An engine cylinder contains 238 mL of gas at a pressure of 3 atm. As the engine runs, it compresses the cylinder, reducing the volume of the gas to 23 mL. What is the new pressure of the gas at this volume? (round your answer to the nearest whole number)

We can solve this problem using **Boyle's Law**, which states that the pressure of a gas is inversely proportional to its volume when the temperature and the amount of gas remain constant. Mathematically, Boyle's Law is expressed as:

\[
P_1 \cdot V_1 = P_2 \cdot V_2
\]

Where:
- \( P_1 \) is the initial pressure,
- \( V_1 \) is the initial volume,
- \( P_2 \) is the final pressure, and
- \( V_2 \) is the final volume.

Given values:
- \( P_1 = 3 \, \text{atm} \),
- \( V_1 = 238 \, \text{mL} \),
- \( V_2 = 23 \, \text{mL} \).

We need to find \( P_2 \), so we rearrange the equation:

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

Substitute the values:

\[
P_2 = \frac{3 \, \text{atm} \times 238 \, \text{mL}}{23 \, \text{mL}}
\]

Let's calculate this.

\[
P_2 = \frac{714 \, \text{atm} \cdot \text{mL}}{23 \, \text{mL}} = 31.04 \, \text{atm}
\]

Rounding to the nearest whole number:

\[
P_2 \approx 31 \, \text{atm}
\]

### The new pressure of the gas is **31 atm**.

Would you like more details or further explanation on any step?

Here are 5 related questions to think about:
1. How would the pressure change if the volume were halved instead of reduced to 23 mL?
2. How does temperature affect Boyle's Law?
3. What happens to the pressure if the gas is cooled while compressed?
4. Could you use Boyle’s Law in scuba diving scenarios?
5. How would increasing the amount of gas in the cylinder affect the pressure?

**Tip:** Boyle's Law is ideal for gases under low pressures and moderate temperatures, but extreme conditions may require other gas laws to account for real gas behavior.

Use Boyle's Law to solve how pressure changes when the volume of gas in a cylinder decreases from 238 mL to 23 mL. This problem explores key concepts in physics and gas laws, suitable for students in Grades 9-12.

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