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This is a gas law problem involving the relationship between pressure and volume while the temperature remains constant, which follows **Boyle's Law**. Boyle's Law states:

\[
P_1 V_1 = P_2 V_2
\]

Where:
- \(P_1\) is the initial pressure (1 atmosphere),
- \(V_1\) is the initial volume (480 liters),
- \(P_2\) is the final pressure (unknown),
- \(V_2\) is the final volume (12 liters).

We need to solve for \(P_2\), the final pressure.

Rearranging Boyle's Law to solve for \(P_2\):

\[
P_2 = \frac{P_1 V_1}{V_2}
\]

Substitute the values:

\[
P_2 = \frac{1 \, \text{atm} \times 480 \, \text{L}}{12 \, \text{L}} = 40 \, \text{atm}
\]

So, the required pressure to confine the gas in a 12-liter cylinder is **40 atmospheres**.

Would you like further details or have any questions?

Here are 5 related questions to expand this topic:
1. What happens to the pressure if the volume is doubled while the temperature remains constant?
2. How does Boyle's Law change if temperature is allowed to vary?
3. How can you use Boyle’s Law in real-life applications like scuba diving?
4. What other gas laws, besides Boyle’s Law, deal with pressure, volume, and temperature?
5. How would adding more gas to the cylinder affect the final pressure?

**Tip:** Always keep units consistent when using gas laws (like pressure in atm and volume in liters).

A certain mass of carbon dioxide occupies a volume of 480 liters at 1 atmosphere pressure. What pressure must be applied to confine it to a cylinder of 12 liters capacity, temperature remaining constant?

Learn how to apply Boyle's Law to find the pressure needed to confine carbon dioxide in a smaller cylinder. This problem involves calculating the pressure needed to compress gas from 480 liters at 1 atm to 12 liters. Suitable for high school students studying gas laws.

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