Cooling Curves and the Purity of Two Wax Samples
Two students are comparing two white candle-wax samples, A and B, for a melting-point practical. Each sample has a mass of 50 g, but A is pressed into a narrow test tube and B into a wider tube. Both are heated in the same water bath to 80 °C, then removed and their temperatures recorded every minute with the same thermometer. The results are: A: 0 min 80 °C, 2 min 74 °C, 4 min 69 °C, 6 min 69 °C, 8 min 69 °C, 10 min 66 °C. B: 0 min 80 °C, 2 min 71 °C, 4 min 67 °C, 6 min 64 °C, 8 min 63 °C, 10 min 61 °C. Student 1 says B must be purer because it cools faster and reaches a lower final temperature. Student 2 says the plateau is the important feature and that B is likely impure. The teacher asks them to justify a conclusion using particle theory and to identify one weakness in the experiment.
1. State the freezing point shown by sample A and explain, in terms of particles, why the temperature stays constant during the plateau.
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The plateau for A is at 69 °C, so this is its freezing point (and would also be its melting point).
During the plateau the wax is changing from liquid to solid. Energy is still being removed from the sample, but it is not reducing the average kinetic energy of the particles. Instead, it is reducing the potential energy of the particles as they become held in fixed positions in the solid lattice. Since temperature is a measure of average kinetic energy, the temperature does not fall until the change of state is complete. After that, further cooling reduces the average kinetic energy and the temperature falls again.
2. Evaluate Student 1's conclusion that sample B is purer. Use the data and identify a flaw in the comparison.
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Student 1's conclusion is not supported. A pure substance normally freezes at a sharp, constant temperature, giving a horizontal plateau like the one shown by A at 69 °C. Sample B has no clear plateau: its temperature falls from 80 °C to 61 °C with no constant region. A melting/freezing range like this is characteristic of an impure substance or a mixture, because the impurity lowers and spreads out the freezing point.
A lower final temperature does not indicate purity; it depends on how fast heat is lost. The comparison is also unfair because the tubes are different widths. B in the wider tube has a larger exposed surface area, so it may lose heat faster. That could explain the faster cooling without saying anything about purity. The conclusion should be that A is likely purer, while B is likely impure or a mixture.
3. Student 2 wants to improve the experiment to compare purity fairly. Describe two changes and explain how each improves the reliability of the comparison.
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Two useful changes are:
Use identical tubes and insulation for both samples. The tube width and exposed surface area affect cooling rate. Keeping these the same means any difference in the curve is more likely to be caused by the substance itself, not by different heat losses.
Record the temperature more frequently, for example every 15 s, and repeat each run. A short plateau can be missed with 1-minute readings. More frequent readings make the plateau easier to detect, and repeating and averaging reduces the effect of random errors such as slight thermometer reading differences or draughts.
A further improvement would be to use a data logger, which reduces reading error and records a continuous cooling curve.