Preparing and Testing a Phosphate Buffer at pH 7.40
Theoretical classroom model only. Use the supplied constants and idealizations; this is not authorization to handle unknown samples, run a combustion experiment or alter an operating chemical plant. 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. For this ideal concentration-ratio exercise, take pKa2 = 7.20 at25 °C and neglect activity-coefficient changes; actual assay preparation would require separate validation. 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.
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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
Both methods can reach the same ideal phosphate composition if their quantities, purity and final volume are controlled. In method A, converting approximately0.0613 mol of the initial0.100 mol dihydrogen phosphate with NaOH leaves0.0387 mol acid form and0.0613 mol base form; make the final volume1.00 L. The sodium-ion amount then matches direct mixing. Neither method is inherently superior merely because one uses NaOH. Method A requires verified base concentration and avoidance of carbonate contamination; method B requires correct hydration states and accurate masses. Both require calibrated pH measurement, stated activity assumptions and verification against the assay’s ionic-strength and buffer-capacity specification.