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States of Matter and Diffusion: Question 7

Syllabus 1.1

Structured Extended 8 marks

A school laboratory technician places a beaker of crushed ice, initially at −10 ∘C-10\,^{\circ}\text{C}, onto a hot plate that supplies heat energy to the beaker's contents at a constant rate. The technician records the temperature of the contents every minute as the ice warms, melts, and the resulting water is then heated until it boils:

Time / min 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Temperature / ∘C^{\circ}\text{C} -10 -5 0 0 0 0 25 50 75 100 100 100 100 100 100 100 110

(a) State the melting point and the boiling point of the substance in the beaker, and explain how you identified each value from the table. [3]

(b) State the state(s) of matter present in the beaker at t=3t = 3 min and at t=12t = 12 min. [2]

(c) Using the particle model, explain why the plateau at 100 ∘C100\,^{\circ}\text{C} lasts longer than the plateau at 0 ∘C0\,^{\circ}\text{C}, even though the hot plate supplies heat energy to the beaker's contents at the same constant rate throughout the experiment. [3]

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Worked solution

Part (a): Melting point and boiling point

Reading down the temperature row, the value stops increasing and stays constant at 0 ∘C0\,^{\circ}\text{C} for four consecutive readings, from t=2t=2 min to t=5t=5 min. This plateau is where the solid ice is turning into liquid water. Both states are present together at one fixed temperature.

Further along, the temperature stops increasing again and stays constant at 100 ∘C100\,^{\circ}\text{C} for seven consecutive readings, from t=9t=9 min to t=15t=15 min. This second plateau is where the liquid water is turning into steam.

Melting point =0 ∘C= \boxed{0\,^{\circ}\text{C}} and boiling point =100 ∘C= \boxed{100\,^{\circ}\text{C}}, each identified from a plateau (a section where the temperature stays constant) in the recorded data.

Part (b): States present at t=3t = 3 min and t=12t = 12 min

  • t=3t = 3 min falls within the 0 ∘C0\,^{\circ}\text{C} plateau (which runs from t=2t=2 min to t=5t=5 min), so the beaker contains a mixture of solid ice and liquid water at this moment. The ice has not all finished melting.
  • t=12t = 12 min falls within the 100 ∘C100\,^{\circ}\text{C} plateau (which runs from t=9t=9 min to t=15t=15 min), so the beaker contains a mixture of liquid water and steam (gas) at this moment. The water has not all finished boiling away.

Part (c): Why the boiling plateau lasts longer

Checking the table directly: the 0 ∘C0\,^{\circ}\text{C} plateau runs from t=2t=2 min to t=5t=5 min, a length of 3 minutes, while the 100 ∘C100\,^{\circ}\text{C} plateau runs from t=9t=9 min to t=15t=15 min, a length of 6 minutes. The boiling plateau is twice as long as the melting plateau in this data.

This can be explained using the particle model. During melting, the particles in solid ice are held in fixed positions by strong forces of attraction. The energy supplied only needs to weaken these forces enough to let the particles start sliding past one another as a liquid. The particles remain close together throughout, so the increase in particle separation is relatively small.

During boiling, the particles must gain enough energy to overcome the forces of attraction between them almost completely, separating fully into a gas where the particles are far apart and move freely in all directions. This is a much bigger change in particle arrangement and separation than during melting.

As a result, boiling the water needs a much greater total amount of energy than melting the ice did. Since the hot plate supplies energy at the same constant rate throughout the experiment, supplying this much larger amount of energy simply takes more time, so the plateau at 100 ∘C100\,^{\circ}\text{C} lasts longer than the plateau at 0 ∘C0\,^{\circ}\text{C}, exactly as shown by the recorded times.

Final answers

  • (a) Melting point =0 ∘C= \boxed{0\,^{\circ}\text{C}} (plateau from t=2t=2 to t=5t=5 min); boiling point =100 ∘C= \boxed{100\,^{\circ}\text{C}} (plateau from t=9t=9 to t=15t=15 min).
  • (b) t=3t=3 min: solid and liquid present together. t=12t=12 min: liquid and gas present together.
  • (c) The 0 ∘C0\,^{\circ}\text{C} plateau lasts 3 minutes and the 100 ∘C100\,^{\circ}\text{C} plateau lasts 6 minutes. Boiling requires overcoming far more of the forces between particles than melting does, so it needs much more total energy; at the same constant supply rate, this takes more time, giving the longer plateau seen in the table.