Buffer recipe check before pH-meter calibration
A school laboratory needs 250.0 mL of a pH 4.75 buffer to calibrate a newly purchased pH meter before a practical examination. The stock cupboard contains 0.200 M acetic acid (pKa = 4.76) and solid sodium acetate trihydrate, CH3COONa·3H2O (M = 136.1 g/mol). A student proposes to mix 125.0 mL of the acetic acid with 0.0500 mol of the solid acetate and then dilute to the 250.0 mL mark. The laboratory technician is uneasy: the pH meter is the only one available, and the calibration must be within ±0.05 pH unit. There is also 1.00 M HCl available for a buffer-capacity demonstration. The student has not accounted for the water of crystallization or for the final volume when weighing. The technician asks you to check the plan before any solution is made.
1. Calculate the pH the student's recipe would actually give. Is the plan acceptable for the ±0.05 pH-unit requirement? Show the calculation and state the correction needed.
Read the worked answer
n(HA) = 0.200 × 0.1250 = 0.0250 mol; n(A-) = 0.0500 mol.
Henderson–Hasselbalch: pH = 4.76 + log(0.0500/0.0250) = 4.76 + 0.301 = 5.06.
This is 0.31 pH unit above the target, so it is unacceptable. For pH 4.75, the required ratio is A-/HA = 10^(4.75-4.76) = 0.977. With 0.0250 mol HA, n(A-) = 0.0244 mol. Mass of NaOAc·3H2O = 0.0244 × 136.1 = 3.32 g. The student should weigh 3.32 g, not 6.81 g, and then dilute to 250.0 mL.
2. Using the corrected recipe, calculate the pH after adding 2.00 mL of 1.00 M HCl. What does the result show about buffer capacity, and what would happen in the same volume of unbuffered 0.100 M acetic acid?
Read the worked answer
n(HCl) = 0.00200 mol. It converts 0.00200 mol A- into HA: n(HA) = 0.0250 + 0.00200 = 0.0270 mol; n(A-) = 0.0244 - 0.00200 = 0.0224 mol.
pH = 4.76 + log(0.0224/0.0270) = 4.68. The change is only about 0.08 pH unit because the buffer ratio changes modestly and the acetate is far from exhausted.
In 0.252 L of unbuffered 0.100 M acetic acid, the added strong acid gives about 0.0079 M H+, so the pH falls to roughly 2.1. The buffer therefore prevents a drop of more than 2.5 pH units, which is the intended demonstration.
3. The technician later finds the pH meter reads 4.62 in the fresh buffer and 4.60 after 10 minutes. List two likely causes and a check for each.
Read the worked answer
Likely causes: (i) electrode calibration drift or a dirty junction - check with fresh pH 4.01 and 7.00 buffers and clean/rehydrate the electrode; (ii) CO2 uptake by the alkaline acetate buffer - keep the beaker covered and measure promptly. Also check temperature compensation and whether the buffer was made to volume after equilibration.
A steady 0.02-unit low reading after 10 minutes points more to CO2 ingress than to random electrical noise. The buffer should be stored in a tightly capped bottle and discarded if its pH drifts outside the calibration tolerance.