Compressing a Sealed Gas Sample
During a matter unit, students fill a sealed 60 mL syringe with air. The empty syringe has a mass of 18.42 g; with the air sample it reads 18.49 g on a balance that measures to 0.01 g. A student pushes the plunger until the trapped air occupies 30 mL and holds it there while the temperature remains 22 °C. The seal does not leak. The balance reading stays 18.49 g. In a notebook entry, one student writes, 'The gas particles must have shrunk because they fit in half the space.' Another writes, 'The air got destroyed, so the mass should drop.' The teacher asks the group to use the particle model and density calculations to decide which claim, if either, is supported.
1. Calculate the density of the trapped air before and after compression. Use the mass values given and state whether the number of gas particles changed. Show your work.
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The mass of the trapped air is the difference between the filled and empty syringe: 18.49 g - 18.42 g = 0.07 g.
Before compression:
- density = mass / volume = 0.07 g / 60 mL = 0.00117 g/mL, about 0.0012 g/mL.
After compression:
- density = 0.07 g / 30 mL = 0.00233 g/mL, about 0.0023 g/mL.
The density doubles because the same mass is packed into half the volume. The number of gas particles does not change: the syringe is sealed, so no particles enter or leave. The constant balance reading of 18.49 g supports this. The calculation does not show particles shrinking; it shows the same particles occupying less space.
2. Use the particle model to explain what happens to the spacing and motion of the gas particles as the volume is halved. Address why the particles themselves do not shrink.
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In the particle model, gas particles have their own fixed size and mass and are separated by empty space. Pushing the plunger does not make the particles smaller; it reduces the empty space between them. The particles become closer together and collide with the syringe walls more often, which increases the pressure.
Temperature stays at 22 °C, so the average kinetic energy and average speed of the particles stay about the same. The particles are not 'squished'; they simply travel shorter distances between collisions. This is why a gas can be compressed: the space between particles changes, but the particles themselves do not shrink. The claim that particles shrank confuses the compressible empty space with the size of the particles.
3. Evaluate the two notebook claims. Which parts, if any, are correct, and what evidence supports your judgment?
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The first claim is incorrect. The particles did not shrink. The density increased because the same number of particles occupies half the volume, so the spacing decreased. The second claim is also incorrect for this sealed system. Mass is conserved, and the balance reading stayed at 18.49 g. No air escaped, so the mass of the trapped air remained 0.07 g.
The evidence is the constant total mass and the density calculation: 0.07 g in 60 mL becomes 0.07 g in 30 mL. If the syringe were opened and gas escaped, the measured mass of what remained could drop, but that would be an open-system effect, not destruction of matter. In a sealed system, the particle count and total mass stay the same.