Preparing a Phosphate Buffer for an Enzyme Assay
An undergraduate preparing an enzyme kinetics practical is asked to make 500.0 cm³ of 0.100 mol dm⁻³ sodium phosphate buffer at pH 7.40. The stock cupboard contains solid NaH₂PO₄·2H₂O (M = 156.01 g mol⁻¹) and Na₂HPO₄·12H₂O (M = 358.14 g mol⁻¹), together with 1.000 mol dm⁻³ HCl and NaOH. The practical manual states only: 'weigh equal masses of the two phosphate salts, dissolve, and adjust to pH 7.40 with NaOH.' The student calculates that equal masses would save time and follows the manual. A demonstrator checks the pH and finds it near 6.84 before any adjustment. The student then adds NaOH until the meter reads 7.40, makes the volume up, and uses the buffer. Later, 100.0 cm³ of the buffer is challenged with 5.00 cm³ of 0.100 mol dm⁻³ HCl. The relevant pKa2 of phosphoric acid is 7.20 at 25°C. The student needs to know whether the buffer is fit for purpose, how much acid it can absorb, and what the manual's shortcut ignores.
1. Calculate the masses of the two phosphate salts needed for 500.0 cm³ of 0.100 mol dm⁻³ buffer at pH 7.40. Show why equal masses give a pH near 6.84.
Read the worked answer
Total phosphate required:
n(total) = 0.100 mol dm⁻³ × 0.5000 dm³ = 0.05000 mol.
For the H₂PO₄⁻/HPO₄²⁻ couple:
pH = pKa2 + log([HPO₄²⁻]/[H₂PO₄⁻])
7.40 = 7.20 + log(B/A)
log(B/A) = 0.20
B/A = 10^0.20 = 1.585.
Let A = mol H₂PO₄⁻ and B = mol HPO₄²⁻. Then A + B = 0.05000 and B = 1.585A.
2.585A = 0.05000
A = 0.01934 mol; B = 0.03066 mol.
Mass NaH₂PO₄·2H₂O = 0.01934 × 156.01 = 3.017 g.
Mass Na₂HPO₄·12H₂O = 0.03066 × 358.14 = 10.98 g.
For equal masses m of the two salts:
B/A = (m/358.14)/(m/156.01) = 156.01/358.14 = 0.4356.
pH = 7.20 + log(0.4356) = 7.20 − 0.361 = 6.839.
So equal masses give the acid form in excess and a pH close to 6.84, exactly as observed. The manual's shortcut is not a neutral starting point; it requires a large addition of NaOH to convert H₂PO₄⁻ into HPO₄²⁻.
2. Calculate the pH after adding 5.00 cm³ of 0.100 mol dm⁻³ HCl to 100.0 cm³ of the correctly prepared buffer. Is the buffer fit for purpose? Include the buffer capacity in your reasoning.
Read the worked answer
In 100.0 cm³ of the correct buffer:
n(H₂PO₄⁻) = 0.100 × 0.01934 = 0.003868 mol
n(HPO₄²⁻) = 0.100 × 0.03066 = 0.006132 mol.
Added HCl:
n(H⁺) = 0.00500 dm³ × 0.100 mol dm⁻³ = 0.000500 mol.
The strong acid converts HPO₄²⁻ into H₂PO₄⁻:
HPO₄²⁻ + H⁺ → H₂PO₄⁻.
New amounts:
n(H₂PO₄⁻) = 0.003868 + 0.000500 = 0.004368 mol
n(HPO₄²⁻) = 0.006132 − 0.000500 = 0.005632 mol.
New ratio B/A = 0.005632/0.004368 = 1.289.
pH = 7.20 + log(1.289) = 7.20 + 0.110 = 7.31.
The pH falls by only about 0.09 unit, so the buffer is doing its job. The added acid consumes about 8% of the available HPO₄²⁻, which is well within the buffer's capacity. The buffer is fit for purpose provided the enzyme is not sensitive to the extra sodium ions introduced by the NaOH adjustment and provided the pH meter was calibrated at the working temperature. If the student had not adjusted the equal-mass mixture, the starting pH would have been about 6.84 and the same acid addition would have pushed it further from 7.40.
3. Critique the manual's shortcut and the student's correction procedure. What should the student have done, and what practical factors could still make the prepared buffer unreliable?
Read the worked answer
The manual's instruction to weigh equal masses is poor practice for a pH-specified buffer. Equal masses give a pH near 6.84, not 7.40, because the two hydrated salts have very different molar masses and the required base:acid ratio is 1.585:1. The student's correction, adding NaOH until the meter reads 7.40, can produce the right pH, but it does so by converting a substantial amount of H₂PO₄⁻ into HPO₄²⁻ and adding a corresponding amount of sodium ions. The final total phosphate may still be 0.100 mol dm⁻³ if the initial masses were chosen correctly, but the ionic strength is higher than a buffer made directly from the calculated salt masses. That can affect an enzyme assay.
A better procedure is to weigh 3.017 g NaH₂PO₄·2H₂O and 10.98 g Na₂HPO₄·12H₂O, dissolve them in about 400 cm³ of water, check the pH, adjust only slightly if necessary, and then make up to 500.0 cm³. The pH meter should be calibrated with fresh standard buffers at the temperature of use.
Practical factors that could still make the buffer unreliable include:
- temperature: pKa2 and the electrode response change with temperature, so a buffer set to 7.40 at 25°C may not be 7.40 at 37°C;
- CO₂ absorption from air, which lowers the pH of phosphate buffers;
- activity effects at ionic strength around 0.1 mol dm⁻³, so the simple Henderson–Hasselbalch calculation is an approximation;
- evaporation or incomplete make-up to volume;
- microbial growth if the buffer is stored without filtration.
The student should record the actual mass, final volume, calibration temperature, and any pH adjustment so that the buffer can be reproduced.