1 g `H_(2)` gas expand at STP to occupy double of its original volume. The wok done during the process is

Options

A. 260 cal
B. 180 cal
C. 130 cal
D. 270 cal

Answer

To solve the problem of calculating the work done during the expansion of 1 g of \( H_2 \) gas at STP to occupy double its original volume, we can follow these steps:

### Step 1: Understand the Conditions
At STP (Standard Temperature and Pressure):
- Temperature (T) = 273 K
- Pressure (P) = 1 atm
- Standard molar volume = 22.4 L

### Step 2: Calculate the Number of Moles of \( H_2 \)
The molecular weight of \( H_2 \) (hydrogen gas) is 2 g/mol. We can calculate the number of moles (\( n \)) using the formula:
\[ n = \frac{\text{mass}}{\text{molecular weight}} = \frac{1 \text{ g}}{2 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 3: Determine the Initial and Final Volume
At STP, 1 mole of gas occupies 22.4 L. Therefore, the initial volume (\( V_i \)) for 0.5 moles is:
\[ V_i = n \times 22.4 \text{ L} = 0.5 \times 22.4 \text{ L} = 11.2 \text{ L} \]
Since the gas expands to occupy double its original volume, the final volume (\( V_f \)) is:
\[ V_f = 2 \times V_i = 2 \times 11.2 \text{ L} = 22.4 \text{ L} \]

### Step 4: Calculate the Change in Volume (\( \Delta V \))
\[ \Delta V = V_f - V_i = 22.4 \text{ L} - 11.2 \text{ L} = 11.2 \text{ L} \]

### Step 5: Convert Volume from Liters to Cubic Meters
Since we need to use SI units for pressure (1 atm = 101.325 kPa) and volume (in m³), we convert the volume:
\[ 11.2 \text{ L} = 11.2 \times 10^{-3} \text{ m}^3 \]

### Step 6: Calculate Work Done (W)
The work done during expansion at constant pressure is given by:
\[ W = P \Delta V \]
Substituting the values:
\[ W = 101.325 \text{ kPa} \times 11.2 \times 10^{-3} \text{ m}^3 \]
Converting kPa to atm for consistency:
\[ W = 1 \text{ atm} \times 11.2 \text{ L} = 1 \times 11.2 \times 101.325 \text{ J} \]
Calculating:
\[ W \approx 1.13 \text{ kJ} \approx 1130 \text{ J} \]

### Step 7: Convert Work Done to Calories
To convert joules to calories (1 cal = 4.184 J):
\[ W \approx \frac{1130 \text{ J}}{4.184 \text{ J/cal}} \approx 270.6 \text{ cal} \]

### Final Answer
The work done during the expansion of 1 g of \( H_2 \) gas at STP to occupy double its original volume is approximately **270.6 calories**.

---