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?

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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.