How do you prepare a buffer with the Henderson-Hasselbalch equation?
Short answer
Use pH = pKa + log10(base ÷ acid) to find the ratio of base to acid, which is 10 raised to (target pH − pKa). Split the total moles of buffer between the two forms by that ratio, then weigh each as moles × molar mass. For a 0.100 M phosphate buffer at pH 7.40 in 1 L, that is 8.70 g of base and 4.64 g of acid.
A buffer resists changes in pH because it holds a weak acid and its conjugate base together. The Henderson-Hasselbalch equation tells you the proportions that give a target pH.
What are the steps?
- Choose a buffer system whose pKa is within about 1 pH unit of the target.
- Base ÷ acid ratio = 10^(target pH − pKa).
- Fraction of base = ratio ÷ (1 + ratio). Fraction of acid = 1 ÷ (1 + ratio).
- Total moles = concentration × volume in liters. Moles of each form = total moles × its fraction.
- Grams of each form = moles × molar mass ÷ purity.
What does a worked example look like?
Make 1.000 L of 0.100 M phosphate buffer at pH 7.40 from the anhydrous salts. The relevant pKa is the second one, 7.20 at 25 °C, a typical literature value.
- Ratio = 10^(7.40 − 7.20) = 10^0.20 = 1.585.
- Fraction of base = 1.585 ÷ 2.585 = 0.613. Fraction of acid = 0.387.
- Total moles = 0.100 × 1.000 = 0.100 mol, so base 0.0613 mol and acid 0.0387 mol.
- Disodium hydrogen phosphate (base, 141.96 g/mol): 0.0613 × 141.96 = 8.70 g.
- Sodium dihydrogen phosphate (acid, 119.98 g/mol): 0.0387 × 119.98 = 4.64 g.
Dissolve both in less than 1 L of water, check the pH with a calibrated meter, adjust, and make up to the final volume.
Why does the real pH differ from the calculation?
pKa values shift with temperature and ionic strength, and the equation ignores activity effects and the pH change from the salts themselves. Treat the calculated amounts as a starting point and finish by measuring. A target more than 1 pH unit from the pKa leaves the buffer with little capacity and makes the ratio less reliable.
What if you only have the acid form?
Start with the whole buffer amount as the acid form and titrate with strong base to the target pH. The moles of base needed equal the moles of the base form, and the volume is those moles divided by the base concentration.
The buffer preparation calculator holds six buffer systems with their pKa and molar masses, warns when the target is outside the useful range and calculates the titration route.