A mixture of helium and hydrogen gas is compressed from a volume of

65.0L

to a volume of

23.0L

, while the pressure is held constant at

63.0atm

. 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.

kJ

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,
- \( P \) is the constant pressure,
- \( \Delta V \) is the change in volume (\( V_{\text{final}} - V_{\text{initial}} \)).

Given:
- Initial volume, \( V_{\text{initial}} = 65.0 \, \text{L} \)
- Final volume, \( V_{\text{final}} = 23.0 \, \text{L} \)
- Pressure, \( P = 63.0 \, \text{atm} \)

### Step 1: Calculate the Change in Volume
\[
\Delta V = V_{\text{final}} - V_{\text{initial}} = 23.0 \, \text{L} - 65.0 \, \text{L} = -42.0 \, \text{L}
\]

### Step 2: Calculate Work in Liter-atm
Since \( W = -P \Delta V \):
\[
W = -(63.0 \, \text{atm})(-42.0 \, \text{L}) = 2646 \, \text{L·atm}
\]

### Step 3: Convert Work to kJ
To convert from L·atm to kJ, use the conversion factor \( 1 \, \text{L·atm} = 0.101325 \, \text{kJ} \):
\[
W = 2646 \, \text{L·atm} \times 0.101325 \, \text{kJ/L·atm} = 268.12 \, \text{kJ}
\]

### Step 4: Determine the Sign and Significant Figures
Since the gas is being compressed, work is done **on** the gas, meaning \( W \) should be **positive**.

With three significant figures in the given values, we round to:
\[
W = 268 \, \text{kJ}
\]

### Final Answer
The work done on the gas mixture is:
\[
\boxed{268 \, \text{kJ}}
\]

Would you like further details on the calculation steps, or do you have any questions?

---

Here are five related questions for practice:

1. What would the work done be if the gas expanded instead of being compressed?
2. How does changing the pressure affect the work done in a similar process?
3. What if the initial volume were increased to 100.0 L—how would that change the result?
4. How is the sign of work determined in thermodynamic processes?
5. How would we calculate work if pressure were not constant?

**Tip:** Always double-check the units and the sign conventions for work in thermodynamics, as they can vary with different processes and setups.

A mixture of helium and hydrogen gas is compressed from a volume of 65.0L to a volume of 23.0L, while the pressure is held constant at 63.0atm. 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. kJ

Learn how to calculate the work done on a gas mixture of helium and hydrogen compressed from 65.0L to 23.0L under a constant pressure of 63.0 atm. Follow step-by-step calculations with key thermodynamic concepts, including significant figures. Ideal for Grades 11-12.

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