while you measure.

Limits and common mistakes

Using an anhydrous molar mass for a hydrate gives too little salt: nearly half too little for Na₂HPO₄·7H₂O (268.07 g/mol).
Entering the volume in mL instead of litres gives masses 1000 times too large.

Frequently Asked Questions

How do I make a pH 7.4 phosphate buffer from NaH2PO4 and Na2HPO4?

For 0.5 L at 100 mM, about 2.321 g anhydrous NaH2PO4 and 4.352 g anhydrous Na2HPO4, then adjust on a pH meter.

What is pKa2 of phosphoric acid?

About 7.20 at 25 °C, for H2PO4− giving HPO4 2−; it is lower at higher ionic strength.

Formula used

in ph | Target pH | - | 7.4 | 0 | 14
in c | Total phosphate concentration | mM | 100 | 0
in v | Final volume | L | 0.5 | 0
in pka | pKa2 of phosphoric acid | - | 7.20 | 0 | 14
in ma | Molar mass of NaH2PO4 | g/mol | 119.98 | 0.001
in mb | Molar mass of Na2HPO4 | g/mol | 141.96 | 0.001
out ga | Monosodium phosphate NaH2PO4 | g | c / 1000 * v / (1 + 10^(ph - pka)) * ma | 3
out gb | Disodium phosphate Na2HPO4 | g | c / 1000 * v * (1 - 1 / (1 + 10^(ph - pka))) * mb | 3
out ratio | Mole ratio Na2HPO4 : NaH2PO4 | - | 10^(ph - pka) | 3

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation with the constants and conversion factors written on the page, rounded as each result states. See method and constants, the disclaimer or report an error.