A Javascript that calculates the amount of monosodium phosphate and disodium phosphate necessary to achieve a buffer at a given pH and buffer strength.

pH     Buffer Strength mM Monosodium phosphate, monohydrate % Disodium phosphate, heptahydrate %

How to use
Type the desired pH into the first cell, and type the intended buffer strength (in millimoles per liter) in the second cell. Press the calculate button, and the approximate percentages of monosodium phosphate, monohydrate and disodium phosphate, heptahydrate will be displayed. For example, a pH of about 7.4 with a buffer strength of 50 mM is obtained using 0.1558% monosodium phosphate monohydrate and 1.0374% disodium phosphate, heptahydrate. The buffer may be made by adding 0.16 g monosodium phosphate monohydrate and 1.04 g disodium phosphate, heptahydrate to 100 ml water.

How the calculation works
Using the three pK's of phosphoric acid and the pH, the ratio's of each of the phosphoric pairs is calculated. For example, the first ionization is given by:

H₃PO₄ --> H⁺ + H₂PO₄^-

K₁ = [H⁺][H₂PO₄^-] / [H₃PO₄], or

[H₂PO₄^-] / [H₃PO₄] = K₁ / [H⁺]

Normalizing the amount of each of the four moieties, their relative amounts are calculated. The molar amounts of monosodium phosphate and disodium phosphate are derived from the following two equations.

Monosodium Phosphate = [H₃PO₄] + [H₂PO₄^-]

Disodium Phosphate = [PO₄^3-] + [HPO₄^2-]

Using the molecular weights for monosodium phosphate, monohydrate and disodium phosphate, heptahydrate (the typical lab forms) together with the buffer strength, the actual percentages are calculated.

The pK's used for phosphoric acid are 2.148, 6.795 and 12.319. Different values for the pKa's of phosphoric acid appear in the literature. For pure water at 38 C, RL Jungas (Analyt Biochem 349; 1-15) concludes that the best value for the second dissocation constant of phosphoric is 7.18. However, under physiological conditions of ionic strength and pH, the best estimate is 6.795. It's best to buffer at a pH close to one of the pK's, so use this calculation only for phosphate buffers in the pH range 4.8 to 8.8.

What buffer strength to use? Too low will give a weak, drifting buffer, while too much may negatively affect other desired properties, such as taste. A 10 mM buffer is in general a good starting point.

A more general buffer page by Dave Robinson