What is the amount of work done when 0.5 mole of methane, `CH_(4)`(g) is subjected to combustion at 300 K? (given, `R=8.314 Jk^(-1) mol^(-1))`

Options

A. `-2494J`
B. `-4988J`
C. `+4988J`
D. `+2494J`

Answer

To calculate the amount of work done when 0.5 moles of methane (CH₄) is subjected to combustion at 300 K, we can follow these steps:

### Step 1: Write the balanced combustion reaction for methane.
The balanced equation for the combustion of methane is:
\[ \text{CH}_4(g) + 2 \text{O}_2(g) \rightarrow \text{CO}_2(g) + 2 \text{H}_2O(l) \]

### Step 2: Determine the change in the number of moles of gas (Δn).
From the balanced equation:
- Reactants: 1 mole of CH₄ + 2 moles of O₂ = 3 moles of gas
- Products: 1 mole of CO₂ + 0 moles of H₂O (since H₂O is in liquid form)

Thus, the change in the number of moles of gas (Δn) is:
\[ \Delta n = \text{moles of products} - \text{moles of reactants} = 1 - 3 = -2 \]

### Step 3: Calculate the work done using the formula.
The work done (W) during the combustion can be calculated using the formula:
\[ W = -\Delta n \cdot R \cdot T \]

Where:
- \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \)
- \( T = 300 \, \text{K} \)

Substituting the values:
\[ W = -(-2) \cdot 8.314 \cdot 300 \]
\[ W = 2 \cdot 8.314 \cdot 300 \]
\[ W = 4988.4 \, \text{J} \]

### Step 4: Adjust for the amount of methane used (0.5 moles).
Since we are using 0.5 moles of methane, we need to adjust the work done:
\[ W = 0.5 \cdot 4988.4 \]
\[ W = 2494.2 \, \text{J} \]

### Final Answer:
The amount of work done when 0.5 moles of methane is subjected to combustion at 300 K is approximately **2494 J**.

---