Boiling-Point Elevation: Is the NaCl Data Conclusive?
Two students each dissolve 0.10 mol of solute in 500 g of water in identical beakers: Beaker A gets glucose (C6H12O6), Beaker B gets sodium chloride (NaCl). Both beakers are at the same atmospheric pressure, and the students stir until all solid has dissolved. They heat both to boiling and record 100.10 °C for A and 100.17 °C for B using a thermometer with ±0.05 °C precision. Their textbook gives Kb = 0.51 K·kg·mol⁻¹ for water and states that NaCl dissociates completely. A classmate claims B's reading 'proves' NaCl does not fully dissociate. The students must decide whether the data support that claim, whether the thermometer precision matters, and what additional measurement would discriminate between incomplete dissociation and experimental error. They may assume the solute is non-volatile and the solution is dilute.
1. Calculate the expected boiling-point elevation for each beaker, compare with the measurements, and judge whether the classmate's claim is supported.
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Molality is 0.10 mol ÷ 0.500 kg = 0.200 mol/kg. For glucose, i = 1, so ΔTb = 1 × 0.51 × 0.200 = 0.102 K, predicting 100.102 °C; the measured 100.10 °C agrees well.
For NaCl with complete dissociation, i = 2, so ΔTb = 2 × 0.51 × 0.200 = 0.204 K, predicting 100.204 °C. The measured 100.17 °C is 0.034 K lower. That gap is smaller than the thermometer's ±0.05 °C precision, and two readings' uncertainties combine to roughly ±0.07 K, so the discrepancy is not meaningful.
The classmate's claim is therefore not supported: the data are consistent with complete dissociation within experimental resolution. They are also not precise enough to rule out a small degree of ion pairing or non-ideal behaviour. The correct judgement is 'inconclusive, leaning consistent with i ≈ 2', not 'proof of incomplete dissociation'.
2. Describe two additional measurements that would help distinguish incomplete dissociation from thermometer error, and explain why each works.
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First, measure freezing-point depression instead of boiling-point elevation. Water's Kf is 1.86 K·kg/mol, so the same 0.200 mol/kg solution should give about 0.372 K for NaCl versus 0.186 K for glucose - roughly twice the boiling-point signal and easier to resolve above ±0.05 °C.
Second, calibrate and replicate: measure pure water's boiling point with the same thermometer, take several readings of each solution, and compare means and standard deviations. This separates a systematic offset from random error.
A third option is to increase concentration, but that amplifies non-ideal effects, so it must be interpreted carefully. Conductivity or vapour-pressure osmometry would count particles more directly: conductivity rises with free ions, while osmometry yields the van't Hoff factor from colligative behaviour. Each method targets the dissociation question rather than only the thermometer's precision.