A mixture of nitrogen and neon gas is compressed from a volume of 91.0L to a volume of 89.0L, while the pressure is held constant at 95.0 atm . Calculate the work done on the gas mixture. Be sure your answer has the correct sign (positive or negative) and the correct number of significant digits.
 


To calculate the work done on a gas during compression at constant pressure, we use the formula:

\[
W = -P \Delta V
\]

where:
- \( W \) is the work done on the gas,
- \( P \) is the pressure,
- \( \Delta V \) is the change in volume (\( V_{\text{final}} - V_{\text{initial}} \)).

### Step 1: Calculate \(\Delta V\)

Given:
- \( V_{\text{initial}} = 91.0 \, \text{L} \)
- \( V_{\text{final}} = 89.0 \, \text{L} \)

\[
\Delta V = V_{\text{final}} - V_{\text{initial}} = 89.0 \, \text{L} - 91.0 \, \text{L} = -2.0 \, \text{L}
\]

### Step 2: Calculate the Work \( W \)

Given:
- \( P = 95.0 \, \text{atm} \)
- \( \Delta V = -2.0 \, \text{L} \)

Substitute these values into the work formula:

\[
W = - (95.0 \, \text{atm}) \times (-2.0 \, \text{L}) = 190 \, \text{L} \cdot \text{atm}
\]

The positive sign indicates that work is done **on** the gas (compression). The answer should have three significant figures to match the given values.

### Final Answer
\[
W = 190 \, \text{L} \cdot \text{atm}
\]

Would you like further explanation on this process?

---

1. How does work change if the gas expands instead of being compressed?
2. What is the significance of the negative sign in the work formula?
3. How would work be affected if the pressure were not constant?
4. How do temperature changes affect work in gas processes?
5. What other conditions might alter the amount of work done in gas compression?

**Tip:** Always track the sign in work calculations to understand if work is done *on* or *by* the system.

A mixture of nitrogen and neon gas is compressed from a volume of 91.0L to a volume of 89.0L, while the pressure is held constant at 95.0 atm. Calculate the work done on the gas mixture. Be sure your answer has the correct sign (positive or negative) and the correct number of significant digits.

Learn how to calculate the work done on a nitrogen and neon gas mixture when compressed from 91.0L to 89.0L at a constant pressure of 95.0 atm. This solution includes a detailed breakdown of using the work formula W = -P * ΔV and emphasizes correct significant figures. Suitable for advanced high school and college-level students.

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