The volume of mole of a perfect gas at NTP is

Options

A. 22.4 litres
B. 2.24 litres
C. 100 litres
D. none of these

Answer

To find the volume of one mole of a perfect gas at Normal Temperature and Pressure (NTP), we can use the Ideal Gas Law, which is represented by the equation:

\[ PV = nRT \]

Where:
- \( P \) = Pressure
- \( V \) = Volume
- \( n \) = Number of moles
- \( R \) = Universal gas constant
- \( T \) = Temperature in Kelvin

### Step-by-Step Solution:

1. **Identify the conditions for NTP**:
- At NTP, the temperature \( T \) is 273 K (0°C).
- The pressure \( P \) is 1 atm.

2. **Set the number of moles**:
- We are considering 1 mole of gas, so \( n = 1 \).

3. **Use the value of the universal gas constant \( R \)**:
- The value of \( R \) is \( 0.0821 \, \text{L} \cdot \text{atm} \cdot \text{K}^{-1} \cdot \text{mol}^{-1} \).

4. **Substitute the values into the Ideal Gas Law**:
\[ V = \frac{nRT}{P} \]
Substituting the known values:
\[ V = \frac{1 \, \text{mol} \times 0.0821 \, \text{L} \cdot \text{atm} \cdot \text{K}^{-1} \cdot \text{mol}^{-1} \times 273 \, \text{K}}{1 \, \text{atm}} \]

5. **Calculate the volume**:
\[ V = \frac{0.0821 \times 273}{1} = 22.4 \, \text{L} \]

6. **Conclusion**:
- The volume of one mole of a perfect gas at NTP is **22.4 liters**.

### Final Answer:
The volume of one mole of a perfect gas at NTP is **22.4 liters**.