Let’s go step by step to solve this problem.
We are told that a gas is in a container with fixed volume (so the space doesn’t change). We’re also told that temperature and pressure are being measured as we add more particles of gas. The table shows:
| Number of Particles | Pressure (atm) |
|---------------------|----------------|
| 10 | 0.5 |
| 20 | 1.0 |
| 30 | 1.5 |
| 40 | 2.0 |
We need to find out how pressure changes when we increase the number of particles — and then describe what happens if we keep adding particles.
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Step 1: Look at the pattern in the table.
When particles = 10 → pressure = 0.5
When particles = 20 → pressure = 1.0
That’s double the particles, and pressure doubled too.
When particles = 30 → pressure = 1.5
That’s triple the original 10 particles, and pressure is triple 0.5 → 1.5 ✔️
When particles = 40 → pressure = 2.0
That’s 4 times 10 particles, and pressure is 4 × 0.5 = 2.0 ✔️
So every time we multiply the number of particles by some number, the pressure gets multiplied by the same number.
This means:
Pressure is directly proportional to the number of particles — as long as volume and temperature stay the same.
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Step 2: What does “directly proportional” mean?
It means if you double the particles, pressure doubles. If you triple them, pressure triples. If you make it 5 times bigger, pressure becomes 5 times bigger.
In math terms:
Pressure = k × (number of particles)
where k is a constant.
From the first row:
0.5 = k × 10 → so k = 0.5 / 10 = 0.05
Check with second row:
k × 20 = 0.05 × 20 = 1.0 ✔️
Third row: 0.05 × 30 = 1.5 ✔️
Fourth row: 0.05 × 40 = 2.0 ✔️
Perfect! So the formula is:
Pressure = 0.05 × (number of particles)
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Step 3: Answer part (a)
> Is there a relationship between the number of particles and the pressure? Briefly describe this.
Yes! As the number of gas particles increases, the pressure increases by the same factor. For example, doubling the particles doubles the pressure. This is called a direct proportion.
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Step 4: Answer part (b)
> If the pressure in the container keeps increasing, what physical assumption are we making?
We are assuming that the container can handle any amount of pressure without breaking or changing size. In real life, containers have limits — they might burst if pressure gets too high. But here, we’re pretending the container is perfectly strong and its volume never changes, no matter how many particles we add.
Also, we’re assuming temperature stays constant — because if temperature changed, it would affect pressure too, and our simple relationship wouldn’t hold.
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Final Answer:
(a) Yes, pressure is directly proportional to the number of particles. When the number of particles doubles, pressure doubles; when it triples, pressure triples, etc.
(b) We are assuming the container’s volume stays fixed and it can withstand any pressure without breaking, and that temperature remains constant.
Parent Tip: Review the logic above to help your child master the concept of behavior of gases worksheet.
