Four Cups of Sugar, Four Dissolving Times
Four teams each placed one identical sugar cube into 200 mL of water measured in a graduated cylinder and timed how long the cube took to disappear completely without any stirring. The stopwatch started the moment the cube touched the water. Team 1 used 20 °C water and a whole cube: 9 minutes. Team 2 used 40 °C water and a whole cube: 4 minutes. Team 3 used 60 °C water and a whole cube: 2 minutes. Team 4 used 60 °C water and a cube crushed into small grains: 45 seconds. All four cups looked clear at the end. One student says, 'In the hot cups the sugar melted and turned into a different substance, and that is why you cannot see it.' Another says, 'The sugar is still there, just broken into pieces too small to see.' A fifth team wants to know whether stirring also matters.
1. Which claim about the hot cups is correct, and what evidence or further test would settle the question?
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The second claim is correct. Dissolving spreads sugar particles through the water; it does not create a new substance. Sugar does not melt at 60 °C, since melting sugar requires temperatures far above boiling water, so melting cannot explain a clear cup at 60 °C. The investigation itself shows that temperature only changed how fast the cube vanished, from 9 minutes to 2 minutes, while every cup ended up clear and, if tasted, sweet. A direct test is to mass the cup and water before and after the cube dissolves: if the sugar were gone, the mass would drop, but it stays the same. Another test is to let a small sample of the 60 °C solution evaporate and look for sugar crystals left behind.
2. Use the data to explain two factors that affect how fast sugar dissolves, and identify which factor had the larger effect here.
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The two factors are water temperature and particle size. For temperature, holding cube size constant, the sugar took 9 minutes at 20 °C, 4 minutes at 40 °C, and 2 minutes at 60 °C, so warmer water dissolves the cube faster because its particles move faster and reach the sugar sooner. For particle size, holding temperature at 60 °C, the whole cube took 2 minutes while the crushed cube took 45 seconds, because crushing exposes much more surface to the water at once. Here crushing had the larger effect: it cut the time by roughly two-thirds, a bigger change than going from 20 °C to 60 °C. To be fair, the class should also test a crushed cube at 20 °C, so particle size is compared with temperature held fixed.
3. Design a fair test for the fifth team's question about stirring. Describe the setup, the measurements, and how the class should decide whether stirring matters.
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Use two cups of water at the same temperature, say 20 °C, each with 200 mL measured in the same graduated cylinder and one identical whole sugar cube. Stir one cup with the same spoon in the same pattern for the entire trial and leave the other completely still. Start both stopwatches when the cube touches the water, stop when no sugar is visible, and check the bottom for grains before declaring it dissolved. Repeat each condition at least twice and average, because a single trial can be thrown off by a bump or a slightly different cube. Keep water volume, temperature, cube size, and cup type the same so stirring is the only difference. If the stirred cup is consistently faster, stirring speeds dissolving by moving fresh water past the sugar.