If molecular mass of `O_(2)` and `SO_(2)` are 32 and 64 respectively. If one litre of `O_(2)` at `15^(@)C` and 759mm pressure contains N molecules, the number of molecuels in two litre of `SO_(2)` under the same conditions of temperature and pressure will be:

Options

A. N/2
B. N
C. 2N
D. 4N

Explanation

To solve the problem, we will use Avogadro's law, which states that equal volumes of gases at the same temperature and pressure contain an equal number of molecules.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Molecular mass of \( O_2 = 32 \, \text{g/mol} \)
- Molecular mass of \( SO_2 = 64 \, \text{g/mol} \)
- Volume of \( O_2 = 1 \, \text{L} \)
- Volume of \( SO_2 = 2 \, \text{L} \)
- Number of molecules of \( O_2 = N \)

2. **Apply Avogadro's Law:**
According to Avogadro's law, the number of molecules is directly proportional to the volume when temperature and pressure are constant. Therefore, we can set up the following relationship:
\[ \frac{V_{O_2}}{N_{O_2}} = \frac{V_{SO_2}}{N_{SO_2}} \]

3. **Substitute the Known Values:**
Substitute the values into the equation:
\[ \frac{1 \, \text{L}}{N} = \frac{2 \, \text{L}}{N_{SO_2}} \]

4. **Cross Multiply to Solve for \( N_{SO_2} \):**
Cross multiplying gives:
\[ N_{SO_2} = 2N \]

5. **Conclusion:**
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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