Preparing a Phosphate Buffer for a Teaching Laboratory in Phnom Penh
A laboratory technician at a teaching hospital in Phnom Penh must prepare 1.0 L of 0.05 M sodium phosphate buffer at pH 7.40 for a practical class on enzyme kinetics. The laboratory has two solid stocks: sodium dihydrogen phosphate dihydrate (NaH2PO4·2H2O, molar mass 156.01 g/mol) and disodium hydrogen phosphate dodecahydrate (Na2HPO4·12H2O, molar mass 358.14 g/mol). The second dissociation constant of phosphoric acid is pKa2 = 7.20 at 25 °C. The technician plans to use the Henderson–Hasselbalch equation to calculate the required masses, dissolve them in about 800 mL of distilled water, adjust the pH if necessary, and make up to 1.0 L. A pH meter is available, but its last calibration was two days ago using pH 4.00 and pH 7.00 buffers. The class will use the buffer at room temperature, and the enzyme is sensitive to pH outside 7.3–7.5. The technician must decide whether to recalibrate, how to verify the buffer, and what to do if the measured pH is 7.55.
1. Calculate the masses of NaH2PO4·2H2O and Na2HPO4·12H2O needed to prepare 1.0 L of 0.05 M phosphate buffer at pH 7.40, using pKa2 = 7.20. Show your reasoning.
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Use the Henderson–Hasselbalch equation for the second dissociation: pH = pKa2 + log([HPO4^2-]/[H2PO4^-]). Substituting gives 7.40 = 7.20 + log(base/acid), so log(base/acid) = 0.20 and base/acid = 10^0.20 = 1.585. Let the acid concentration be x. Then the base concentration is 1.585x, and the total phosphate concentration is x + 1.585x = 2.585x = 0.050 M. Therefore x = 0.01934 M acid and the base concentration is 0.03066 M. In 1.0 L, the moles are 0.01934 mol NaH2PO4·2H2O and 0.03066 mol Na2HPO4·12H2O. Mass of acid = 0.01934 mol × 156.01 g/mol = 3.02 g. Mass of base = 0.03066 mol × 358.14 g/mol = 10.98 g. The technician should weigh about 3.02 g NaH2PO4·2H2O and 10.98 g Na2HPO4·12H2O, dissolve them in about 800 mL distilled water, check the pH, and then make up to 1.0 L. Because the salts are hydrates, they must not be dried in an oven before weighing.
2. The pH meter was last calibrated two days ago at pH 4.00 and pH 7.00. Is this calibration adequate for measuring pH 7.40? What error sources could arise, and how would you verify the buffer before use?
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A two-point calibration at pH 4.00 and 7.00 establishes the electrode slope between those points, but pH 7.40 lies just outside that bracket. Extrapolating beyond the upper calibration point can introduce a small systematic error, especially if the electrode response is slightly non-linear or drifting. A better calibration for a pH 7.40 buffer is pH 7.00 and pH 10.00, or a three-point calibration at 4.00, 7.00, and 10.00. The two-day-old calibration is also a concern because electrode drift, junction contamination, and temperature changes can shift readings. Before use, the technician should recalibrate with fresh buffers and then verify the prepared buffer against a fresh pH 7.00 standard. If the meter reads within about ±0.05 pH unit of the standard, the electrode is performing acceptably. The buffer itself should be measured at the temperature at which it will be used, because phosphate pKa and pH are temperature-dependent. If the reading is 7.55, the technician should not assume the calculation was wrong; the meter or the weighing may be at fault, so verification with an independent standard is essential.
3. If the measured pH is 7.55 and the enzyme is sensitive outside 7.3–7.5, what should the technician do? Explain quantitatively how much 1 M HCl might be needed, or why a simpler approach is better.
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The buffer is outside the acceptable range and must be adjusted before the class. The technician should add small aliquots of 1 M HCl or 1 M NaH2PO4, mix thoroughly, and measure after each addition. A rough estimate uses buffer capacity. For 0.05 M phosphate at pH 7.4, the buffer capacity is approximately 0.027 mol per litre per pH unit. To lower the pH by 0.15 unit, about 0.027 × 0.15 = 0.0041 mol of H+ per litre is needed. Using 1 M HCl, that is about 4.1 mL per litre. However, adding 4.1 mL changes the final volume and the total phosphate concentration slightly, and the exact amount depends on the true buffer capacity and temperature. A simpler and more reliable approach is to adjust the pH before making up to the final volume, using a calibrated meter and adding acid dropwise. If the buffer has already been made to 1.0 L, small volume corrections are acceptable for a teaching class, but the technician should recalculate the final concentration and document the adjustment. If the pH cannot be brought into range reliably, prepare a fresh batch rather than risk exposing students to a failed enzyme practical.