Buffer Capacity at the Edge
A first-year lab group prepares 1.00 L of an ethanoate buffer containing 0.100 mol CH3COOH (pKa = 4.76) and 0.050 mol CH3COONa. Their freshly calibrated pH meter reads 4.44 at 25 °C, while the Henderson–Hasselbalch (HH) prediction is 4.46. The solution is open to air and stirred for 10 min before each reading. They add 0.020 mol HCl in a small volume, then measure again. A classmate proposes adding a further 0.040 mol HCl and predicts that the pH will fall by the same amount as after the first addition, because 'the buffer will absorb it'.
1. Calculate the pH after the first HCl addition and judge whether HH is reliable here. Show the mole bookkeeping.
Read the worked answer
Moles after adding 0.020 mol H+:
- CH3COO−: 0.050 − 0.020 = 0.030 mol
- CH3COOH: 0.100 + 0.020 = 0.120 mol
pH = 4.76 + log10(0.030/0.120) = 4.76 − 0.602 = 4.16.
HH is acceptable as a first estimate because both buffer components remain in comparable amount (ratio 0.25, within roughly 0.1–10) and [H+] (about 7 × 10^−5 M) is negligible compared with 0.03–0.12 M. An exact charge-balance treatment shifts the answer by less than 0.01 pH unit. However, the buffer is now much closer to its capacity limit: only 0.030 mol of the basic component remains. HH should not be used outside the buffer region.
2. Evaluate the classmate's prediction for the extra 0.040 mol HCl. Is the pH change the same? Calculate an approximate final pH and state what assumption fails.
Read the worked answer
No. Only 0.030 mol acetate remains, so 0.040 mol H+ exceeds the buffer capacity by 0.010 mol. Stoichiometrically, acetate is essentially consumed, acetic acid becomes 0.160 mol, and 0.010 mol strong acid remains in about 1.00 L. The excess strong acid gives pH ≈ −log10(0.010) = 2.00; acetic acid contributes a little more H+ (Ka = 1.8 × 10^−5, x ≈ 3 × 10^−4 M), giving pH ≈ 1.99.
The drop from 4.16 to about 2.0 is much larger than the first 0.28-unit drop. The classmate assumes the buffer can keep absorbing H+ indefinitely. HH fails because [A−] is no longer a meaningful buffer concentration; the system is no longer a buffer.
3. The measured pH is 0.02 units below the HH prediction. Propose two plausible causes and describe an observation that would distinguish them. Should the group report 4.44 or 4.46?
Read the worked answer
Plausible causes include: (i) activity coefficients-HH uses concentrations, but at ionic strength around 0.05–0.10 the effective acid dissociation differs; (ii) calibration or electrode-slope error, or CO2 absorption lowering the pH; (iii) temperature different from 25 °C; (iv) impurity or volumetric error.
Distinguish by recalibrating with fresh pH 4.00 and 7.00 buffers and checking the meter slope; measuring the solution temperature; repeating with CO2-free water under nitrogen; and computing activities from ionic strength.
The 0.02 difference is small relative to typical combined uncertainty, so the group should report 4.44 as the measured value with an estimated uncertainty (e.g. ±0.03) and 4.46 as the model value. They should not silently 'correct' the data to match the model.