If `1L` of `O_(2)` at `15^(@)C` and `750 mm` pressure contains `N` molecules, the number of molecules in 2 litre of `SO_(2)` under the same conditions of temperature and pressure will be

Options

A. `N//2`
B. `N`
C. `2N`
D. `N`

Explanation

To solve the problem, we need to understand the relationship between the volume of gas and the number of molecules it contains under the same conditions of temperature and pressure.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We have 1 liter of \( O_2 \) gas at a temperature of \( 15^\circ C \) and a pressure of \( 750 \, mm \) of mercury.
- This volume contains \( N \) molecules.

2. **Applying Avogadro's Law**:
- Avogadro's law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules.
- Therefore, if 1 liter of \( O_2 \) contains \( N \) molecules, then 1 liter of any other gas (in this case, \( SO_2 \)) under the same conditions will also contain \( N \) molecules.

3. **Calculating for 2 Liters of \( SO_2 \)**:
- Since we want to find the number of molecules in 2 liters of \( SO_2 \), we can use the relationship from Avogadro's law.
- If 1 liter of \( SO_2 \) contains \( N \) molecules, then 2 liters of \( SO_2 \) will contain \( 2N \) molecules.

4. **Conclusion**:
- Therefore, the number of molecules in 2 liters of \( SO_2 \) under the same conditions of temperature and pressure is \( 2N \).

### Final Answer:
The number of molecules in 2 liters of \( SO_2 \) is \( 2N \).

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