Two moles of an ideal gas are allowed to expand from a volume of `10 dm^3` to 2 `m^3` at 300 K against a pressure of 101.325 kPa. Calcualte the work done.

Options

A. `-201.6 kJ`
B. `13.22 kJ`
C. `-810 kJ`
D. `-18.96 kJ`

Answer

To calculate the work done during the expansion of an ideal gas, we can follow these steps:

### Step 1: Identify the initial and final volumes
- Initial volume (V1) = 10 dm³
- Final volume (V2) = 2 m³

### Step 2: Convert the initial volume to cubic meters
- 1 dm³ = 10^-3 m³
- Therefore, V1 = 10 dm³ = 10 × 10^-3 m³ = 0.01 m³

### Step 3: Calculate the change in volume (ΔV)
- ΔV = V2 - V1
- ΔV = 2 m³ - 0.01 m³ = 1.99 m³

### Step 4: Identify the pressure
- Given pressure (P) = 101.325 kPa
- Convert pressure to Pascals:
- 1 kPa = 1000 Pa
- P = 101.325 kPa = 101.325 × 10^3 Pa = 101325 Pa

### Step 5: Calculate the work done (W)
- The formula for work done during expansion against a constant pressure is:
\[ W = -P \times \Delta V \]
- Substitute the values:
\[ W = -101325 \, \text{Pa} \times 1.99 \, \text{m}^3 \]
- Calculate:
\[ W = -201325.75 \, \text{J} \]

### Step 6: Convert work done to kilojoules
- Since 1 kJ = 1000 J,
\[ W = -201.32575 \, \text{kJ} \approx -201.3 \, \text{kJ} \]

### Final Answer
The work done during the expansion is approximately **-201.3 kJ**.

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