How do I prepare a phosphate buffer solution with a specific pH?

Here is an abbreviated phosphate buffer table taken from Clark's Determination of Hydrogen Ions:

Clark and Lubs standard buffer solutions. Add the indicated number of mL of 0.2 M NaOH to 50 mL 0f 0.2 M KH₂PO₄ and dilute to 200 mL. Taken from Determination of Hydrogen Ions, William and Wilkins, Baltimore, 1928.

pH	mL NaOH	pH	mL NaOH
5.8	3.72	7.0	29.63
6.0	5.70	7.2	35.00
6.2	8.60	7.4	39.50
6.4	12.60	7.6	42.80
6.6	17.80	7.8	45.20
6.8	23.65	8.0	46.80

Be sure you're using the correct phosphate. There are several potassium phosphates which can NOT be used interchangeably in buffer solutions! You want KH₂PO₄.

Formula	Systematic name	Other names
KH2PO4	potassium dihydrogen phosphate	acid potassium phosphate monobasic potassium phosphate monopotassium phosphate potassium biphosphate
K2HPO4	potassium hydrogen phosphate	dipotassium phosphate dibasic potassium phosphate
K3PO4	potassium phosphate	tripotassium phosphate tribasic potassium phosphate

If you can't find such a recipe, follow this procedure:

1. Use the Henderson-Hasselbalch equation to compute the ratio of the base form to acid form at the desired pH. The Henderson-Hasselbalch equation is

   pH = pKa + log

   (

   CA- CHA

   )

   where C_A- is the concentration of base form, C_HA is the concentration of acid form, and pK_a is - log K_a, with K_a being the acid dissociation constant. For your buffer, pH = 6.10, pK_a = 7.20, and so log C_A-/C_HA = -1.1 and C_A-/C_HA = 0.0794.
2. Prepare a rough buffer using the calculated ratio as a guide. You could mix about 8 mL of 0.1 M K₂HPO₄ with 100 mL of 0.1 M KH₂PO₄, or you could neutralize the KH₂PO₄ solution with enough NaOH to obtain the desired ratio.
3. Adjust the pH to the desired value by adding acid or base. The Henderson-Hasselbalch equation isn't accurate for concentrated solutions, and the tabulated values of K_a contain experimental error and sometimes apply to experimental conditions different than those in your buffer. You'll have to use a pH meter to guide you to the correct pH.

References

CRC Handbook of Chemistry and Physics (CRC Press)

This quintessential handbook contains data for about 2500 inorganic compounds and 12000 organic compounds. Relevant physical properties listed include crystal structure, color, solubility, melting points, boiling points, heats of formation, heats of vaporization, heats of fusion, entropies, heat capacities, critical pressure and temperature, vapor pressure, and optical properties. (Book/CDROM; no Web access). http://www.crcpress.com/catalog/9720.htm (12/12/98)

Determination of Hydrogen Ions, William and Wilkins, Baltimore, 1928.

Author: Fred Senese senese@antoine.frostburg.edu