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The problem is asking for the final volume of nitrogen gas, given certain conditions of a gas cylinder. Let's break it down step by step:

### Known Data:
- Cylinder diameter = 7.6 cm
- Cylinder height = 30.0 cm
- Gas pressure inside the cylinder = 11.0 atm

We can assume the external pressure (at which the gas will be released) is 1 atm, as it would be at standard atmospheric conditions. The final volume is calculated using the following key steps.

### Step 1: Volume of the Cylinder
The cylinder is a right circular cylinder, and the volume \( V \) can be calculated using the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
Where:
- \( r \) is the radius (half the diameter), and
- \( h \) is the height.

We can convert dimensions from cm to dm (decimeters) because the answer needs to be in liters, and 1 dm³ = 1 L.

### Step 2: Use Boyle's Law for Gas Expansion
Boyle's Law relates the initial pressure and volume to the final pressure and volume under constant temperature:
\[
P_1 V_1 = P_2 V_2
\]
Where:
- \( P_1 = 11.0 \, \text{atm} \) (initial pressure),
- \( V_1 \) is the volume of the gas in the cylinder,
- \( P_2 = 1.0 \, \text{atm} \) (final pressure after the gas escapes),
- \( V_2 \) is the final volume (which we need to find).

### Let me calculate this for you.### Results:
- The initial volume of nitrogen gas in the cylinder (\(V_1\)) is approximately **1.36 liters**.
- After the gas is released into the plastic bag at 1 atm, the final volume (\(V_2\)) is approximately **14.97 liters**.

Would you like further clarification or additional details?

Here are 5 related questions to explore:
1. How does Boyle’s Law apply to situations involving changing temperatures?
2. What would happen if the cylinder were opened in a vacuum instead of at 1 atm?
3. How would the volume change if the gas inside the cylinder was at a higher pressure than 11 atm?
4. How is the relationship between pressure and volume different for ideal gases versus real gases?
5. What is the significance of significant digits in gas law calculations?

**Tip:** Always ensure your units are consistent when performing physics or chemistry calculations!

If the cylinder is opened and the gas is allowed to escape into a large empty plastic bag, what will be the final volume of nitrogen gas, including what's collected in the plastic bag and what's left over in the cylinder?

Discover how to calculate the final volume of nitrogen gas released from a laboratory cylinder into a plastic bag, using the cylinder's dimensions and Boyle's Law. This detailed guide includes step-by-step calculations suitable for high school students.

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