phos

Buffer Calculation

This form calculates the amount of two buffer components necessary to achieve a buffer at a given pH and strength.

pH     Buffer Strength mM

Most protonated component:

0 g/L, 0 mM

Least protonated component:

0 g/L, 0 mM

Buffer capacity:

0 mM NaOH per pH

Instructions

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 concentrations of monosodium phosphate, monohydrate and disodium phosphate, heptahydrate will be displayed.

How the calculation works

Using Phosphate as the example: Before calculations can begin, the pKa's of phosphoric acid must be adjusted. The ions interfere with the idealized numbers provided by the pKa's at the link. To adjust for these, we apply the Debye-Huckel equation using A at 0.509 and calculating I by assuming that half of the buffer strength is divided between the conjugate acid and base of each stage of the buffer. So, for a buffer strength of 0.1 M, the program assumes that [H3PO4] = 0.05 M and [H2PO4-] = 0.05 M to calculate the pKa change for H3PO4. It goes on to assume the same thing for  [H2PO4-] and [HPO4-2]. For phosphoric acid the ion size parameter is usually taken as 4 for all ions, but 5 fits the experimental data better, so that is what we are using.

Using the three adjusted pKa's of phosphoric acid and the pH, the ratios of each of the phosphoric pairs are 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 phosphate moieties, their relative amounts are calculated. Knowing that the absolute amounts of the phosphate species sum to the buffer strength, the absolute concentrations can be calculated. Then, because the total charge in the buffer must be zero, the sodium ion concentration can be obtained. The final concentrations can be obtained by:
[Na2HPO4] = [Na] - Buffer Strength
[NaH2PO4] = Buffer Strength - [Na2HPO4]
The pKa's for phosphoric acid are 2.15, 7.20, and 12.38 at 25°C. Buffers made with the above salts work best in the pH range 6-10. What buffer strength to use? Too low will give a weak, drifting buffer (low buffer capacity), while too much may negatively affect other desired properties, such as taste.

Version 2, Dec 2, 2011. Scott Calabrese Barton (source code)

Version 1.1, Jan 19, 2000. Scott Calabrese Barton

Version No. 1, December 31, 2000. Jeffrey Clymer

Index of other pages by Jeffrey Clymer