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

Options

A. number of molecules in P is less than that in Q.
B. number of molecules in Pand Q is same.
C. number of molecules in Q is less than that in P.
D. either (a) or (b).

Explanation

To solve the problem, we need to calculate the number of moles of \(O_2\) and \(SO_2\) in the two containers and then determine which container has more molecules.

### Step-by-Step Solution:

1. **Calculate the number of moles of \(O_2\)**:
- Given mass of \(O_2 = 6 \, \text{g}\)
- Molar mass of \(O_2 = 32 \, \text{g/mol}\) (since \(O\) has a molar mass of \(16 \, \text{g/mol}\) and \(O_2\) has two oxygen atoms).
- Number of moles of \(O_2\) is calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{6 \, \text{g}}{32 \, \text{g/mol}} = 0.1875 \, \text{mol} \]

2. **Calculate the number of moles of \(SO_2\)**:
- Given mass of \(SO_2 = 6 \, \text{g}\)
- Molar mass of \(SO_2 = 32 \, \text{g/mol (S)} + 2 \times 16 \, \text{g/mol (O)} = 64 \, \text{g/mol}\)
- Number of moles of \(SO_2\) is calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{6 \, \text{g}}{64 \, \text{g/mol}} = 0.09375 \, \text{mol} \]

3. **Compare the number of moles**:
- We have:
- Moles of \(O_2 = 0.1875 \, \text{mol}\)
- Moles of \(SO_2 = 0.09375 \, \text{mol}\)
- Since \(0.1875 \, \text{mol} > 0.09375 \, \text{mol}\), there are more moles of \(O_2\) than \(SO_2\).

4. **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 of \(O_2\):
\[ \text{Number of molecules} = 0.1875 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 1.129 \times 10^{23} \, \text{molecules} \]
- Number of molecules of \(SO_2\):
\[ \text{Number of molecules} = 0.09375 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 0.564 \times 10^{23} \, \text{molecules} \]

5. **Conclusion**:
- The number of molecules of \(O_2\) is greater than that of \(SO_2\). Therefore, container P (which contains \(O_2\)) has more molecules than container Q (which contains \(SO_2\)).