Preparing and Testing a Phosphate Buffer at pH 7.40
A teaching laboratory needs 1.00 L of a 0.100 M phosphate buffer at pH 7.40 for an enzyme assay. The stock cupboard contains anhydrous sodium dihydrogen phosphate (NaH2PO4, M = 119.98 g mol−1), anhydrous disodium hydrogen phosphate (Na2HPO4, M = 141.96 g mol−1), 1.00 M HCl and 1.00 M NaOH. The second dissociation constant of phosphoric acid has pKa2 = 7.20 at 25 °C. Technician A proposes dissolving 0.100 mol of NaH2PO4 and adding NaOH until the pH meter reads 7.40. Technician B proposes weighing out both solids and dissolving them directly. The assay is sensitive to ionic strength, and the buffer must not change pH by more than 0.05 units when 5.0 cm3 of 1.00 M HCl is added to 1.00 L.
1. Calculate the masses of the two solids needed for Technician B's direct-mixing method.
Read the worked answer
Henderson–Hasselbalch: pH = pKa + log([HPO4^2−]/[H2PO4^−]). 7.40 = 7.20 + log(A−/HA), so A−/HA = 10^0.20 = 1.585. Total phosphate = 0.100 M = [HA] + [A−]. Let [HA] = x, [A−] = 1.585x; 2.585x = 0.100, x = 0.0387 M, [A−] = 0.0613 M. For 1.00 L: n(NaH2PO4) = 0.0387 mol, mass = 0.0387 × 119.98 = 4.64 g. n(Na2HPO4) = 0.0613 mol, mass = 0.0613 × 141.96 = 8.70 g. Dissolve and make up to 1.00 L; check the final pH with a calibrated meter.
2. Determine whether the buffer meets the pH-change specification when 5.0 cm3 of 1.00 M HCl is added. Show your reasoning.
Read the worked answer
Added HCl = 0.0050 dm3 × 1.00 mol dm−3 = 0.0050 mol. It converts HPO4^2− to H2PO4^−: new n(A−) = 0.0613 − 0.0050 = 0.0563 mol; new n(HA) = 0.0387 + 0.0050 = 0.0437 mol. The volume becomes 1.005 L, but the ratio is unchanged by the common volume. pH = 7.20 + log(0.0563/0.0437) = 7.20 + 0.110 = 7.31. ΔpH = 7.40 − 7.31 = 0.09, which exceeds the 0.05 specification. So the buffer fails. To meet it, increase the buffer concentration (more moles of both components) or reduce the amount of HCl; the ratio, not the total concentration, sets the pH, but the total concentration sets the buffer capacity.
3. Compare the two preparation methods. Which is more reliable for this assay, and why? Include one chemical or practical risk in each method.
Read the worked answer
Direct mixing is more reliable for a defined ionic strength because the amounts are stoichiometric and the final composition is known; adding NaOH relies on a pH meter and on the exact equivalence, and the pH changes steeply near the endpoint. Risk in A: carbonate in NaOH or a miscalibrated electrode gives a wrong ratio. Risk in B: weighing errors and water of hydration; the solids are hygroscopic, and if the monohydrate or heptahydrate is used instead of the anhydrous salt, the mole calculation is wrong. For the assay, B is preferred, with the pH checked and adjusted only if necessary.