Volume of 0.5 mole of a gas at 1 atm. pressure and `273^@C` is

Options

A. 22.4 litres
B. 11.2 litres
C. 44.8 litres
D. 5.6 litres

Answer

To find the volume of 0.5 moles of a gas at 1 atm pressure and 273°C, we can use the ideal gas equation:

### Step-by-Step Solution:

1. **Understand the Ideal Gas Equation**:
The ideal gas equation is given by:
\[ PV = nRT \]
where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles of gas
- \( R \) = universal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = absolute temperature (in Kelvin)

2. **Convert Temperature to Kelvin**:
The given temperature is 273°C. To convert this to Kelvin:
\[ T(K) = T(°C) + 273 \]
\[ T = 273 + 273 = 546 \, K \]

3. **Identify Given Values**:
- Number of moles (\( n \)) = 0.5 moles
- Pressure (\( P \)) = 1 atm
- Temperature (\( T \)) = 546 K
- Universal gas constant (\( R \)) = 0.0821 L·atm/(K·mol)

4. **Rearrange the Ideal Gas Equation to Solve for Volume**:
We want to find \( V \), so we rearrange the equation:
\[ V = \frac{nRT}{P} \]

5. **Substitute the Values into the Equation**:
Now, substitute the known values into the equation:
\[ V = \frac{0.5 \, \text{mol} \times 0.0821 \, \text{L·atm/(K·mol)} \times 546 \, K}{1 \, \text{atm}} \]

6. **Calculate the Volume**:
Performing the calculation:
\[ V = \frac{0.5 \times 0.0821 \times 546}{1} \]
\[ V = \frac{22.4}{1} = 22.4 \, \text{L} \]

7. **Conclusion**:
Therefore, the volume of 0.5 moles of a gas at 1 atm pressure and 273°C is:
\[ V = 22.4 \, \text{liters} \]