In a flask, the weight ratio of `CH_(4)`(g) and `SO_(2)`(g) at 298 K and 1 bar is `1 : 2`. The ratio of the number of molecules of `SO_(2)` (g) and `CH_4` (g) is

Options

A. `1:4`
B. `4:1`
C. `1:2`
D. `2:1`

Explanation

To solve the problem, we need to find the ratio of the number of molecules of \( SO_2 \) (sulfur dioxide) and \( CH_4 \) (methane) given their weight ratio. The weight ratio of \( CH_4 \) to \( SO_2 \) is given as \( 1:2 \).

### Step-by-Step Solution:

1. **Identify the Weight Ratio**:
- The weight ratio of \( CH_4 \) to \( SO_2 \) is \( 1:2 \). This means if the weight of \( CH_4 \) is \( 1 \) gram, the weight of \( SO_2 \) is \( 2 \) grams.

2. **Calculate Moles of \( CH_4 \)**:
- The molecular weight of \( CH_4 \) (methane) is calculated as follows:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol (4 Hydrogen atoms)
- Molecular weight of \( CH_4 = 12 + (4 \times 1) = 16 \) g/mol.
- Moles of \( CH_4 \):
\[ \text{Moles of } CH_4 = \frac{\text{Weight}}{\text{Molecular Weight}} = \frac{1 \text{ g}}{16 \text{ g/mol}} = \frac{1}{16} \text{ mol} \]

3. **Calculate Moles of \( SO_2 \)**:
- The molecular weight of \( SO_2 \) (sulfur dioxide) is calculated as follows:
- Sulfur (S) = 32 g/mol
- Oxygen (O) = 16 g/mol (2 Oxygen atoms)
- Molecular weight of \( SO_2 = 32 + (2 \times 16) = 64 \) g/mol.
- Moles of \( SO_2 \):
\[ \text{Moles of } SO_2 = \frac{\text{Weight}}{\text{Molecular Weight}} = \frac{2 \text{ g}}{64 \text{ g/mol}} = \frac{2}{64} = \frac{1}{32} \text{ mol} \]

4. **Calculate the Number of Molecules**:
- Using Avogadro's number (\( 6.022 \times 10^{23} \) molecules/mol):
- Number of molecules of \( CH_4 \):
\[ \text{Number of molecules of } CH_4 = \left(\frac{1}{16} \text{ mol}\right) \times (6.022 \times 10^{23} \text{ molecules/mol}) = \frac{6.022 \times 10^{23}}{16} \]
- Number of molecules of \( SO_2 \):
\[ \text{Number of molecules of } SO_2 = \left(\frac{1}{32} \text{ mol}\right) \times (6.022 \times 10^{23} \text{ molecules/mol}) = \frac{6.022 \times 10^{23}}{32} \]

5. **Calculate the Ratio of Molecules**:
- The ratio of the number of molecules of \( SO_2 \) to \( CH_4 \):
\[ \text{Ratio} = \frac{\frac{6.022 \times 10^{23}}{32}}{\frac{6.022 \times 10^{23}}{16}} = \frac{1/32}{1/16} = \frac{1}{32} \times \frac{16}{1} = \frac{16}{32} = \frac{1}{2} \]
- Therefore, the ratio of the number of molecules of \( SO_2 \) to \( CH_4 \) is \( 1:2 \).

### Final Answer:
The ratio of the number of molecules of \( SO_2 \) to \( CH_4 \) is \( 1:2 \).