Two containers P and Q of equal volume (1 litre each) contain 6 g of `O_(2)` and `SO_(2)` respectively at 300 K and 1 atmosphere. Then

Options

A. Number of molecules in P ie less than that in Q
B. Number of molecules in Q is less that in P
C. Number of molecules in P and Q are same
D. None of these

Explanation

To solve the problem, we need to calculate the number of moles of \( O_2 \) and \( SO_2 \) in containers P and Q respectively, and then determine the number of molecules in each container.

### Step-by-Step Solution:

1. **Determine the number of moles of \( O_2 \) in container P:**
- Given mass of \( O_2 \) = 6 g
- Molecular weight of \( O_2 \) = 32 g/mol (since \( O \) has an atomic weight of 16, and \( O_2 \) has 2 oxygen atoms)
- Number of moles of \( O_2 \) = \( \frac{\text{mass}}{\text{molecular weight}} = \frac{6 \, \text{g}}{32 \, \text{g/mol}} = 0.1875 \, \text{mol} \)

2. **Determine the number of moles of \( SO_2 \) in container Q:**
- Given mass of \( SO_2 \) = 6 g
- Molecular weight of \( SO_2 \) = 64 g/mol (Sulfur has an atomic weight of 32 and each oxygen has an atomic weight of 16, so \( 32 + 2 \times 16 = 64 \))
- Number of moles of \( SO_2 \) = \( \frac{6 \, \text{g}}{64 \, \text{g/mol}} = 0.09375 \, \text{mol} \)

3. **Calculate the number of molecules in each container:**
- Using Avogadro's number \( N_A = 6.022 \times 10^{23} \, \text{molecules/mol} \)
- Number of molecules in container P (for \( O_2 \)):
\[ \text{Number of molecules in P} = 0.1875 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 1.13 \times 10^{23} \, \text{molecules} \]
- Number of molecules in container Q (for \( SO_2 \)):
\[ \text{Number of molecules in Q} = 0.09375 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 5.64 \times 10^{22} \, \text{molecules} \]

4. **Comparison of the number of molecules:**
- From the calculations, we find that:
- Number of molecules in P \( \approx 1.13 \times 10^{23} \)
- Number of molecules in Q \( \approx 5.64 \times 10^{22} \)
- Therefore, the number of molecules in container P is greater than that in container Q.

### Conclusion:
- The number of molecules in container P is greater than in container Q.

### Final Answer:
- The correct option is: "Number of molecules in Q is less than that of P."