What is the vapour density of `SO_(3)` w.r.t. `CH_(4)` ?

Options

A. `4`
B. `5`
C. `8`
D. `9`

Explanation

To find the vapor density of \( SO_3 \) with respect to \( CH_4 \), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Molecular Mass of \( SO_3 \)**:
- The molecular mass of \( SO_3 \) can be calculated by adding the atomic masses of sulfur and oxygen.
- Atomic mass of sulfur (S) = 32 g/mol.
- Atomic mass of oxygen (O) = 16 g/mol. Since there are 3 oxygen atoms in \( SO_3 \), we multiply by 3.
- Therefore, the molecular mass of \( SO_3 \) = \( 32 + (3 \times 16) = 32 + 48 = 80 \) g/mol.

2. **Identify the Molecular Mass of \( CH_4 \)**:
- The molecular mass of \( CH_4 \) can be calculated by adding the atomic masses of carbon and hydrogen.
- Atomic mass of carbon (C) = 12 g/mol.
- Atomic mass of hydrogen (H) = 1 g/mol. Since there are 4 hydrogen atoms in \( CH_4 \), we multiply by 4.
- Therefore, the molecular mass of \( CH_4 \) = \( 12 + (4 \times 1) = 12 + 4 = 16 \) g/mol.

3. **Calculate the Vapor Density**:
- The formula for relative vapor density (RVD) is given by:
\[ \text{Relative Vapor Density} = \frac{\text{Molecular Mass of } SO_3}{\text{Molecular Mass of } CH_4} \]
- Substituting the values we calculated:
\[ \text{Relative Vapor Density} = \frac{80}{16} = 5 \]

### Final Answer:
The vapor density of \( SO_3 \) with respect to \( CH_4 \) is **5**.

---