0.14kg of nitrogen at 300K is expanded isothermally and reversibly until its volume becomes doubled. Calculate the work done by the gas. 

Answer

To calculate the work done by the gas during an isothermal and reversible expansion, we can follow these steps:

### Step 1: Identify the Given Data
- Mass of nitrogen (m) = 0.14 kg
- Temperature (T) = 300 K
- Final volume (Vf) = 2 * Initial volume (Vi)

### Step 2: Convert Mass to Grams
Convert the mass of nitrogen from kilograms to grams:
\[ m = 0.14 \, \text{kg} \times 1000 \, \text{g/kg} = 140 \, \text{g} \]

### Step 3: Calculate the Number of Moles (n)
The molar mass of nitrogen (N₂) is approximately 28 g/mol (14 g/mol for each nitrogen atom). We can calculate the number of moles using the formula:
\[ n = \frac{m}{\text{Molar mass}} \]
\[ n = \frac{140 \, \text{g}}{28 \, \text{g/mol}} = 5 \, \text{mol} \]

### Step 4: Use the Work Done Formula for Isothermal Expansion
The formula for work done (W) during an isothermal and reversible expansion is given by:
\[ W = -nRT \ln\left(\frac{V_f}{V_i}\right) \]
Since \( V_f = 2V_i \), we can substitute:
\[ W = -nRT \ln(2) \]

### Step 5: Substitute the Values
We know:
- \( R = 8.314 \, \text{J/(mol K)} \)
- \( T = 300 \, \text{K} \)
- \( n = 5 \, \text{mol} \)

Now substituting these values into the work done formula:
\[ W = -5 \times 8.314 \times 300 \times \ln(2) \]

### Step 6: Calculate \( \ln(2) \)
The natural logarithm of 2 is approximately:
\[ \ln(2) \approx 0.693 \]

### Step 7: Complete the Calculation
Now substituting \( \ln(2) \):
\[ W = -5 \times 8.314 \times 300 \times 0.693 \]
Calculating this step-by-step:
1. Calculate \( 8.314 \times 300 = 2494.2 \, \text{J} \)
2. Calculate \( 2494.2 \times 0.693 \approx 1720.5 \, \text{J} \)
3. Finally, calculate \( W = -5 \times 1720.5 \approx -8602.5 \, \text{J} \)

### Step 8: Convert to Kilojoules
Convert the work done from Joules to kilojoules:
\[ W \approx -8.6025 \, \text{kJ} \]

### Final Answer
The work done by the gas is approximately:
\[ W \approx -8.60 \, \text{kJ} \]